1 // Simd fixed_size ABI specific implementations -*- C++ -*-
2 
3 // Copyright (C) 2020-2021 Free Software Foundation, Inc.
4 //
5 // This file is part of the GNU ISO C++ Library.  This library is free
6 // software; you can redistribute it and/or modify it under the
7 // terms of the GNU General Public License as published by the
8 // Free Software Foundation; either version 3, or (at your option)
9 // any later version.
10 
11 // This library is distributed in the hope that it will be useful,
12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14 // GNU General Public License for more details.
15 
16 // Under Section 7 of GPL version 3, you are granted additional
17 // permissions described in the GCC Runtime Library Exception, version
18 // 3.1, as published by the Free Software Foundation.
19 
20 // You should have received a copy of the GNU General Public License and
21 // a copy of the GCC Runtime Library Exception along with this program;
22 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
23 // <http://www.gnu.org/licenses/>.
24 
25 /*
26  * The fixed_size ABI gives the following guarantees:
27  *  - simd objects are passed via the stack
28  *  - memory layout of `simd<_Tp, _Np>` is equivalent to `array<_Tp, _Np>`
29  *  - alignment of `simd<_Tp, _Np>` is `_Np * sizeof(_Tp)` if _Np is __a
30  *    power-of-2 value, otherwise `std::__bit_ceil(_Np * sizeof(_Tp))` (Note:
31  *    if the alignment were to exceed the system/compiler maximum, it is bounded
32  *    to that maximum)
33  *  - simd_mask objects are passed like bitset<_Np>
34  *  - memory layout of `simd_mask<_Tp, _Np>` is equivalent to `bitset<_Np>`
35  *  - alignment of `simd_mask<_Tp, _Np>` is equal to the alignment of
36  *    `bitset<_Np>`
37  */
38 
39 #ifndef _GLIBCXX_EXPERIMENTAL_SIMD_FIXED_SIZE_H_
40 #define _GLIBCXX_EXPERIMENTAL_SIMD_FIXED_SIZE_H_
41 
42 #if __cplusplus >= 201703L
43 
44 #include <array>
45 
46 _GLIBCXX_SIMD_BEGIN_NAMESPACE
47 
48 // __simd_tuple_element {{{
49 template <size_t _I, typename _Tp>
50   struct __simd_tuple_element;
51 
52 template <typename _Tp, typename _A0, typename... _As>
53   struct __simd_tuple_element<0, _SimdTuple<_Tp, _A0, _As...>>
54   { using type = simd<_Tp, _A0>; };
55 
56 template <size_t _I, typename _Tp, typename _A0, typename... _As>
57   struct __simd_tuple_element<_I, _SimdTuple<_Tp, _A0, _As...>>
58   {
59     using type =
60       typename __simd_tuple_element<_I - 1, _SimdTuple<_Tp, _As...>>::type;
61   };
62 
63 template <size_t _I, typename _Tp>
64   using __simd_tuple_element_t = typename __simd_tuple_element<_I, _Tp>::type;
65 
66 // }}}
67 // __simd_tuple_concat {{{
68 
69 template <typename _Tp, typename... _A0s, typename... _A1s>
70   _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple<_Tp, _A0s..., _A1s...>
71   __simd_tuple_concat(const _SimdTuple<_Tp, _A0s...>& __left,
72 		      const _SimdTuple<_Tp, _A1s...>& __right)
73   {
74     if constexpr (sizeof...(_A0s) == 0)
75       return __right;
76     else if constexpr (sizeof...(_A1s) == 0)
77       return __left;
78     else
79       return {__left.first, __simd_tuple_concat(__left.second, __right)};
80   }
81 
82 template <typename _Tp, typename _A10, typename... _A1s>
83   _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple<_Tp, simd_abi::scalar, _A10,
84 					       _A1s...>
85   __simd_tuple_concat(const _Tp& __left,
86 		      const _SimdTuple<_Tp, _A10, _A1s...>& __right)
87   { return {__left, __right}; }
88 
89 // }}}
90 // __simd_tuple_pop_front {{{
91 // Returns the next _SimdTuple in __x that has _Np elements less.
92 // Precondition: _Np must match the number of elements in __first (recursively)
93 template <size_t _Np, typename _Tp>
94   _GLIBCXX_SIMD_INTRINSIC constexpr decltype(auto)
95   __simd_tuple_pop_front(_Tp&& __x)
96   {
97     if constexpr (_Np == 0)
98       return static_cast<_Tp&&>(__x);
99     else
100       {
101 	using _Up = __remove_cvref_t<_Tp>;
102 	static_assert(_Np >= _Up::_S_first_size);
103 	return __simd_tuple_pop_front<_Np - _Up::_S_first_size>(__x.second);
104       }
105   }
106 
107 // }}}
108 // __get_simd_at<_Np> {{{1
109 struct __as_simd {};
110 
111 struct __as_simd_tuple {};
112 
113 template <typename _Tp, typename _A0, typename... _Abis>
114   _GLIBCXX_SIMD_INTRINSIC constexpr simd<_Tp, _A0>
115   __simd_tuple_get_impl(__as_simd, const _SimdTuple<_Tp, _A0, _Abis...>& __t,
116 			_SizeConstant<0>)
117   { return {__private_init, __t.first}; }
118 
119 template <typename _Tp, typename _A0, typename... _Abis>
120   _GLIBCXX_SIMD_INTRINSIC constexpr const auto&
121   __simd_tuple_get_impl(__as_simd_tuple,
122 			const _SimdTuple<_Tp, _A0, _Abis...>& __t,
123 			_SizeConstant<0>)
124   { return __t.first; }
125 
126 template <typename _Tp, typename _A0, typename... _Abis>
127   _GLIBCXX_SIMD_INTRINSIC constexpr auto&
128   __simd_tuple_get_impl(__as_simd_tuple, _SimdTuple<_Tp, _A0, _Abis...>& __t,
129 			_SizeConstant<0>)
130   { return __t.first; }
131 
132 template <typename _R, size_t _Np, typename _Tp, typename... _Abis>
133   _GLIBCXX_SIMD_INTRINSIC constexpr auto
134   __simd_tuple_get_impl(_R, const _SimdTuple<_Tp, _Abis...>& __t,
135 			_SizeConstant<_Np>)
136   { return __simd_tuple_get_impl(_R(), __t.second, _SizeConstant<_Np - 1>()); }
137 
138 template <size_t _Np, typename _Tp, typename... _Abis>
139   _GLIBCXX_SIMD_INTRINSIC constexpr auto&
140   __simd_tuple_get_impl(__as_simd_tuple, _SimdTuple<_Tp, _Abis...>& __t,
141 			_SizeConstant<_Np>)
142   {
143     return __simd_tuple_get_impl(__as_simd_tuple(), __t.second,
144 				 _SizeConstant<_Np - 1>());
145   }
146 
147 template <size_t _Np, typename _Tp, typename... _Abis>
148   _GLIBCXX_SIMD_INTRINSIC constexpr auto
149   __get_simd_at(const _SimdTuple<_Tp, _Abis...>& __t)
150   { return __simd_tuple_get_impl(__as_simd(), __t, _SizeConstant<_Np>()); }
151 
152 // }}}
153 // __get_tuple_at<_Np> {{{
154 template <size_t _Np, typename _Tp, typename... _Abis>
155   _GLIBCXX_SIMD_INTRINSIC constexpr auto
156   __get_tuple_at(const _SimdTuple<_Tp, _Abis...>& __t)
157   {
158     return __simd_tuple_get_impl(__as_simd_tuple(), __t, _SizeConstant<_Np>());
159   }
160 
161 template <size_t _Np, typename _Tp, typename... _Abis>
162   _GLIBCXX_SIMD_INTRINSIC constexpr auto&
163   __get_tuple_at(_SimdTuple<_Tp, _Abis...>& __t)
164   {
165     return __simd_tuple_get_impl(__as_simd_tuple(), __t, _SizeConstant<_Np>());
166   }
167 
168 // __tuple_element_meta {{{1
169 template <typename _Tp, typename _Abi, size_t _Offset>
170   struct __tuple_element_meta : public _Abi::_SimdImpl
171   {
172     static_assert(is_same_v<typename _Abi::_SimdImpl::abi_type,
173 			    _Abi>); // this fails e.g. when _SimdImpl is an
174 				    // alias for _SimdImplBuiltin<_DifferentAbi>
175     using value_type = _Tp;
176     using abi_type = _Abi;
177     using _Traits = _SimdTraits<_Tp, _Abi>;
178     using _MaskImpl = typename _Abi::_MaskImpl;
179     using _MaskMember = typename _Traits::_MaskMember;
180     using simd_type = simd<_Tp, _Abi>;
181     static constexpr size_t _S_offset = _Offset;
182     static constexpr size_t _S_size() { return simd_size<_Tp, _Abi>::value; }
183     static constexpr _MaskImpl _S_mask_impl = {};
184 
185     template <size_t _Np, bool _Sanitized>
186       _GLIBCXX_SIMD_INTRINSIC static auto
187       _S_submask(_BitMask<_Np, _Sanitized> __bits)
188       { return __bits.template _M_extract<_Offset, _S_size()>(); }
189 
190     template <size_t _Np, bool _Sanitized>
191       _GLIBCXX_SIMD_INTRINSIC static _MaskMember
192       _S_make_mask(_BitMask<_Np, _Sanitized> __bits)
193       {
194 	return _MaskImpl::template _S_convert<_Tp>(
195 	  __bits.template _M_extract<_Offset, _S_size()>()._M_sanitized());
196       }
197 
198     _GLIBCXX_SIMD_INTRINSIC static _ULLong
199     _S_mask_to_shifted_ullong(_MaskMember __k)
200     { return _MaskImpl::_S_to_bits(__k).to_ullong() << _Offset; }
201   };
202 
203 template <size_t _Offset, typename _Tp, typename _Abi, typename... _As>
204   __tuple_element_meta<_Tp, _Abi, _Offset>
205   __make_meta(const _SimdTuple<_Tp, _Abi, _As...>&)
206   { return {}; }
207 
208 // }}}1
209 // _WithOffset wrapper class {{{
210 template <size_t _Offset, typename _Base>
211   struct _WithOffset : public _Base
212   {
213     static inline constexpr size_t _S_offset = _Offset;
214 
215     _GLIBCXX_SIMD_INTRINSIC char* _M_as_charptr()
216     {
217       return reinterpret_cast<char*>(this)
218 	     + _S_offset * sizeof(typename _Base::value_type);
219     }
220 
221     _GLIBCXX_SIMD_INTRINSIC const char* _M_as_charptr() const
222     {
223       return reinterpret_cast<const char*>(this)
224 	     + _S_offset * sizeof(typename _Base::value_type);
225     }
226   };
227 
228 // make _WithOffset<_WithOffset> ill-formed to use:
229 template <size_t _O0, size_t _O1, typename _Base>
230   struct _WithOffset<_O0, _WithOffset<_O1, _Base>> {};
231 
232 template <size_t _Offset, typename _Tp>
233   decltype(auto)
234   __add_offset(_Tp& __base)
235   { return static_cast<_WithOffset<_Offset, __remove_cvref_t<_Tp>>&>(__base); }
236 
237 template <size_t _Offset, typename _Tp>
238   decltype(auto)
239   __add_offset(const _Tp& __base)
240   {
241     return static_cast<const _WithOffset<_Offset, __remove_cvref_t<_Tp>>&>(
