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      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2013 Christian Seiler <christian (at) iwakd.de>
      5 //
      6 // This Source Code Form is subject to the terms of the Mozilla
      7 // Public License v. 2.0. If a copy of the MPL was not distributed
      8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
      9 
     10 #ifndef EIGEN_CXX11META_H
     11 #define EIGEN_CXX11META_H
     12 
     13 #include <vector>
     14 #include "EmulateArray.h"
     15 
     16 // Emulate the cxx11 functionality that we need if the compiler doesn't support it.
     17 // Visual studio 2015 doesn't advertise itself as cxx11 compliant, although it
     18 // supports enough of the standard for our needs
     19 #if __cplusplus > 199711L || EIGEN_COMP_MSVC >= 1900
     20 
     21 #include "CXX11Workarounds.h"
     22 
     23 namespace Eigen {
     24 
     25 namespace internal {
     26 
     27 /** \internal
     28   * \file CXX11/util/CXX11Meta.h
     29   * This file contains generic metaprogramming classes which are not specifically related to Eigen.
     30   * This file expands upon Core/util/Meta.h and adds support for C++11 specific features.
     31   */
     32 
     33 template<typename... tt>
     34 struct type_list { constexpr static int count = sizeof...(tt); };
     35 
     36 template<typename t, typename... tt>
     37 struct type_list<t, tt...> { constexpr static int count = sizeof...(tt) + 1; typedef t first_type; };
     38 
     39 template<typename T, T... nn>
     40 struct numeric_list { constexpr static std::size_t count = sizeof...(nn); };
     41 
     42 template<typename T, T n, T... nn>
     43 struct numeric_list<T, n, nn...> { constexpr static std::size_t count = sizeof...(nn) + 1; constexpr static T first_value = n; };
     44 
     45 /* numeric list constructors
     46  *
     47  * equivalencies:
     48  *     constructor                                              result
     49  *     typename gen_numeric_list<int, 5>::type                  numeric_list<int, 0,1,2,3,4>
     50  *     typename gen_numeric_list_reversed<int, 5>::type         numeric_list<int, 4,3,2,1,0>
     51  *     typename gen_numeric_list_swapped_pair<int, 5,1,2>::type numeric_list<int, 0,2,1,3,4>
     52  *     typename gen_numeric_list_repeated<int, 0, 5>::type      numeric_list<int, 0,0,0,0,0>
     53  */
     54 
     55 template<typename T, std::size_t n, T start = 0, T... ii> struct gen_numeric_list                     : gen_numeric_list<T, n-1, start, start + n-1, ii...> {};
     56 template<typename T, T start, T... ii>                    struct gen_numeric_list<T, 0, start, ii...> { typedef numeric_list<T, ii...> type; };
     57 
     58 template<typename T, std::size_t n, T start = 0, T... ii> struct gen_numeric_list_reversed                     : gen_numeric_list_reversed<T, n-1, start, ii..., start + n-1> {};
     59 template<typename T, T start, T... ii>                    struct gen_numeric_list_reversed<T, 0, start, ii...> { typedef numeric_list<T, ii...> type; };
     60 
     61 template<typename T, std::size_t n, T a, T b, T start = 0, T... ii> struct gen_numeric_list_swapped_pair                           : gen_numeric_list_swapped_pair<T, n-1, a, b, start, (start + n-1) == a ? b : ((start + n-1) == b ? a : (start + n-1)), ii...> {};
     62 template<typename T, T a, T b, T start, T... ii>                    struct gen_numeric_list_swapped_pair<T, 0, a, b, start, ii...> { typedef numeric_list<T, ii...> type; };
     63 
     64 template<typename T, std::size_t n, T V, T... nn> struct gen_numeric_list_repeated                 : gen_numeric_list_repeated<T, n-1, V, V, nn...> {};
     65 template<typename T, T V, T... nn>                struct gen_numeric_list_repeated<T, 0, V, nn...> { typedef numeric_list<T, nn...> type; };
     66 
     67 /* list manipulation: concatenate */
     68 
     69 template<class a, class b> struct concat;
     70 
     71 template<typename... as, typename... bs> struct concat<type_list<as...>,       type_list<bs...>>        { typedef type_list<as..., bs...> type; };
     72 template<typename T, T... as, T... bs>   struct concat<numeric_list<T, as...>, numeric_list<T, bs...> > { typedef numeric_list<T, as..., bs...> type; };
     73 
     74 template<typename... p> struct mconcat;
     75 template<typename a>                             struct mconcat<a>           { typedef a type; };
     76 template<typename a, typename b>                 struct mconcat<a, b>        : concat<a, b> {};
