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