242       __base);
243   }
244 
245 template <size_t _Offset, size_t _ExistingOffset, typename _Tp>
246   decltype(auto)
247   __add_offset(_WithOffset<_ExistingOffset, _Tp>& __base)
248   {
249     return static_cast<_WithOffset<_Offset + _ExistingOffset, _Tp>&>(
250       static_cast<_Tp&>(__base));
251   }
252 
253 template <size_t _Offset, size_t _ExistingOffset, typename _Tp>
254   decltype(auto)
255   __add_offset(const _WithOffset<_ExistingOffset, _Tp>& __base)
256   {
257     return static_cast<const _WithOffset<_Offset + _ExistingOffset, _Tp>&>(
258       static_cast<const _Tp&>(__base));
259   }
260 
261 template <typename _Tp>
262   constexpr inline size_t __offset = 0;
263 
264 template <size_t _Offset, typename _Tp>
265   constexpr inline size_t __offset<_WithOffset<_Offset, _Tp>>
266     = _WithOffset<_Offset, _Tp>::_S_offset;
267 
268 template <typename _Tp>
269   constexpr inline size_t __offset<const _Tp> = __offset<_Tp>;
270 
271 template <typename _Tp>
272   constexpr inline size_t __offset<_Tp&> = __offset<_Tp>;
273 
274 template <typename _Tp>
275   constexpr inline size_t __offset<_Tp&&> = __offset<_Tp>;
276 
277 // }}}
278 // _SimdTuple specializations {{{1
279 // empty {{{2
280 template <typename _Tp>
281   struct _SimdTuple<_Tp>
282   {
283     using value_type = _Tp;
284     static constexpr size_t _S_tuple_size = 0;
285     static constexpr size_t _S_size() { return 0; }
286   };
287 
288 // _SimdTupleData {{{2
289 template <typename _FirstType, typename _SecondType>
290   struct _SimdTupleData
291   {
292     _FirstType first;
293     _SecondType second;
294 
295     _GLIBCXX_SIMD_INTRINSIC
296     constexpr bool _M_is_constprop() const
297     {
298       if constexpr (is_class_v<_FirstType>)
299 	return first._M_is_constprop() && second._M_is_constprop();
300       else
301 	return __builtin_constant_p(first) && second._M_is_constprop();
302     }
303   };
304 
305 template <typename _FirstType, typename _Tp>
306   struct _SimdTupleData<_FirstType, _SimdTuple<_Tp>>
307   {
308     _FirstType first;
309     static constexpr _SimdTuple<_Tp> second = {};
310 
311     _GLIBCXX_SIMD_INTRINSIC
312     constexpr bool _M_is_constprop() const
313     {
314       if constexpr (is_class_v<_FirstType>)
315 	return first._M_is_constprop();
316       else
317 	return __builtin_constant_p(first);
318     }
319   };
320 
321 // 1 or more {{{2
322 template <typename _Tp, typename _Abi0, typename... _Abis>
323   struct _SimdTuple<_Tp, _Abi0, _Abis...>
324     : _SimdTupleData<typename _SimdTraits<_Tp, _Abi0>::_SimdMember,
325 		     _SimdTuple<_Tp, _Abis...>>
326   {
327     static_assert(!__is_fixed_size_abi_v<_Abi0>);
328     using value_type = _Tp;
329     using _FirstType = typename _SimdTraits<_Tp, _Abi0>::_SimdMember;
330     using _FirstAbi = _Abi0;
331     using _SecondType = _SimdTuple<_Tp, _Abis...>;
332     static constexpr size_t _S_tuple_size = sizeof...(_Abis) + 1;
333 
334     static constexpr size_t _S_size()
335     { return simd_size_v<_Tp, _Abi0> + _SecondType::_S_size(); }
336 
337     static constexpr size_t _S_first_size = simd_size_v<_Tp, _Abi0>;
338     static constexpr bool _S_is_homogeneous = (is_same_v<_Abi0, _Abis> && ...);
339 
340     using _Base = _SimdTupleData<typename _SimdTraits<_Tp, _Abi0>::_SimdMember,
341 				 _SimdTuple<_Tp, _Abis...>>;
342     using _Base::first;
343     using _Base::second;
344 
345     _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple() = default;
346     _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple(const _SimdTuple&) = default;
347     _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple& operator=(const _SimdTuple&)
348       = default;
349 
350     template <typename _Up>
351       _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple(_Up&& __x)
352       : _Base{static_cast<_Up&&>(__x)} {}
353 
354     template <typename _Up, typename _Up2>
355       _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple(_Up&& __x, _Up2&& __y)
356       : _Base{static_cast<_Up&&>(__x), static_cast<_Up2&&>(__y)} {}
357 
358     template <typename _Up>
359       _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple(_Up&& __x, _SimdTuple<_Tp>)
360       : _Base{static_cast<_Up&&>(__x)} {}
361 
362     _GLIBCXX_SIMD_INTRINSIC char* _M_as_charptr()
363     { return reinterpret_cast<char*>(this); }
364 
365     _GLIBCXX_SIMD_INTRINSIC const char* _M_as_charptr() const
366     { return reinterpret_cast<const char*>(this); }
367 
368     template <size_t _Np>
369       _GLIBCXX_SIMD_INTRINSIC constexpr auto& _M_at()
370       {
371 	if constexpr (_Np == 0)
372 	  return first;
373 	else
374 	  return second.template _M_at<_Np - 1>();
375       }
376 
377     template <size_t _Np>
378       _GLIBCXX_SIMD_INTRINSIC constexpr const auto& _M_at() const
379       {
380 	if constexpr (_Np == 0)
381 	  return first;
382 	else
383 	  return second.template _M_at<_Np - 1>();
384       }
385 
386     template <size_t _Np>
387       _GLIBCXX_SIMD_INTRINSIC constexpr auto _M_simd_at() const
388       {
389 	if constexpr (_Np == 0)
390 	  return simd<_Tp, _Abi0>(__private_init, first);
391 	else
392 	  return second.template _M_simd_at<_Np - 1>();
393       }
394 
395     template <size_t _Offset = 0, typename _Fp>
396       _GLIBCXX_SIMD_INTRINSIC static constexpr _SimdTuple
397       _S_generate(_Fp&& __gen, _SizeConstant<_Offset> = {})
398       {
399 	auto&& __first = __gen(__tuple_element_meta<_Tp, _Abi0, _Offset>());
400 	if constexpr (_S_tuple_size == 1)
401 	  return {__first};
402 	else
403 	  return {__first,
404 		  _SecondType::_S_generate(
405 		    static_cast<_Fp&&>(__gen),
406 		    _SizeConstant<_Offset + simd_size_v<_Tp, _Abi0>>())};
407       }
408 
409     template <size_t _Offset = 0, typename _Fp, typename... _More>
410       _GLIBCXX_SIMD_INTRINSIC _SimdTuple
411       _M_apply_wrapped(_Fp&& __fun, const _More&... __more) const
412       {
413 	auto&& __first
414 	  = __fun(__make_meta<_Offset>(*this), first, __more.first...);
415 	if constexpr (_S_tuple_size == 1)
416 	  return {__first};
417 	else
418 	  return {
419 	    __first,
420 	    second.template _M_apply_wrapped<_Offset + simd_size_v<_Tp, _Abi0>>(
421 	      static_cast<_Fp&&>(__fun), __more.second...)};
422       }
423 
424     template <typename _Tup>
425       _GLIBCXX_SIMD_INTRINSIC constexpr decltype(auto)
426       _M_extract_argument(_Tup&& __tup) const
427       {
428 	using _TupT = typename __remove_cvref_t<_Tup>::value_type;
429 	if constexpr (is_same_v<_SimdTuple, __remove_cvref_t<_Tup>>)
430 	  return __tup.first;
431 	else if (__builtin_is_constant_evaluated())
432 	  return __fixed_size_storage_t<_TupT, _S_first_size>::_S_generate([&](
433 	    auto __meta) constexpr {
434 	    return __meta._S_generator(
435 	      [&](auto __i) constexpr { return __tup[__i]; },
436 	      static_cast<_TupT*>(nullptr));
437 	  });
438 	else
439 	  return [&]() {
440 	    __fixed_size_storage_t<_TupT, _S_first_size> __r;
441 	    __builtin_memcpy(__r._M_as_charptr(), __tup._M_as_charptr(),
442 			     sizeof(__r));
443 	    return __r;
444 	  }();
445       }
446 
447     template <typename _Tup>
448       _GLIBCXX_SIMD_INTRINSIC constexpr auto&
449       _M_skip_argument(_Tup&& __tup) const
450       {
451 	static_assert(_S_tuple_size > 1);
452 	using _Up = __remove_cvref_t<_Tup>;
453 	constexpr size_t __off = __offset<_Up>;
454 	if constexpr (_S_first_size == _Up::_S_first_size && __off == 0)
455 	  return __tup.second;
456 	else if constexpr (_S_first_size > _Up::_S_first_size
457 			   && _S_first_size % _Up::_S_first_size == 0
458 			   && __off == 0)
459 	  return __simd_tuple_pop_front<_S_first_size>(__tup);
460 	else if constexpr (_S_first_size + __off < _Up::_S_first_size)
461 	  return __add_offset<_S_first_size>(__tup);
462 	else if constexpr (_S_first_size + __off == _Up::_S_first_size)
463 	  return __tup.second;
464 	else
465 	  __assert_unreachable<_Tup>();
466       }
467 
468     template <size_t _Offset, typename... _More>
469       _GLIBCXX_SIMD_INTRINSIC constexpr void
470       _M_assign_front(const _SimdTuple<_Tp, _Abi0, _More...>& __x) &
471       {
472 	static_assert(_Offset == 0);
473 	first = __x.first;
474 	if constexpr (sizeof...(_More) > 0)
475 	  {
476 	    static_assert(sizeof...(_Abis) >= sizeof...(_More));
477 	    second.template _M_assign_front<0>(__x.second);
478 	  }
479       }
480 
481     template <size_t _Offset>
482       _GLIBCXX_SIMD_INTRINSIC constexpr void
483       _M_assign_front(const _FirstType& __x) &
484       {
485 	static_assert(_Offset == 0);
486 	first = __x;
487       }
488 
489     template <size_t _Offset, typename... _As>
490       _GLIBCXX_SIMD_INTRINSIC constexpr void
491       _M_assign_front(const _SimdTuple<_Tp, _As...>& __x) &
492       {
493 	__builtin_memcpy(_M_as_charptr() + _Offset * sizeof(value_type),
494 			 __x._M_as_charptr(),
495 			 sizeof(_Tp) * _SimdTuple<_Tp, _As...>::_S_size());
496       }
497 
498     /*
499      * Iterate over the first objects in this _SimdTuple and call __fun for each
500      * of them. If additional arguments are passed via __more, chunk them into
501      * _SimdTuple or __vector_type_t objects of the same number of values.