     77 template<typename a, typename b, typename... cs> struct mconcat<a, b, cs...> : concat<a, typename mconcat<b, cs...>::type> {};
     78 
     79 /* list manipulation: extract slices */
     80 
     81 template<int n, typename x> struct take;
     82 template<int n, typename a, typename... as> struct take<n, type_list<a, as...>> : concat<type_list<a>, typename take<n-1, type_list<as...>>::type> {};
     83 template<int n>                             struct take<n, type_list<>>         { typedef type_list<> type; };
     84 template<typename a, typename... as>        struct take<0, type_list<a, as...>> { typedef type_list<> type; };
     85 template<>                                  struct take<0, type_list<>>         { typedef type_list<> type; };
     86 
     87 template<typename T, int n, T a, T... as> struct take<n, numeric_list<T, a, as...>> : concat<numeric_list<T, a>, typename take<n-1, numeric_list<T, as...>>::type> {};
     88 template<typename T, int n>               struct take<n, numeric_list<T>>           { typedef numeric_list<T> type; };
     89 template<typename T, T a, T... as>        struct take<0, numeric_list<T, a, as...>> { typedef numeric_list<T> type; };
     90 template<typename T>                      struct take<0, numeric_list<T>>           { typedef numeric_list<T> type; };
     91 
     92 template<typename T, int n, T... ii>      struct h_skip_helper_numeric;
     93 template<typename T, int n, T i, T... ii> struct h_skip_helper_numeric<T, n, i, ii...> : h_skip_helper_numeric<T, n-1, ii...> {};
     94 template<typename T, T i, T... ii>        struct h_skip_helper_numeric<T, 0, i, ii...> { typedef numeric_list<T, i, ii...> type; };
     95 template<typename T, int n>               struct h_skip_helper_numeric<T, n>           { typedef numeric_list<T> type; };
     96 template<typename T>                      struct h_skip_helper_numeric<T, 0>           { typedef numeric_list<T> type; };
     97 
     98 template<int n, typename... tt>             struct h_skip_helper_type;
     99 template<int n, typename t, typename... tt> struct h_skip_helper_type<n, t, tt...> : h_skip_helper_type<n-1, tt...> {};
    100 template<typename t, typename... tt>        struct h_skip_helper_type<0, t, tt...> { typedef type_list<t, tt...> type; };
    101 template<int n>                             struct h_skip_helper_type<n>           { typedef type_list<> type; };
    102 template<>                                  struct h_skip_helper_type<0>           { typedef type_list<> type; };
    103 
    104 template<int n>
    105 struct h_skip {
    106   template<typename T, T... ii>
    107   constexpr static inline typename h_skip_helper_numeric<T, n, ii...>::type helper(numeric_list<T, ii...>) { return typename h_skip_helper_numeric<T, n, ii...>::type(); }
    108   template<typename... tt>
    109   constexpr static inline typename h_skip_helper_type<n, tt...>::type helper(type_list<tt...>) { return typename h_skip_helper_type<n, tt...>::type(); }
    110 };
    111 
    112 template<int n, typename a> struct skip { typedef decltype(h_skip<n>::helper(a())) type; };
    113 
    114 template<int start, int count, typename a> struct slice : take<count, typename skip<start, a>::type> {};
    115 
    116 /* list manipulation: retrieve single element from list */
    117 
    118 template<int n, typename x> struct get;
    119 
    120 template<int n, typename a, typename... as>               struct get<n, type_list<a, as...>>   : get<n-1, type_list<as...>> {};
    121 template<typename a, typename... as>                      struct get<0, type_list<a, as...>>   { typedef a type; };
    122 
    123 template<typename T, int n, T a, T... as>                        struct get<n, numeric_list<T, a, as...>>   : get<n-1, numeric_list<T, as...>> {};
    124 template<typename T, T a, T... as>                               struct get<0, numeric_list<T, a, as...>>   { constexpr static T value = a; };
    125 
    126 /* always get type, regardless of dummy; good for parameter pack expansion */
    127 
    128 template<typename T, T dummy, typename t> struct id_numeric  { typedef t type; };
    129 template<typename dummy, typename t>      struct id_type     { typedef t type; };
    130 
    131 /* equality checking, flagged version */
    132 
    133 template<typename a, typename b> struct is_same_gf : is_same<a, b> { constexpr static int global_flags = 0; };
    134 
    135 /* apply_op to list */
    136 
    137 template<
    138   bool from_left, // false
    139   template<typename, typename> class op,
    140   typename additional_param,
    141   typename... values
    142 >
    143 struct h_apply_op_helper                                        { typedef type_list<typename op<values, additional_param>::type...> type; };
    144 template<
    145   template<typename, typename> class op,
    146   typename additional_param,
    147   typename... values
    148 >
    149 struct h_apply_op_helper<true, op, additional_param, values...> { typedef type_list<typename op<additional_param, values>::type...> type; };
    150 
    151 template<
    152   bool from_left,
    153   template<typename, typename> class op,
    154   typename additional_param
    155 >
    156 struct h_apply_op
    157 {
    158   template<typename... values>
    159   constexpr static typename h_apply_op_helper<from_left, op, additional_param, values...>::type helper(type_list<values...>)
    160   { return typename h_apply_op_helper<from_left, op, additional_param, values...>::type(); }
    161 };
    162 
    163 template<
    164   template<typename, typename> class op,
    165   typename additional_param,
    166   typename a
    167 >
    168 struct apply_op_from_left { typedef decltype(h_apply_op<true, op, additional_param>::helper(a())) type; };
    169 
    170 template<
    171   template<typename, typename> class op,
    172   typename additional_param,
    173   typename a
    174 >
    175 struct apply_op_from_right { typedef decltype(h_apply_op<false, op, additional_param>::helper(a())) type; };
    176 
    177 /* see if an element is in a list */
    178 
    179 template<
    180   template<typename, typename> class test,
    181   typename check_against,
    182   typename h_list,
    183   bool last_check_positive = false
    184 >
    185 struct contained_in_list;
    186 
    187 template<
    188   template<typename, typename> class test,
    189   typename check_against,
    190   typename h_list
    191 >
    192 struct contained_in_list<test, check_against, h_list, true>
    193 {
    194   constexpr static bool value = true;
    195 };
    196 
    197 template<
    198   template<typename, typename> class test,
    199   typename check_against,
    200   typename a,
    201   typename... as
    202 >
    203 struct contained_in_list<test, check_against, type_list<a, as...>, false> : contained_in_list<test, check_against, type_list<as...>, test<check_against, a>::value> {};
    204 
    205 template<
    206   template<typename, typename> class test,
    207   typename check_against
    208   EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty)
    209 >
    210 struct contained_in_list<test, check_against, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, false> { constexpr static bool value = false; };
    211 
    212 /* see if an element is in a list and check for global flags */
    213 
    214 template<
    215   template<typename, typename> class test,
    216   typename check_against,
    217   typename h_list,
    218   int default_flags = 0,
    219   bool last_check_positive = false,
    220   int last_check_flags = default_flags
    221 >
    222 struct contained_in_list_gf;
    223 
    224 template<
    225   template<typename, typename> class test,
    226   typename check_against,
    227   typename h_list,
    228   int default_flags,
    229   int last_check_flags
    230 >
    231 struct contained_in_list_gf<test, check_against, h_list, default_flags, true, last_check_flags>
    232 {
    233   constexpr static bool value = true;
    234   constexpr static int global_flags = last_check_flags;
    235 };
    236 
    237 template<
    238   template<typename, typename> class test,
    239   typename check_against,
    240   typename a,
    241   typename... as,
    242   int default_flags,
    243   int last_check_flags
    244 >
    245 struct contained_in_list_gf<test, check_against, type_list<a, as...>, default_flags, false, last_check_flags> : contained_in_list_gf<test, check_against, type_list<as...>, default_flags, test<check_against, a>::value, test<check_against, a>::global_flags> {};
    246 
    247 template<
    248   template<typename, typename> class test,
    249   typename check_against
    250   EIGEN_TPL_PP_SPEC_HACK_DEFC(typename, empty),
    251   int default_flags,
    252   int last_check_flags
    253 >
    254 struct contained_in_list_gf<test, check_against, type_list<EIGEN_TPL_PP_SPEC_HACK_USE(empty)>, default_flags, false, last_check_flags> { constexpr static bool value = false; constexpr static int global_flags = default_flags; };
    255 
    256 /* generic reductions */
    257 
    258 template<
    259   typename Reducer,
    260   typename... Ts