502      */
503     template <typename _Fp, typename... _More>
504       _GLIBCXX_SIMD_INTRINSIC constexpr _SimdTuple
505       _M_apply_per_chunk(_Fp&& __fun, _More&&... __more) const
506       {
507 	if constexpr ((...
508 		       || conjunction_v<
509 			 is_lvalue_reference<_More>,
510 			 negation<is_const<remove_reference_t<_More>>>>) )
511 	  {
512 	    // need to write back at least one of __more after calling __fun
513 	    auto&& __first = [&](auto... __args) constexpr
514 	    {
515 	      auto __r = __fun(__tuple_element_meta<_Tp, _Abi0, 0>(), first,
516 			       __args...);
517 	      [[maybe_unused]] auto&& __ignore_me = {(
518 		[](auto&& __dst, const auto& __src) {
519 		  if constexpr (is_assignable_v<decltype(__dst),
520 						decltype(__dst)>)
521 		    {
522 		      __dst.template _M_assign_front<__offset<decltype(__dst)>>(
523 			__src);
524 		    }
525 		}(static_cast<_More&&>(__more), __args),
526 		0)...};
527 	      return __r;
528 	    }
529 	    (_M_extract_argument(__more)...);
530 	    if constexpr (_S_tuple_size == 1)
531 	      return {__first};
532 	    else
533 	      return {__first,
534 		      second._M_apply_per_chunk(static_cast<_Fp&&>(__fun),
535 						_M_skip_argument(__more)...)};
536 	  }
537 	else
538 	  {
539 	    auto&& __first = __fun(__tuple_element_meta<_Tp, _Abi0, 0>(), first,
540 				   _M_extract_argument(__more)...);
541 	    if constexpr (_S_tuple_size == 1)
542 	      return {__first};
543 	    else
544 	      return {__first,
545 		      second._M_apply_per_chunk(static_cast<_Fp&&>(__fun),
546 						_M_skip_argument(__more)...)};
547 	  }
548       }
549 
550     template <typename _R = _Tp, typename _Fp, typename... _More>
551       _GLIBCXX_SIMD_INTRINSIC auto _M_apply_r(_Fp&& __fun,
552 					      const _More&... __more) const
553       {
554 	auto&& __first = __fun(__tuple_element_meta<_Tp, _Abi0, 0>(), first,
555 			       __more.first...);
556 	if constexpr (_S_tuple_size == 1)
557 	  return __first;
558 	else
559 	  return __simd_tuple_concat<_R>(
560 	    __first, second.template _M_apply_r<_R>(static_cast<_Fp&&>(__fun),
561 						    __more.second...));
562       }
563 
564     template <typename _Fp, typename... _More>
565       _GLIBCXX_SIMD_INTRINSIC constexpr friend _SanitizedBitMask<_S_size()>
566       _M_test(const _Fp& __fun, const _SimdTuple& __x, const _More&... __more)
567       {
568 	const _SanitizedBitMask<_S_first_size> __first
569 	  = _Abi0::_MaskImpl::_S_to_bits(
570 	    __fun(__tuple_element_meta<_Tp, _Abi0, 0>(), __x.first,
571 		  __more.first...));
572 	if constexpr (_S_tuple_size == 1)
573 	  return __first;
574 	else
575 	  return _M_test(__fun, __x.second, __more.second...)
576 	    ._M_prepend(__first);
577       }
578 
579     template <typename _Up, _Up _I>
580       _GLIBCXX_SIMD_INTRINSIC constexpr _Tp
581       operator[](integral_constant<_Up, _I>) const noexcept
582       {
583 	if constexpr (_I < simd_size_v<_Tp, _Abi0>)
584 	  return _M_subscript_read(_I);
585 	else
586 	  return second[integral_constant<_Up, _I - simd_size_v<_Tp, _Abi0>>()];
587       }
588 
589     _Tp operator[](size_t __i) const noexcept
590     {
591       if constexpr (_S_tuple_size == 1)
592 	return _M_subscript_read(__i);
593       else
594 	{
595 #ifdef _GLIBCXX_SIMD_USE_ALIASING_LOADS
596 	  return reinterpret_cast<const __may_alias<_Tp>*>(this)[__i];
597 #else
598 	  if constexpr (__is_scalar_abi<_Abi0>())
599 	    {
600 	      const _Tp* ptr = &first;
601 	      return ptr[__i];
602 	    }
603 	  else
604 	    return __i < simd_size_v<_Tp, _Abi0>
605 		     ? _M_subscript_read(__i)
606 		     : second[__i - simd_size_v<_Tp, _Abi0>];
607 #endif
608 	}
609     }
610 
611     void _M_set(size_t __i, _Tp __val) noexcept
612     {
613       if constexpr (_S_tuple_size == 1)
614 	return _M_subscript_write(__i, __val);
615       else
616 	{
617 #ifdef _GLIBCXX_SIMD_USE_ALIASING_LOADS
618 	  reinterpret_cast<__may_alias<_Tp>*>(this)[__i] = __val;
619 #else
620 	  if (__i < simd_size_v<_Tp, _Abi0>)
621 	    _M_subscript_write(__i, __val);
622 	  else
623 	    second._M_set(__i - simd_size_v<_Tp, _Abi0>, __val);
624 #endif
625 	}
626     }
627 
628   private:
629     // _M_subscript_read/_write {{{
630     _Tp _M_subscript_read([[maybe_unused]] size_t __i) const noexcept
631     {
632       if constexpr (__is_vectorizable_v<_FirstType>)
633 	return first;
634       else
635 	return first[__i];
636     }
637 
638     void _M_subscript_write([[maybe_unused]] size_t __i, _Tp __y) noexcept
639     {
640       if constexpr (__is_vectorizable_v<_FirstType>)
641 	first = __y;
642       else
643 	first._M_set(__i, __y);
644     }
645 
646     // }}}
647   };
648 
649 // __make_simd_tuple {{{1
650 template <typename _Tp, typename _A0>
651   _GLIBCXX_SIMD_INTRINSIC _SimdTuple<_Tp, _A0>
652   __make_simd_tuple(simd<_Tp, _A0> __x0)
653   { return {__data(__x0)}; }
654 
655 template <typename _Tp, typename _A0, typename... _As>
656   _GLIBCXX_SIMD_INTRINSIC _SimdTuple<_Tp, _A0, _As...>
657   __make_simd_tuple(const simd<_Tp, _A0>& __x0, const simd<_Tp, _As>&... __xs)
658   { return {__data(__x0), __make_simd_tuple(__xs...)}; }
659 
660 template <typename _Tp, typename _A0>
661   _GLIBCXX_SIMD_INTRINSIC _SimdTuple<_Tp, _A0>
662   __make_simd_tuple(const typename _SimdTraits<_Tp, _A0>::_SimdMember& __arg0)
663   { return {__arg0}; }
664 
665 template <typename _Tp, typename _A0, typename _A1, typename... _Abis>
666   _GLIBCXX_SIMD_INTRINSIC _SimdTuple<_Tp, _A0, _A1, _Abis...>
667   __make_simd_tuple(
668     const typename _SimdTraits<_Tp, _A0>::_SimdMember& __arg0,
669     const typename _SimdTraits<_Tp, _A1>::_SimdMember& __arg1,
670     const typename _SimdTraits<_Tp, _Abis>::_SimdMember&... __args)
671   { return {__arg0, __make_simd_tuple<_Tp, _A1, _Abis...>(__arg1, __args...)}; }
672 
673 // __to_simd_tuple {{{1
674 template <typename _Tp, size_t _Np, typename _V, size_t _NV, typename... _VX>
675   _GLIBCXX_SIMD_INTRINSIC constexpr __fixed_size_storage_t<_Tp, _Np>
676   __to_simd_tuple(const array<_V, _NV>& __from, const _VX... __fromX);
677 
678 template <typename _Tp, size_t _Np,
679 	  size_t _Offset = 0, // skip this many elements in __from0
680 	  typename _R = __fixed_size_storage_t<_Tp, _Np>, typename _V0,
681 	  typename _V0VT = _VectorTraits<_V0>, typename... _VX>
682   _GLIBCXX_SIMD_INTRINSIC _R constexpr __to_simd_tuple(const _V0 __from0,
683 						       const _VX... __fromX)
684   {
685     static_assert(is_same_v<typename _V0VT::value_type, _Tp>);
686     static_assert(_Offset < _V0VT::_S_full_size);
687     using _R0 = __vector_type_t<_Tp, _R::_S_first_size>;
688     if constexpr (_R::_S_tuple_size == 1)
689       {
690 	if constexpr (_Np == 1)
691 	  return _R{__from0[_Offset]};
692 	else if constexpr (_Offset == 0 && _V0VT::_S_full_size >= _Np)
693 	  return _R{__intrin_bitcast<_R0>(__from0)};
694 	else if constexpr (_Offset * 2 == _V0VT::_S_full_size
695 			   && _V0VT::_S_full_size / 2 >= _Np)
696 	  return _R{__intrin_bitcast<_R0>(__extract_part<1, 2>(__from0))};
697 	else if constexpr (_Offset * 4 == _V0VT::_S_full_size
698 			   && _V0VT::_S_full_size / 4 >= _Np)
699 	  return _R{__intrin_bitcast<_R0>(__extract_part<1, 4>(__from0))};
700 	else
701 	  __assert_unreachable<_Tp>();
702       }
703     else
704       {
705 	if constexpr (1 == _R::_S_first_size)
706 	  { // extract one scalar and recurse
707 	    if constexpr (_Offset + 1 < _V0VT::_S_full_size)
708 	      return _R{__from0[_Offset],
709 			__to_simd_tuple<_Tp, _Np - 1, _Offset + 1>(__from0,
710 								   __fromX...)};
711 	    else
712 	      return _R{__from0[_Offset],
713 			__to_simd_tuple<_Tp, _Np - 1, 0>(__fromX...)};
714 	  }
715 
716 	// place __from0 into _R::first and recurse for __fromX -> _R::second
717 	else if constexpr (_V0VT::_S_full_size == _R::_S_first_size
718 			   && _Offset == 0)
719 	  return _R{__from0,
720 		    __to_simd_tuple<_Tp, _Np - _R::_S_first_size>(__fromX...)};
721 