    261 > struct reduce;
    262 
    263 template<
    264   typename Reducer
    265 > struct reduce<Reducer>
    266 {
    267   constexpr static inline int run() { return Reducer::Identity; }
    268 };
    269 
    270 template<
    271   typename Reducer,
    272   typename A
    273 > struct reduce<Reducer, A>
    274 {
    275   constexpr static inline A run(A a) { return a; }
    276 };
    277 
    278 template<
    279   typename Reducer,
    280   typename A,
    281   typename... Ts
    282 > struct reduce<Reducer, A, Ts...>
    283 {
    284   constexpr static inline auto run(A a, Ts... ts) -> decltype(Reducer::run(a, reduce<Reducer, Ts...>::run(ts...))) {
    285     return Reducer::run(a, reduce<Reducer, Ts...>::run(ts...));
    286   }
    287 };
    288 
    289 /* generic binary operations */
    290 
    291 struct sum_op           {
    292   template<typename A, typename B> EIGEN_DEVICE_FUNC constexpr static inline auto run(A a, B b) -> decltype(a + b)   { return a + b;   }
    293   static constexpr int Identity = 0;
    294 };
    295 struct product_op       {
    296   template<typename A, typename B> EIGEN_DEVICE_FUNC constexpr static inline auto run(A a, B b) -> decltype(a * b)   { return a * b;   }
    297   static constexpr int Identity = 1;
    298 };
    299 
    300 struct logical_and_op   { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a && b)  { return a && b;  } };
    301 struct logical_or_op    { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a || b)  { return a || b;  } };
    302 
    303 struct equal_op         { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a == b)  { return a == b;  } };
    304 struct not_equal_op     { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a != b)  { return a != b;  } };
    305 struct lesser_op        { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a < b)   { return a < b;   } };
    306 struct lesser_equal_op  { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a <= b)  { return a <= b;  } };
    307 struct greater_op       { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a > b)   { return a > b;   } };
    308 struct greater_equal_op { template<typename A, typename B> constexpr static inline auto run(A a, B b) -> decltype(a >= b)  { return a >= b;  } };
    309 
    310 /* generic unary operations */
    311 
    312 struct not_op                { template<typename A> constexpr static inline auto run(A a) -> decltype(!a)      { return !a;      } };
    313 struct negation_op           { template<typename A> constexpr static inline auto run(A a) -> decltype(-a)      { return -a;      } };
    314 struct greater_equal_zero_op { template<typename A> constexpr static inline auto run(A a) -> decltype(a >= 0)  { return a >= 0;  } };
    315 
    316 
    317 /* reductions for lists */
    318 
    319 // using auto -> return value spec makes ICC 13.0 and 13.1 crash here, so we have to hack it
    320 // together in front... (13.0 doesn't work with array_prod/array_reduce/... anyway, but 13.1
    321 // does...
    322 template<typename... Ts>
    323 constexpr inline decltype(reduce<product_op, Ts...>::run((*((Ts*)0))...)) arg_prod(Ts... ts)
    324 {
    325   return reduce<product_op, Ts...>::run(ts...);
    326 }
    327 
    328 template<typename... Ts>
    329 constexpr inline decltype(reduce<sum_op, Ts...>::run((*((Ts*)0))...)) arg_sum(Ts... ts)
    330 {
    331   return reduce<sum_op, Ts...>::run(ts...);
    332 }
    333 
    334 /* reverse arrays */
    335 
    336 template<typename Array, int... n>
    337 constexpr inline Array h_array_reverse(Array arr, numeric_list<int, n...>)
    338 {
    339   return {{array_get<sizeof...(n) - n - 1>(arr)...}};
    340 }
    341 
    342 template<typename T, std::size_t N>
    343 constexpr inline array<T, N> array_reverse(array<T, N> arr)
    344 {
    345   return h_array_reverse(arr, typename gen_numeric_list<int, N>::type());
    346 }
    347 
    348 
    349 /* generic array reductions */
    350 
    351 // can't reuse standard reduce() interface above because Intel's Compiler
    352 // *really* doesn't like it, so we just reimplement the stuff
    353 // (start from N - 1 and work down to 0 because specialization for
    354 // n == N - 1 also doesn't work in Intel's compiler, so it goes into
    355 // an infinite loop)
    356 template<typename Reducer, typename T, std::size_t N, std::size_t n = N - 1>
    357 struct h_array_reduce {
    358   EIGEN_DEVICE_FUNC constexpr static inline auto run(array<T, N> arr, T identity) -> decltype(Reducer::run(h_array_reduce<Reducer, T, N, n - 1>::run(arr, identity), array_get<n>(arr)))