722 	// place lower part of __from0 into _R::first and recurse with _Offset
723 	else if constexpr (_V0VT::_S_full_size > _R::_S_first_size
724 			   && _Offset == 0)
725 	  return _R{__intrin_bitcast<_R0>(__from0),
726 		    __to_simd_tuple<_Tp, _Np - _R::_S_first_size,
727 				    _R::_S_first_size>(__from0, __fromX...)};
728 
729 	// place lower part of second quarter of __from0 into _R::first and
730 	// recurse with _Offset
731 	else if constexpr (_Offset * 4 == _V0VT::_S_full_size
732 			   && _V0VT::_S_full_size >= 4 * _R::_S_first_size)
733 	  return _R{__intrin_bitcast<_R0>(__extract_part<2, 4>(__from0)),
734 		    __to_simd_tuple<_Tp, _Np - _R::_S_first_size,
735 				    _Offset + _R::_S_first_size>(__from0,
736 								 __fromX...)};
737 
738 	// place lower half of high half of __from0 into _R::first and recurse
739 	// with _Offset
740 	else if constexpr (_Offset * 2 == _V0VT::_S_full_size
741 			   && _V0VT::_S_full_size >= 4 * _R::_S_first_size)
742 	  return _R{__intrin_bitcast<_R0>(__extract_part<2, 4>(__from0)),
743 		    __to_simd_tuple<_Tp, _Np - _R::_S_first_size,
744 				    _Offset + _R::_S_first_size>(__from0,
745 								 __fromX...)};
746 
747 	// place high half of __from0 into _R::first and recurse with __fromX
748 	else if constexpr (_Offset * 2 == _V0VT::_S_full_size
749 			   && _V0VT::_S_full_size / 2 >= _R::_S_first_size)
750 	  return _R{__intrin_bitcast<_R0>(__extract_part<1, 2>(__from0)),
751 		    __to_simd_tuple<_Tp, _Np - _R::_S_first_size, 0>(
752 		      __fromX...)};
753 
754 	// ill-formed if some unforseen pattern is needed
755 	else
756 	  __assert_unreachable<_Tp>();
757       }
758   }
759 
760 template <typename _Tp, size_t _Np, typename _V, size_t _NV, typename... _VX>
761   _GLIBCXX_SIMD_INTRINSIC constexpr __fixed_size_storage_t<_Tp, _Np>
762   __to_simd_tuple(const array<_V, _NV>& __from, const _VX... __fromX)
763   {
764     if constexpr (is_same_v<_Tp, _V>)
765       {
766 	static_assert(
767 	  sizeof...(_VX) == 0,
768 	  "An array of scalars must be the last argument to __to_simd_tuple");
769 	return __call_with_subscripts(
770 	  __from,
771 	  make_index_sequence<_NV>(), [&](const auto... __args) constexpr {
772 	    return __simd_tuple_concat(
773 	      _SimdTuple<_Tp, simd_abi::scalar>{__args}..., _SimdTuple<_Tp>());
774 	  });
775       }
776     else
777       return __call_with_subscripts(
778 	__from,
779 	make_index_sequence<_NV>(), [&](const auto... __args) constexpr {
780 	  return __to_simd_tuple<_Tp, _Np>(__args..., __fromX...);
781 	});
782   }
783 
784 template <size_t, typename _Tp>
785   using __to_tuple_helper = _Tp;
786 
787 template <typename _Tp, typename _A0, size_t _NOut, size_t _Np,
788 	  size_t... _Indexes>
789   _GLIBCXX_SIMD_INTRINSIC __fixed_size_storage_t<_Tp, _NOut>
790   __to_simd_tuple_impl(index_sequence<_Indexes...>,
791       const array<__vector_type_t<_Tp, simd_size_v<_Tp, _A0>>, _Np>& __args)
792   {
793     return __make_simd_tuple<_Tp, __to_tuple_helper<_Indexes, _A0>...>(
794       __args[_Indexes]...);
795   }
796 
797 template <typename _Tp, typename _A0, size_t _NOut, size_t _Np,
798 	  typename _R = __fixed_size_storage_t<_Tp, _NOut>>
799   _GLIBCXX_SIMD_INTRINSIC _R
800   __to_simd_tuple_sized(
801     const array<__vector_type_t<_Tp, simd_size_v<_Tp, _A0>>, _Np>& __args)
802   {
803     static_assert(_Np * simd_size_v<_Tp, _A0> >= _NOut);
804     return __to_simd_tuple_impl<_Tp, _A0, _NOut>(
805       make_index_sequence<_R::_S_tuple_size>(), __args);
806   }
807 
808 // __optimize_simd_tuple {{{1
809 template <typename _Tp>
810   _GLIBCXX_SIMD_INTRINSIC _SimdTuple<_Tp>
811   __optimize_simd_tuple(const _SimdTuple<_Tp>)
812   { return {}; }
813 
814 template <typename _Tp, typename _Ap>
815   _GLIBCXX_SIMD_INTRINSIC const _SimdTuple<_Tp, _Ap>&
816   __optimize_simd_tuple(const _SimdTuple<_Tp, _Ap>& __x)
817   { return __x; }
818 
819 template <typename _Tp, typename _A0, typename _A1, typename... _Abis,
820 	  typename _R = __fixed_size_storage_t<
821 	    _Tp, _SimdTuple<_Tp, _A0, _A1, _Abis...>::_S_size()>>
822   _GLIBCXX_SIMD_INTRINSIC _R
823   __optimize_simd_tuple(const _SimdTuple<_Tp, _A0, _A1, _Abis...>& __x)
824   {
825     using _Tup = _SimdTuple<_Tp, _A0, _A1, _Abis...>;
826     if constexpr (is_same_v<_R, _Tup>)
827       return __x;
828     else if constexpr (is_same_v<typename _R::_FirstType,
829 				 typename _Tup::_FirstType>)
830       return {__x.first, __optimize_simd_tuple(__x.second)};
831     else if constexpr (__is_scalar_abi<_A0>()
832 		       || _A0::template _S_is_partial<_Tp>)
833       return {__generate_from_n_evaluations<_R::_S_first_size,
834 					    typename _R::_FirstType>(
835 		[&](auto __i) { return __x[__i]; }),
836 	      __optimize_simd_tuple(
837 		__simd_tuple_pop_front<_R::_S_first_size>(__x))};
838     else if constexpr (is_same_v<_A0, _A1>
839 	&& _R::_S_first_size == simd_size_v<_Tp, _A0> + simd_size_v<_Tp, _A1>)
840       return {__concat(__x.template _M_at<0>(), __x.template _M_at<1>()),
841 	      __optimize_simd_tuple(__x.second.second)};
842     else if constexpr (sizeof...(_Abis) >= 2
843 	&& _R::_S_first_size == (4 * simd_size_v<_Tp, _A0>)
844 	&& simd_size_v<_Tp, _A0> == __simd_tuple_element_t<
845 	    (sizeof...(_Abis) >= 2 ? 3 : 0), _Tup>::size())
846       return {
847 	__concat(__concat(__x.template _M_at<0>(), __x.template _M_at<1>()),
848 		 __concat(__x.template _M_at<2>(), __x.template _M_at<3>())),
849 	__optimize_simd_tuple(__x.second.second.second.second)};
850     else
851       {
852 	static_assert(sizeof(_R) == sizeof(__x));
853 	_R __r;
854 	__builtin_memcpy(__r._M_as_charptr(), __x._M_as_charptr(),
855 			 sizeof(_Tp) * _R::_S_size());
856 	return __r;
857       }
858   }
859 
860 // __for_each(const _SimdTuple &, Fun) {{{1
861 template <size_t _Offset = 0, typename _Tp, typename _A0, typename _Fp>
862   _GLIBCXX_SIMD_INTRINSIC constexpr void
863   __for_each(const _SimdTuple<_Tp, _A0>& __t, _Fp&& __fun)
864   { static_cast<_Fp&&>(__fun)(__make_meta<_Offset>(__t), __t.first); }
865 
866 template <size_t _Offset = 0, typename _Tp, typename _A0, typename _A1,
867 	  typename... _As, typename _Fp>
868   _GLIBCXX_SIMD_INTRINSIC constexpr void
869   __for_each(const _SimdTuple<_Tp, _A0, _A1, _As...>& __t, _Fp&& __fun)
870   {
871     __fun(__make_meta<_Offset>(__t), __t.first);
872     __for_each<_Offset + simd_size<_Tp, _A0>::value>(__t.second,
873 						     static_cast<_Fp&&>(__fun));
874   }
875 
876 // __for_each(_SimdTuple &, Fun) {{{1
877 template <size_t _Offset = 0, typename _Tp, typename _A0, typename _Fp>
878   _GLIBCXX_SIMD_INTRINSIC constexpr void
879   __for_each(_SimdTuple<_Tp, _A0>& __t, _Fp&& __fun)
880   { static_cast<_Fp&&>(__fun)(__make_meta<_Offset>(__t), __t.first); }
881 
882 template <size_t _Offset = 0, typename _Tp, typename _A0, typename _A1,
883 	  typename... _As, typename _Fp>
884   _GLIBCXX_SIMD_INTRINSIC constexpr void
885   __for_each(_SimdTuple<_Tp, _A0, _A1, _As...>& __t, _Fp&& __fun)
886   {
887     __fun(__make_meta<_Offset>(__t), __t.first);
888     __for_each<_Offset + simd_size<_Tp, _A0>::value>(__t.second,
889 						     static_cast<_Fp&&>(__fun));
890   }
891 
892 // __for_each(_SimdTuple &, const _SimdTuple &, Fun) {{{1
893 template <size_t _Offset = 0, typename _Tp, typename _A0, typename _Fp>
894   _GLIBCXX_SIMD_INTRINSIC constexpr void
895   __for_each(_SimdTuple<_Tp, _A0>& __a, const _SimdTuple<_Tp, _A0>& __b,
896 	     _Fp&& __fun)
897   {
898     static_cast<_Fp&&>(__fun)(__make_meta<_Offset>(__a), __a.first, __b.first);
899   }
900 
901 template <size_t _Offset = 0, typename _Tp, typename _A0, typename _A1,
902 	  typename... _As, typename _Fp>
903   _GLIBCXX_SIMD_INTRINSIC constexpr void
904   __for_each(_SimdTuple<_Tp, _A0, _A1, _As...>& __a,
905 	     const _SimdTuple<_Tp, _A0, _A1, _As...>& __b, _Fp&& __fun)
906   {
907     __fun(__make_meta<_Offset>(__a), __a.first, __b.first);
908     __for_each<_Offset + simd_size<_Tp, _A0>::value>(__a.second, __b.second,
909 						     static_cast<_Fp&&>(__fun));
910   }
911 
912 // __for_each(const _SimdTuple &, const _SimdTuple &, Fun) {{{1
913 template <size_t _Offset = 0, typename _Tp, typename _A0, typename _Fp>
914   _GLIBCXX_SIMD_INTRINSIC constexpr void
915   __for_each(const _SimdTuple<_Tp, _A0>& __a, const _SimdTuple<_Tp, _A0>& __b,
916 	     _Fp&& __fun)
917   {
918     static_cast<_Fp&&>(__fun)(__make_meta<_Offset>(__a), __a.first, __b.first);
919   }
920 
921 template <size_t _Offset = 0, typename _Tp, typename _A0, typename _A1,
922 	  typename... _As, typename _Fp>
923   _GLIBCXX_SIMD_INTRINSIC constexpr void
924   __for_each(const _SimdTuple<_Tp, _A0, _A1, _As...>& __a,
925 	     const _SimdTuple<_Tp, _A0, _A1, _As...>& __b, _Fp&& __fun)
926   {
927     __fun(__make_meta<_Offset>(__a), __a.first, __b.first);
928     __for_each<_Offset + simd_size<_Tp, _A0>::value>(__a.second, __b.second,
929 						     static_cast<_Fp&&>(__fun));
930   }
931 
932 // }}}1
933 // __extract_part(_SimdTuple) {{{
934 template <int _Index, int _Total, int _Combine, typename _Tp, typename _A0,
935 	  typename... _As>
936   _GLIBCXX_SIMD_INTRINSIC auto // __vector_type_t or _SimdTuple
937   __extract_part(const _SimdTuple<_Tp, _A0, _As...>& __x)
938   {
939     // worst cases:
940     // (a) 4, 4, 4 => 3, 3, 3, 3 (_Total = 4)
941     // (b) 2, 2, 2 => 3, 3       (_Total = 2)
942     // (c) 4, 2 => 2, 2, 2       (_Total = 3)
943     using _Tuple = _SimdTuple<_Tp, _A0, _As...>;
944     static_assert(_Index + _Combine <= _Total && _Index >= 0 && _Total >= 1);
945     constexpr size_t _Np = _Tuple::_S_size();
946     static_assert(_Np >= _Total && _Np % _Total == 0);
947     constexpr size_t __values_per_part = _Np / _Total;
948     [[maybe_unused]] constexpr size_t __values_to_skip
949       = _Index * __values_per_part;
950     constexpr size_t __return_size = __values_per_part * _Combine;
951     using _RetAbi = simd_abi::deduce_t<_Tp, __return_size>;
952 
953     // handle (optimize) the simple cases
954     if constexpr (_Index == 0 && _Tuple::_S_first_size == __return_size)
955       return __x.first._M_data;
956     else if constexpr (_Index == 0 && _Total == _Combine)
957       return __x;
958     else if constexpr (_Index == 0 && _Tuple::_S_first_size >= __return_size)
959       return __intrin_bitcast<__vector_type_t<_Tp, __return_size>>(
960 	__as_vector(__x.first));
961 
962     // recurse to skip unused data members at the beginning of _SimdTuple
963     else if constexpr (__values_to_skip >= _Tuple::_S_first_size)
964       { // recurse
965 	if constexpr (_Tuple::_S_first_size % __values_per_part == 0)
966 	  {
967 	    constexpr int __parts_in_first
968 	      = _Tuple::_S_first_size / __values_per_part;
969 	    return __extract_part<_Index - __parts_in_first,
970 				  _Total - __parts_in_first, _Combine>(
971 	      __x.second);
972 	  }
973 	else
974 	  return __extract_part<__values_to_skip - _Tuple::_S_first_size,
975 				_Np - _Tuple::_S_first_size, __return_size>(
976 	    __x.second);
977       }
978 
979     // extract from multiple _SimdTuple data members
980     else if constexpr (__return_size > _Tuple::_S_first_size - __values_to_skip)
981       {
982 #ifdef _GLIBCXX_SIMD_USE_ALIASING_LOADS
983 	const __may_alias<_Tp>* const element_ptr
984 	  = reinterpret_cast<const __may_alias<_Tp>*>(&__x) + __values_to_skip;
985 	return __as_vector(simd<_Tp, _RetAbi>(element_ptr, element_aligned));
986 #else
987 	[[maybe_unused]] constexpr size_t __offset = __values_to_skip;
988 	return __as_vector(simd<_Tp, _RetAbi>([&](auto __i) constexpr {
989 	  constexpr _SizeConstant<__i + __offset> __k;
990 	  return __x[__k];
991 	}));
992 #endif
993       }
994 
995     // all of the return values are in __x.first
996     else if constexpr (_Tuple::_S_first_size % __values_per_part == 0)
997       return __extract_part<_Index, _Tuple::_S_first_size / __values_per_part,
998 			    _Combine>(__x.first);
999     else
1000       return __extract_part<__values_to_skip, _Tuple::_S_first_size,
1001 			    _Combine * __values_per_part>(__x.first);
1002   }
1003 
1004 // }}}
1005 // __fixed_size_storage_t<_Tp, _Np>{{{
1006 template <typename _Tp, int _Np, typename _Tuple,
1007 	  typename _Next = simd<_Tp, _AllNativeAbis::_BestAbi<_Tp, _Np>>,
1008 	  int _Remain = _Np - int(_Next::size())>
1009   struct __fixed_size_storage_builder;
1010 
1011 template <typename _Tp, int _Np>
1012   struct __fixed_size_storage
1013   : public __fixed_size_storage_builder<_Tp, _Np, _SimdTuple<_Tp>> {};
1014 
1015 template <typename _Tp, int _Np, typename... _As, typename _Next>
1016   struct __fixed_size_storage_builder<_Tp, _Np, _SimdTuple<_Tp, _As...>, _Next,
1017 				      0>
1018   { using type = _SimdTuple<_Tp, _As..., typename _Next::abi_type>; };
1019 
1020 template <typename _Tp, int _Np, typename... _As, typename _Next, int _Remain>
1021   struct __fixed_size_storage_builder<_Tp, _Np, _SimdTuple<_Tp, _As...>, _Next,
1022 				      _Remain>
1023   {
1024     using type = typename __fixed_size_storage_builder<
1025       _Tp, _Remain, _SimdTuple<_Tp, _As..., typename _Next::abi_type>>::type;
1026   };
1027 
1028 // }}}
1029 // _AbisInSimdTuple {{{
1030 template <typename _Tp>
1031   struct _SeqOp;
1032 
1033 template <size_t _I0, size_t... _Is>
1034   struct _SeqOp<index_sequence<_I0, _Is...>>
1035   {
1036     using _FirstPlusOne = index_sequence<_I0 + 1, _Is...>;
1037     using _NotFirstPlusOne = index_sequence<_I0, (_Is + 1)...>;
1038     template <size_t _First, size_t _Add>
1039     using _Prepend = index_sequence<_First, _I0 + _Add, (_Is + _Add)...>;
1040   };
1041 
1042 template <typename _Tp>
1043   struct _AbisInSimdTuple;
1044 
1045 template <typename _Tp>
1046   struct _AbisInSimdTuple<_SimdTuple<_Tp>>
1047   {
1048     using _Counts = index_sequence<0>;
1049     using _Begins = index_sequence<0>;
1050   };
1051 
1052 template <typename _Tp, typename _Ap>
1053   struct _AbisInSimdTuple<_SimdTuple<_Tp, _Ap>>
1054   {
1055     using _Counts = index_sequence<1>;
1056     using _Begins = index_sequence<0>;
1057   };
1058 
1059 template <typename _Tp, typename _A0, typename... _As>
1060   struct _AbisInSimdTuple<_SimdTuple<_Tp, _A0, _A0, _As...>>
1061   {
1062     using _Counts = typename _SeqOp<typename _AbisInSimdTuple<
1063       _SimdTuple<_Tp, _A0, _As...>>::_Counts>::_FirstPlusOne;
1064     using _Begins = typename _SeqOp<typename _AbisInSimdTuple<
1065       _SimdTuple<_Tp, _A0, _As...>>::_Begins>::_NotFirstPlusOne;
1066   };
1067 
1068 template <typename _Tp, typename _A0, typename _A1, typename... _As>
1069   struct _AbisInSimdTuple<_SimdTuple<_Tp, _A0, _A1, _As...>>
1070   {
1071     using _Counts = typename _SeqOp<typename _AbisInSimdTuple<
1072       _SimdTuple<_Tp, _A1, _As...>>::_Counts>::template _Prepend<1, 0>;
1073     using _Begins = typename _SeqOp<typename _AbisInSimdTuple<
1074       _SimdTuple<_Tp, _A1, _As...>>::_Begins>::template _Prepend<0, 1>;
1075   };
1076 
1077 // }}}
1078 // __autocvt_to_simd {{{
1079 template <typename _Tp, bool = is_arithmetic_v<__remove_cvref_t<_Tp>>>
1080   struct __autocvt_to_simd
1081   {
1082     _Tp _M_data;
1083     using _TT = __remove_cvref_t<_Tp>;
1084 
1085     operator _TT()
1086     { return _M_data; }
1087 
1088     operator _TT&()
1089     {
1090       static_assert(is_lvalue_reference<_Tp>::value, "");
1091       static_assert(!is_const<_Tp>::value, "");
1092       return _M_data;
1093     }
1094 
1095     operator _TT*()
1096     {
1097       static_assert(is_lvalue_reference<_Tp>::value, "");
1098       static_assert(!is_const<_Tp>::value, "");
1099       return &_M_data;
1100     }
1101 
1102     constexpr inline __autocvt_to_simd(_Tp dd) : _M_data(dd) {}
1103 
1104     template <typename _Abi>
1105       operator simd<typename _TT::value_type, _Abi>()
1106       { return {__private_init, _M_data}; }
1107 
1108     template <typename _Abi>
1109       operator simd<typename _TT::value_type, _Abi>&()
1110       {
1111 	return *reinterpret_cast<simd<typename _TT::value_type, _Abi>*>(