    359   {
    360     return Reducer::run(h_array_reduce<Reducer, T, N, n - 1>::run(arr, identity), array_get<n>(arr));
    361   }
    362 };
    363 
    364 template<typename Reducer, typename T, std::size_t N>
    365 struct h_array_reduce<Reducer, T, N, 0>
    366 {
    367   EIGEN_DEVICE_FUNC constexpr static inline T run(const array<T, N>& arr, T)
    368   {
    369     return array_get<0>(arr);
    370   }
    371 };
    372 
    373 template<typename Reducer, typename T>
    374 struct h_array_reduce<Reducer, T, 0>
    375 {
    376   EIGEN_DEVICE_FUNC constexpr static inline T run(const array<T, 0>&, T identity)
    377   {
    378     return identity;
    379   }
    380 };
    381 
    382 template<typename Reducer, typename T, std::size_t N>
    383 EIGEN_DEVICE_FUNC constexpr inline auto array_reduce(const array<T, N>& arr, T identity) -> decltype(h_array_reduce<Reducer, T, N>::run(arr, identity))
    384 {
    385   return h_array_reduce<Reducer, T, N>::run(arr, identity);
    386 }
    387 
    388 /* standard array reductions */
    389 
    390 template<typename T, std::size_t N>
    391 EIGEN_DEVICE_FUNC constexpr inline auto array_sum(const array<T, N>& arr) -> decltype(array_reduce<sum_op, T, N>(arr, static_cast<T>(0)))
    392 {
    393   return array_reduce<sum_op, T, N>(arr, static_cast<T>(0));
    394 }
    395 
    396 template<typename T, std::size_t N>
    397 EIGEN_DEVICE_FUNC constexpr inline auto array_prod(const array<T, N>& arr) -> decltype(array_reduce<product_op, T, N>(arr, static_cast<T>(1)))
    398 {
    399   return array_reduce<product_op, T, N>(arr, static_cast<T>(1));
    400 }
    401 
    402 template<typename t>
    403 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE t array_prod(const std::vector<t>& a) {
    404   eigen_assert(a.size() > 0);
    405   t prod = 1;
    406   for (size_t i = 0; i < a.size(); ++i) { prod *= a[i]; }
    407   return prod;
    408 }
    409 
    410 /* zip an array */
    411 
    412 template<typename Op, typename A, typename B, std::size_t N, int... n>
    413 constexpr inline array<decltype(Op::run(A(), B())),N> h_array_zip(array<A, N> a, array<B, N> b, numeric_list<int, n...>)
    414 {
    415   return array<decltype(Op::run(A(), B())),N>{{ Op::run(array_get<n>(a), array_get<n>(b))... }};
    416 }
    417 
    418 template<typename Op, typename A, typename B, std::size_t N>
    419 constexpr inline array<decltype(Op::run(A(), B())),N> array_zip(array<A, N> a, array<B, N> b)
    420 {
    421   return h_array_zip<Op>(a, b, typename gen_numeric_list<int, N>::type());
    422 }
    423 
    424 /* zip an array and reduce the result */
    425 
    426 template<typename Reducer, typename Op, typename A, typename B, std::size_t N, int... n>
    427 constexpr inline auto h_array_zip_and_reduce(array<A, N> a, array<B, N> b, numeric_list<int, n...>) -> decltype(reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A(), B()))>::type...>::run(Op::run(array_get<n>(a), array_get<n>(b))...))
    428 {
    429   return reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A(), B()))>::type...>::run(Op::run(array_get<n>(a), array_get<n>(b))...);
    430 }
    431 
    432 template<typename Reducer, typename Op, typename A, typename B, std::size_t N>
    433 constexpr inline auto array_zip_and_reduce(array<A, N> a, array<B, N> b) -> decltype(h_array_zip_and_reduce<Reducer, Op, A, B, N>(a, b, typename gen_numeric_list<int, N>::type()))
    434 {
    435   return h_array_zip_and_reduce<Reducer, Op, A, B, N>(a, b, typename gen_numeric_list<int, N>::type());
    436 }
    437 
    438 /* apply stuff to an array */
    439 
    440 template<typename Op, typename A, std::size_t N, int... n>
    441 constexpr inline array<decltype(Op::run(A())),N> h_array_apply(array<A, N> a, numeric_list<int, n...>)
    442 {
    443   return array<decltype(Op::run(A())),N>{{ Op::run(array_get<n>(a))... }};
    444 }
    445 
    446 template<typename Op, typename A, std::size_t N>
    447 constexpr inline array<decltype(Op::run(A())),N> array_apply(array<A, N> a)
    448 {
    449   return h_array_apply<Op>(a, typename gen_numeric_list<int, N>::type());
    450 }
    451 
    452 /* apply stuff to an array and reduce */
    453 
    454 template<typename Reducer, typename Op, typename A, std::size_t N, int... n>
    455 constexpr inline auto h_array_apply_and_reduce(array<A, N> arr, numeric_list<int, n...>) -> decltype(reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A()))>::type...>::run(Op::run(array_get<n>(arr))...))
    456 {
    457   return reduce<Reducer, typename id_numeric<int,n,decltype(Op::run(A()))>::type...>::run(Op::run(array_get<n>(arr))...);
    458 }
    459 
    460 template<typename Reducer, typename Op, typename A, std::size_t N>
    461 constexpr inline auto array_apply_and_reduce(array<A, N> a) -> decltype(h_array_apply_and_reduce<Reducer, Op, A, N>(a, typename gen_numeric_list<int, N>::type()))
    462 {
    463   return h_array_apply_and_reduce<Reducer, Op, A, N>(a, typename gen_numeric_list<int, N>::type());
    464 }
    465 
    466 /* repeat a value n times (and make an array out of it
    467  * usage:
    468  *   array<int, 16> = repeat<16>(42);
    469  */
    470 
    471 template<int n>
    472 struct h_repeat
    473 {
    474   template<typename t, int... ii>
    475   constexpr static inline array<t, n> run(t v, numeric_list<int, ii...>)
    476   {
    477     return {{ typename id_numeric<int, ii, t>::type(v)... }};
    478   }
    479 };
    480 
    481 template<int n, typename t>
    482 constexpr array<t, n> repeat(t v) { return h_repeat<n>::run(v, typename gen_numeric_list<int, n>::type()); }
    483 
    484 /* instantiate a class by a C-style array */
    485 template<class InstType, typename ArrType, std::size_t N, bool Reverse, typename... Ps>
    486 struct h_instantiate_by_c_array;
    487 
    488 template<class InstType, typename ArrType, std::size_t N, typename... Ps>
    489 struct h_instantiate_by_c_array<InstType, ArrType, N, false, Ps...>
    490 {
    491   static InstType run(ArrType* arr, Ps... args)
    492   {
    493     return h_instantiate_by_c_array<InstType, ArrType, N - 1, false, Ps..., ArrType>::run(arr + 1, args..., arr[0]);
    494   }
    495 };
    496 
    497 template<class InstType, typename ArrType, std::size_t N, typename... Ps>
    498 struct h_instantiate_by_c_array<InstType, ArrType, N, true, Ps...>
    499 {
    500   static InstType run(ArrType* arr, Ps... args)
    501   {
    502     return h_instantiate_by_c_array<InstType, ArrType, N - 1, false, ArrType, Ps...>::run(arr + 1, arr[0], args...);
    503   }
    504 };
    505 
    506 template<class InstType, typename ArrType, typename... Ps>
    507 struct h_instantiate_by_c_array<InstType, ArrType, 0, false, Ps...>
    508 {
    509   static InstType run(ArrType* arr, Ps... args)
    510   {
    511     (void)arr;
    512     return InstType(args...);
    513   }
    514 };
    515 
    516 template<class InstType, typename ArrType, typename... Ps>
    517 struct h_instantiate_by_c_array<InstType, ArrType, 0, true, Ps...>
    518 {
    519   static InstType run(ArrType* arr, Ps... args)
    520   {
    521     (void)arr;
    522     return InstType(args...);
    523   }
    524 };
    525 
    526 template<class InstType, typename ArrType, std::size_t N, bool Reverse = false>
    527 InstType instantiate_by_c_array(ArrType* arr)
    528 {
    529   return h_instantiate_by_c_array<InstType, ArrType, N, Reverse>::run(arr);
    530 }
    531 
    532 } // end namespace internal
    533 
    534 } // end namespace Eigen
    535 
    536 #else // Non C++11, fallback to emulation mode
    537 
    538 #include "EmulateCXX11Meta.h"
    539 
    540 #endif
    541 
    542 #endif // EIGEN_CXX11META_H
    543