1112 	  &_M_data);
1113       }
1114 
1115     template <typename _Abi>
1116       operator simd<typename _TT::value_type, _Abi>*()
1117       {
1118 	return reinterpret_cast<simd<typename _TT::value_type, _Abi>*>(
1119 	  &_M_data);
1120       }
1121   };
1122 
1123 template <typename _Tp>
1124   __autocvt_to_simd(_Tp &&) -> __autocvt_to_simd<_Tp>;
1125 
1126 template <typename _Tp>
1127   struct __autocvt_to_simd<_Tp, true>
1128   {
1129     using _TT = __remove_cvref_t<_Tp>;
1130     _Tp _M_data;
1131     fixed_size_simd<_TT, 1> _M_fd;
1132 
1133     constexpr inline __autocvt_to_simd(_Tp dd) : _M_data(dd), _M_fd(_M_data) {}
1134 
1135     ~__autocvt_to_simd()
1136     { _M_data = __data(_M_fd).first; }
1137 
1138     operator fixed_size_simd<_TT, 1>()
1139     { return _M_fd; }
1140 
1141     operator fixed_size_simd<_TT, 1> &()
1142     {
1143       static_assert(is_lvalue_reference<_Tp>::value, "");
1144       static_assert(!is_const<_Tp>::value, "");
1145       return _M_fd;
1146     }
1147 
1148     operator fixed_size_simd<_TT, 1> *()
1149     {
1150       static_assert(is_lvalue_reference<_Tp>::value, "");
1151       static_assert(!is_const<_Tp>::value, "");
1152       return &_M_fd;
1153     }
1154   };
1155 
1156 // }}}
1157 
1158 struct _CommonImplFixedSize;
1159 template <int _Np> struct _SimdImplFixedSize;
1160 template <int _Np> struct _MaskImplFixedSize;
1161 // simd_abi::_Fixed {{{
1162 template <int _Np>
1163   struct simd_abi::_Fixed
1164   {
1165     template <typename _Tp> static constexpr size_t _S_size = _Np;
1166     template <typename _Tp> static constexpr size_t _S_full_size = _Np;
1167     // validity traits {{{
1168     struct _IsValidAbiTag : public __bool_constant<(_Np > 0)> {};
1169 
1170     template <typename _Tp>
1171       struct _IsValidSizeFor
1172       : __bool_constant<(_Np <= simd_abi::max_fixed_size<_Tp>)> {};
1173 
1174     template <typename _Tp>
1175       struct _IsValid : conjunction<_IsValidAbiTag, __is_vectorizable<_Tp>,
1176 				    _IsValidSizeFor<_Tp>> {};
1177 
1178     template <typename _Tp>
1179       static constexpr bool _S_is_valid_v = _IsValid<_Tp>::value;
1180 
1181     // }}}
1182     // _S_masked {{{
1183     _GLIBCXX_SIMD_INTRINSIC static constexpr _SanitizedBitMask<_Np>
1184     _S_masked(_BitMask<_Np> __x)
1185     { return __x._M_sanitized(); }
1186 
1187     _GLIBCXX_SIMD_INTRINSIC static constexpr _SanitizedBitMask<_Np>
1188     _S_masked(_SanitizedBitMask<_Np> __x)
1189     { return __x; }
1190 
1191     // }}}
1192     // _*Impl {{{
1193     using _CommonImpl = _CommonImplFixedSize;
1194     using _SimdImpl = _SimdImplFixedSize<_Np>;
1195     using _MaskImpl = _MaskImplFixedSize<_Np>;
1196 
1197     // }}}
1198     // __traits {{{
1199     template <typename _Tp, bool = _S_is_valid_v<_Tp>>
1200       struct __traits : _InvalidTraits {};
1201 
1202     template <typename _Tp>
1203       struct __traits<_Tp, true>
1204       {
1205 	using _IsValid = true_type;
1206 	using _SimdImpl = _SimdImplFixedSize<_Np>;
1207 	using _MaskImpl = _MaskImplFixedSize<_Np>;
1208 
1209 	// simd and simd_mask member types {{{
1210 	using _SimdMember = __fixed_size_storage_t<_Tp, _Np>;
1211 	using _MaskMember = _SanitizedBitMask<_Np>;
1212 
1213 	static constexpr size_t _S_simd_align
1214 	  = std::__bit_ceil(_Np * sizeof(_Tp));
1215 
1216 	static constexpr size_t _S_mask_align = alignof(_MaskMember);
1217 
1218 	// }}}
1219 	// _SimdBase / base class for simd, providing extra conversions {{{
1220 	struct _SimdBase
1221 	{
1222 	  // The following ensures, function arguments are passed via the stack.
1223 	  // This is important for ABI compatibility across TU boundaries
1224 	  _SimdBase(const _SimdBase&) {}
1225 	  _SimdBase() = default;
1226 
1227 	  explicit operator const _SimdMember &() const
1228 	  { return static_cast<const simd<_Tp, _Fixed>*>(this)->_M_data; }
1229 
1230 	  explicit operator array<_Tp, _Np>() const
1231 	  {
1232 	    array<_Tp, _Np> __r;
1233 	    // _SimdMember can be larger because of higher alignment
1234 	    static_assert(sizeof(__r) <= sizeof(_SimdMember), "");
1235 	    __builtin_memcpy(__r.data(), &static_cast<const _SimdMember&>(*this),
1236 			     sizeof(__r));
1237 	    return __r;
1238 	  }
1239 	};
1240 
1241 	// }}}
1242 	// _MaskBase {{{
1243 	// empty. The bitset interface suffices
1244 	struct _MaskBase {};
1245 
1246 	// }}}
1247 	// _SimdCastType {{{
1248 	struct _SimdCastType
1249 	{
1250 	  _SimdCastType(const array<_Tp, _Np>&);
1251 	  _SimdCastType(const _SimdMember& dd) : _M_data(dd) {}
1252 	  explicit operator const _SimdMember &() const { return _M_data; }
1253 
1254 	private:
1255 	  const _SimdMember& _M_data;
1256 	};
1257 
1258 	// }}}
1259 	// _MaskCastType {{{
1260 	class _MaskCastType
1261 	{
1262 	  _MaskCastType() = delete;
1263 	};
1264 	// }}}
1265       };
1266     // }}}
1267   };
1268 
1269 // }}}
1270 // _CommonImplFixedSize {{{
1271 struct _CommonImplFixedSize
1272 {
1273   // _S_store {{{
1274   template <typename _Tp, typename... _As>
1275     _GLIBCXX_SIMD_INTRINSIC static void
1276     _S_store(const _SimdTuple<_Tp, _As...>& __x, void* __addr)
1277     {
1278       constexpr size_t _Np = _SimdTuple<_Tp, _As...>::_S_size();
1279       __builtin_memcpy(__addr, &__x, _Np * sizeof(_Tp));
1280     }
1281 
1282   // }}}
1283 };
1284 
1285 // }}}
1286 // _SimdImplFixedSize {{{1
1287 // fixed_size should not inherit from _SimdMathFallback in order for
1288 // specializations in the used _SimdTuple Abis to get used
1289 template <int _Np>
1290   struct _SimdImplFixedSize
1291   {
1292     // member types {{{2
1293     using _MaskMember = _SanitizedBitMask<_Np>;
1294 
1295     template <typename _Tp>
1296       using _SimdMember = __fixed_size_storage_t<_Tp, _Np>;
1297 
1298     template <typename _Tp>
1299       static constexpr size_t _S_tuple_size = _SimdMember<_Tp>::_S_tuple_size;
1300 
1301     template <typename _Tp>
1302       using _Simd = simd<_Tp, simd_abi::fixed_size<_Np>>;
1303 
1304     template <typename _Tp>
1305       using _TypeTag = _Tp*;
1306 
1307     // broadcast {{{2
1308     template <typename _Tp>
1309       static constexpr inline _SimdMember<_Tp> _S_broadcast(_Tp __x) noexcept
1310       {
1311 	return _SimdMember<_Tp>::_S_generate([&](auto __meta) constexpr {
1312 	  return __meta._S_broadcast(__x);
1313 	});
1314       }
1315 
1316     // _S_generator {{{2
1317     template <typename _Fp, typename _Tp>
1318       static constexpr inline _SimdMember<_Tp> _S_generator(_Fp&& __gen,
1319 							    _TypeTag<_Tp>)
1320       {
1321 	return _SimdMember<_Tp>::_S_generate([&__gen](auto __meta) constexpr {
1322 	  return __meta._S_generator(
1323 	    [&](auto __i) constexpr {
1324 	      return __i < _Np ? __gen(_SizeConstant<__meta._S_offset + __i>())
1325 			       : 0;
1326 	    },
1327 	    _TypeTag<_Tp>());
1328 	});
1329       }
1330 
1331     // _S_load {{{2
1332     template <typename _Tp, typename _Up>
1333       static inline _SimdMember<_Tp> _S_load(const _Up* __mem,
1334 					     _TypeTag<_Tp>) noexcept
1335       {
1336 	return _SimdMember<_Tp>::_S_generate([&](auto __meta) {
1337 	  return __meta._S_load(&__mem[__meta._S_offset], _TypeTag<_Tp>());
1338 	});
1339       }
1340 
1341     // _S_masked_load {{{2
1342     template <typename _Tp, typename... _As, typename _Up>
1343       static inline _SimdTuple<_Tp, _As...>
1344       _S_masked_load(const _SimdTuple<_Tp, _As...>& __old,
1345 		     const _MaskMember __bits, const _Up* __mem) noexcept
1346       {
1347 	auto __merge = __old;
1348 	__for_each(__merge, [&](auto __meta, auto& __native) {
1349 	  if (__meta._S_submask(__bits).any())
1350 #pragma GCC diagnostic push
1351 	  // __mem + __mem._S_offset could be UB ([expr.add]/4.3, but it punts
1352 	  // the responsibility for avoiding UB to the caller of the masked load
1353 	  // via the mask. Consequently, the compiler may assume this branch is
1354 	  // unreachable, if the pointer arithmetic is UB.
1355 #pragma GCC diagnostic ignored "-Warray-bounds"
1356 	    __native
1357 	      = __meta._S_masked_load(__native, __meta._S_make_mask(__bits),
1358 				      __mem + __meta._S_offset);
1359 #pragma GCC diagnostic pop
1360 	});
1361 	return __merge;
1362       }
1363 
1364     // _S_store {{{2
1365     template <typename _Tp, typename _Up>
1366       static inline void _S_store(const _SimdMember<_Tp>& __v, _Up* __mem,
1367 				  _TypeTag<_Tp>) noexcept
1368       {
1369 	__for_each(__v, [&](auto __meta, auto __native) {
1370 	  __meta._S_store(__native, &__mem[__meta._S_offset], _TypeTag<_Tp>());
1371 	});
1372       }
1373 
1374     // _S_masked_store {{{2
1375     template <typename _Tp, typename... _As, typename _Up>
1376       static inline void _S_masked_store(const _SimdTuple<_Tp, _As...>& __v,
1377 					 _Up* __mem,
1378 					 const _MaskMember __bits) noexcept
1379       {
1380 	__for_each(__v, [&](auto __meta, auto __native) {
1381 	  if (__meta._S_submask(__bits).any())
1382 #pragma GCC diagnostic push
1383 	  // __mem + __mem._S_offset could be UB ([expr.add]/4.3, but it punts
1384 	  // the responsibility for avoiding UB to the caller of the masked
1385 	  // store via the mask. Consequently, the compiler may assume this
1386 	  // branch is unreachable, if the pointer arithmetic is UB.
1387 #pragma GCC diagnostic ignored "-Warray-bounds"
1388 	    __meta._S_masked_store(__native, __mem + __meta._S_offset,
1389 				   __meta._S_make_mask(__bits));
1390 #pragma GCC diagnostic pop
1391 	});
1392       }
1393 
1394     // negation {{{2
1395     template <typename _Tp, typename... _As>
1396       static inline _MaskMember
1397       _S_negate(const _SimdTuple<_Tp, _As...>& __x) noexcept
1398       {
1399 	_MaskMember __bits = 0;
1400 	__for_each(
1401 	  __x, [&__bits](auto __meta, auto __native) constexpr {
1402 	    __bits
1403 	      |= __meta._S_mask_to_shifted_ullong(__meta._S_negate(__native));
1404 	  });
1405 	return __bits;
1406       }
1407 
1408     // reductions {{{2
1409     template <typename _Tp, typename _BinaryOperation>
1410       static constexpr inline _Tp _S_reduce(const _Simd<_Tp>& __x,
1411 					    const _BinaryOperation& __binary_op)
1412       {
1413 	using _Tup = _SimdMember<_Tp>;
1414 	const _Tup& __tup = __data(__x);
1415 	if constexpr (_Tup::_S_tuple_size == 1)
1416 	  return _Tup::_FirstAbi::_SimdImpl::_S_reduce(
1417 	    __tup.template _M_simd_at<0>(), __binary_op);
1418 	else if constexpr (_Tup::_S_tuple_size == 2 && _Tup::_S_size() > 2
1419 			   && _Tup::_SecondType::_S_size() == 1)
1420 	  {
1421 	    return __binary_op(simd<_Tp, simd_abi::scalar>(
1422 				 reduce(__tup.template _M_simd_at<0>(),
1423 					__binary_op)),
1424 			       __tup.template _M_simd_at<1>())[0];
1425 	  }
1426 	else if constexpr (_Tup::_S_tuple_size == 2 && _Tup::_S_size() > 4
1427 			   && _Tup::_SecondType::_S_size() == 2)
1428 	  {
1429 	    return __binary_op(
1430 	      simd<_Tp, simd_abi::scalar>(
1431 		reduce(__tup.template _M_simd_at<0>(), __binary_op)),
1432 	      simd<_Tp, simd_abi::scalar>(
1433 		reduce(__tup.template _M_simd_at<1>(), __binary_op)))[0];
1434 	  }
1435 	else
1436 	  {
1437 	    const auto& __x2 = __call_with_n_evaluations<
1438 	      __div_roundup(_Tup::_S_tuple_size, 2)>(
1439 	      [](auto __first_simd, auto... __remaining) {
1440 		if constexpr (sizeof...(__remaining) == 0)
1441 		  return __first_simd;
1442 		else
1443 		  {
1444 		    using _Tup2
1445 		      = _SimdTuple<_Tp,
1446 				   typename decltype(__first_simd)::abi_type,
1447 				   typename decltype(__remaining)::abi_type...>;
1448 		    return fixed_size_simd<_Tp, _Tup2::_S_size()>(
1449 		      __private_init,
1450 		      __make_simd_tuple(__first_simd, __remaining...));
1451 		  }
1452 	      },
1453 	      [&](auto __i) {
1454 		auto __left = __tup.template _M_simd_at<2 * __i>();
1455 		if constexpr (2 * __i + 1 == _Tup::_S_tuple_size)
1456 		  return __left;
1457 		else
1458 		  {
1459 		    auto __right = __tup.template _M_simd_at<2 * __i + 1>();
1460 		    using _LT = decltype(__left);
1461 		    using _RT = decltype(__right);
1462 		    if constexpr (_LT::size() == _RT::size())
1463 		      return __binary_op(__left, __right);
1464 		    else
1465 		      {
1466 			_GLIBCXX_SIMD_USE_CONSTEXPR_API
1467 			typename _LT::mask_type __k(
1468 			  __private_init,
1469 			  [](auto __j) constexpr { return __j < _RT::size(); });
1470 			_LT __ext_right = __left;
1471 			where(__k, __ext_right)
1472 			  = __proposed::resizing_simd_cast<_LT>(__right);
1473 			where(__k, __left) = __binary_op(__left, __ext_right);
1474 			return __left;
1475 		      }
1476 		  }
1477 	      });
1478 	    return reduce(__x2, __binary_op);
1479 	  }
1480       }
1481 
1482     // _S_min, _S_max {{{2
1483     template <typename _Tp, typename... _As>
1484       static inline constexpr _SimdTuple<_Tp, _As...>
1485       _S_min(const _SimdTuple<_Tp, _As...>& __a,
1486 	     const _SimdTuple<_Tp, _As...>& __b)
1487       {
1488 	return __a._M_apply_per_chunk(
1489 	  [](auto __impl, auto __aa, auto __bb) constexpr {
1490 	    return __impl._S_min(__aa, __bb);
1491 	  },
1492 	  __b);
1493       }
1494 
1495     template <typename _Tp, typename... _As>
1496       static inline constexpr _SimdTuple<_Tp, _As...>
1497       _S_max(const _SimdTuple<_Tp, _As...>& __a,
1498 	     const _SimdTuple<_Tp, _As...>& __b)
1499       {
1500 	return __a._M_apply_per_chunk(
1501 	  [](auto __impl, auto __aa, auto __bb) constexpr {
1502 	    return __impl._S_max(__aa, __bb);
1503 	  },
1504 	  __b);
1505       }
1506 
1507     // _S_complement {{{2
1508     template <typename _Tp, typename... _As>
1509       static inline constexpr _SimdTuple<_Tp, _As...>
1510       _S_complement(const _SimdTuple<_Tp, _As...>& __x) noexcept
1511       {
1512 	return __x._M_apply_per_chunk([](auto __impl, auto __xx) constexpr {
1513 	  return __impl._S_complement(__xx);
1514 	});
1515       }
1516 
1517     // _S_unary_minus {{{2
1518     template <typename _Tp, typename... _As>
1519       static inline constexpr _SimdTuple<_Tp, _As...>
1520       _S_unary_minus(const _SimdTuple<_Tp, _As...>& __x) noexcept
1521       {
1522 	return __x._M_apply_per_chunk([](auto __impl, auto __xx) constexpr {
1523 	  return __impl._S_unary_minus(__xx);
1524 	});
1525       }
1526 
1527     // arithmetic operators {{{2
1528 
1529 #define _GLIBCXX_SIMD_FIXED_OP(name_, op_)                                     \
1530     template <typename _Tp, typename... _As>                                   \
1531       static inline constexpr _SimdTuple<_Tp, _As...> name_(                   \
1532 	const _SimdTuple<_Tp, _As...> __x, const _SimdTuple<_Tp, _As...> __y)  \
1533       {                                                                        \
1534 	return __x._M_apply_per_chunk(                                         \
1535 	  [](auto __impl, auto __xx, auto __yy) constexpr {                    \
1536 	    return __impl.name_(__xx, __yy);                                   \
1537 	  },                                                                   \
1538 	  __y);                                                                \
1539       }
1540 
1541     _GLIBCXX_SIMD_FIXED_OP(_S_plus, +)
1542     _GLIBCXX_SIMD_FIXED_OP(_S_minus, -)
1543     _GLIBCXX_SIMD_FIXED_OP(_S_multiplies, *)
1544     _GLIBCXX_SIMD_FIXED_OP(_S_divides, /)
1545     _GLIBCXX_SIMD_FIXED_OP(_S_modulus, %)
1546     _GLIBCXX_SIMD_FIXED_OP(_S_bit_and, &)
1547     _GLIBCXX_SIMD_FIXED_OP(_S_bit_or, |)
1548     _GLIBCXX_SIMD_FIXED_OP(_S_bit_xor, ^)
1549     _GLIBCXX_SIMD_FIXED_OP(_S_bit_shift_left, <<)
1550     _GLIBCXX_SIMD_FIXED_OP(_S_bit_shift_right, >>)
1551 #undef _GLIBCXX_SIMD_FIXED_OP
1552 
1553     template <typename _Tp, typename... _As>
1554       static inline constexpr _SimdTuple<_Tp, _As...>
1555       _S_bit_shift_left(const _SimdTuple<_Tp, _As...>& __x, int __y)
1556       {
1557 	return __x._M_apply_per_chunk([__y](auto __impl, auto __xx) constexpr {
1558 	  return __impl._S_bit_shift_left(__xx, __y);
1559 	});
1560       }
1561 
1562     template <typename _Tp, typename... _As>
1563       static inline constexpr _SimdTuple<_Tp, _As...>
1564       _S_bit_shift_right(const _SimdTuple<_Tp, _As...>& __x, int __y)
1565       {
1566 	return __x._M_apply_per_chunk([__y](auto __impl, auto __xx) constexpr {
1567 	  return __impl._S_bit_shift_right(__xx, __y);
1568 	});
1569       }
1570 
1571   // math {{{2
1572 #define _GLIBCXX_SIMD_APPLY_ON_TUPLE(_RetTp, __name)                           \
1573     template <typename _Tp, typename... _As, typename... _More>                \
1574       static inline __fixed_size_storage_t<_RetTp, _Np>                        \
1575 	_S_##__name(const _SimdTuple<_Tp, _As...>& __x,                        \
1576 		    const _More&... __more)                                    \
1577       {                                                                        \
1578 	if constexpr (sizeof...(_More) == 0)                                   \
1579 	  {                                                                    \
1580 	    if constexpr (is_same_v<_Tp, _RetTp>)                              \
1581 	      return __x._M_apply_per_chunk(                                   \
1582 		[](auto __impl, auto __xx) constexpr {                         \
1583 		  using _V = typename decltype(__impl)::simd_type;             \
1584 		  return __data(__name(_V(__private_init, __xx)));             \
1585 		});                                                            \
1586 	    else                                                               \
1587 	      return __optimize_simd_tuple(                                    \
1588 		__x.template _M_apply_r<_RetTp>([](auto __impl, auto __xx) {   \
1589 		  return __impl._S_##__name(__xx);                             \
1590 		}));                                                           \
1591 	  }                                                                    \
1592 	else if constexpr (                                                    \
1593 	  is_same_v<                                                           \
1594 	    _Tp,                                                               \
1595 	    _RetTp> && (... && is_same_v<_SimdTuple<_Tp, _As...>, _More>) )    \
1596 	  return __x._M_apply_per_chunk(                                       \
1597 	    [](auto __impl, auto __xx, auto... __pack) constexpr {             \
1598 	      using _V = typename decltype(__impl)::simd_type;                 \
1599 	      return __data(__name(_V(__private_init, __xx),                   \
1600 				   _V(__private_init, __pack)...));            \
1601 	    },                                                                 \
1602 	    __more...);                                                        \
1603 	else if constexpr (is_same_v<_Tp, _RetTp>)                             \
1604 	  return __x._M_apply_per_chunk(                                       \
1605 	    [](auto __impl, auto __xx, auto... __pack) constexpr {             \
1606 	      using _V = typename decltype(__impl)::simd_type;                 \
1607 	      return __data(__name(_V(__private_init, __xx),                   \
1608 				   __autocvt_to_simd(__pack)...));             \
1609 	    },                                                                 \
1610 	    __more...);                                                        \
1611 	else                                                                   \
1612 	  __assert_unreachable<_Tp>();                                         \
1613       }
1614 
1615     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, acos)
1616     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, asin)
1617     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, atan)
1618     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, atan2)
1619     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, cos)
1620     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, sin)
1621     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, tan)
1622     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, acosh)
1623     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, asinh)
1624     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, atanh)
1625     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, cosh)
1626     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, sinh)
1627     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, tanh)
1628     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, exp)
1629     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, exp2)
1630     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, expm1)
1631     _GLIBCXX_SIMD_APPLY_ON_TUPLE(int, ilogb)
1632     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, log)
1633     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, log10)
1634     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, log1p)
1635     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, log2)
1636     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, logb)
1637     // modf implemented in simd_math.h
1638     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp,
1639 				 scalbn) // double scalbn(double x, int exp);
1640     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, scalbln)
1641     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, cbrt)
1642     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, abs)
1643     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, fabs)
1644     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, pow)
1645     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, sqrt)
1646     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, erf)
1647     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, erfc)
1648     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, lgamma)
1649     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, tgamma)
1650     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, trunc)
1651     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, ceil)
1652     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, floor)
1653     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, nearbyint)
1654 
1655     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, rint)
1656     _GLIBCXX_SIMD_APPLY_ON_TUPLE(long, lrint)
1657     _GLIBCXX_SIMD_APPLY_ON_TUPLE(long long, llrint)
1658 
1659     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, round)
1660     _GLIBCXX_SIMD_APPLY_ON_TUPLE(long, lround)
1661     _GLIBCXX_SIMD_APPLY_ON_TUPLE(long long, llround)
1662 
1663     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, ldexp)
1664     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, fmod)
1665     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, remainder)
1666     // copysign in simd_math.h
1667     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, nextafter)
1668     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, fdim)
1669     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, fmax)
1670     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, fmin)
1671     _GLIBCXX_SIMD_APPLY_ON_TUPLE(_Tp, fma)
1672     _GLIBCXX_SIMD_APPLY_ON_TUPLE(int, fpclassify)
1673 #undef _GLIBCXX_SIMD_APPLY_ON_TUPLE
1674 
1675     template <typename _Tp, typename... _Abis>
1676       static _SimdTuple<_Tp, _Abis...> _S_remquo(
1677 	const _SimdTuple<_Tp, _Abis...>& __x,
1678 	const _SimdTuple<_Tp, _Abis...>& __y,
1679 	__fixed_size_storage_t<int, _SimdTuple<_Tp, _Abis...>::_S_size()>* __z)
1680       {
1681 	return __x._M_apply_per_chunk(
1682 	  [](auto __impl, const auto __xx, const auto __yy, auto& __zz) {
1683 	    return __impl._S_remquo(__xx, __yy, &__zz);
1684 	  },
1685 	  __y, *__z);
1686       }
1687 
1688     template <typename _Tp, typename... _As>
1689       static inline _SimdTuple<_Tp, _As...>
1690       _S_frexp(const _SimdTuple<_Tp, _As...>& __x,
1691 	       __fixed_size_storage_t<int, _Np>& __exp) noexcept
1692       {
1693 	return __x._M_apply_per_chunk(
1694 	  [](auto __impl, const auto& __a, auto& __b) {
1695 	    return __data(
1696 	      frexp(typename decltype(__impl)::simd_type(__private_init, __a),
1697 		    __autocvt_to_simd(__b)));
1698 	  },
1699 	  __exp);
1700       }
1701 
1702 #define _GLIBCXX_SIMD_TEST_ON_TUPLE_(name_)                                    \
1703     template <typename _Tp, typename... _As>                                   \
1704       static inline _MaskMember                                                \
1705 	_S_##name_(const _SimdTuple<_Tp, _As...>& __x) noexcept                \
1706       {                                                                        \
1707 	return _M_test([](auto __impl,                                         \
1708 			  auto __xx) { return __impl._S_##name_(__xx); },      \
1709 		       __x);                                                   \
1710       }
1711 
1712     _GLIBCXX_SIMD_TEST_ON_TUPLE_(isinf)
1713     _GLIBCXX_SIMD_TEST_ON_TUPLE_(isfinite)
1714     _GLIBCXX_SIMD_TEST_ON_TUPLE_(isnan)
1715     _GLIBCXX_SIMD_TEST_ON_TUPLE_(isnormal)
1716     _GLIBCXX_SIMD_TEST_ON_TUPLE_(signbit)
1717 #undef _GLIBCXX_SIMD_TEST_ON_TUPLE_
1718 
1719     // _S_increment & _S_decrement{{{2
1720     template <typename... _Ts>
1721       _GLIBCXX_SIMD_INTRINSIC static constexpr void
1722       _S_increment(_SimdTuple<_Ts...>& __x)
1723       {
1724 	__for_each(
1725 	  __x, [](auto __meta, auto& native) constexpr {
1726 	    __meta._S_increment(native);
1727 	  });
1728       }
1729 
1730     template <typename... _Ts>
1731       _GLIBCXX_SIMD_INTRINSIC static constexpr void
1732       _S_decrement(_SimdTuple<_Ts...>& __x)
1733       {
1734 	__for_each(
1735 	  __x, [](auto __meta, auto& native) constexpr {
1736 	    __meta._S_decrement(native);
1737 	  });
1738       }
1739 
1740     // compares {{{2
1741 #define _GLIBCXX_SIMD_CMP_OPERATIONS(__cmp)                                    \
1742     template <typename _Tp, typename... _As>                                   \
1743       _GLIBCXX_SIMD_INTRINSIC constexpr static _MaskMember                     \
1744       __cmp(const _SimdTuple<_Tp, _As...>& __x,                                \
1745 	    const _SimdTuple<_Tp, _As...>& __y)                                \
1746       {                                                                        \
1747 	return _M_test(                                                        \
1748 	  [](auto __impl, auto __xx, auto __yy) constexpr {                    \
1749 	    return __impl.__cmp(__xx, __yy);                                   \
1750 	  },                                                                   \
1751 	  __x, __y);                                                           \
1752       }
1753 
1754     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_equal_to)
1755     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_not_equal_to)
1756     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_less)
1757     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_less_equal)
1758     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_isless)
1759     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_islessequal)
1760     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_isgreater)
1761     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_isgreaterequal)
1762     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_islessgreater)
1763     _GLIBCXX_SIMD_CMP_OPERATIONS(_S_isunordered)
1764 #undef _GLIBCXX_SIMD_CMP_OPERATIONS
1765 
1766     // smart_reference access {{{2
1767     template <typename _Tp, typename... _As, typename _Up>
1768       _GLIBCXX_SIMD_INTRINSIC static void _S_set(_SimdTuple<_Tp, _As...>& __v,
1769 						 int __i, _Up&& __x) noexcept
1770       { __v._M_set(__i, static_cast<_Up&&>(__x)); }
1771 
1772     // _S_masked_assign {{{2
1773     template <typename _Tp, typename... _As>
1774       _GLIBCXX_SIMD_INTRINSIC static void
1775       _S_masked_assign(const _MaskMember __bits, _SimdTuple<_Tp, _As...>& __lhs,
1776 		       const __type_identity_t<_SimdTuple<_Tp, _As...>>& __rhs)
1777       {
1778 	__for_each(
1779 	  __lhs, __rhs,
1780 	  [&](auto __meta, auto& __native_lhs, auto __native_rhs) constexpr {
1781 	    __meta._S_masked_assign(__meta._S_make_mask(__bits), __native_lhs,
1782 				    __native_rhs);
1783 	  });
1784       }
1785 
1786     // Optimization for the case where the RHS is a scalar. No need to broadcast
1787     // the scalar to a simd first.
1788     template <typename _Tp, typename... _As>
1789       _GLIBCXX_SIMD_INTRINSIC static void
1790       _S_masked_assign(const _MaskMember __bits, _SimdTuple<_Tp, _As...>& __lhs,
1791 		       const __type_identity_t<_Tp> __rhs)
1792       {
1793 	__for_each(
1794 	  __lhs, [&](auto __meta, auto& __native_lhs) constexpr {
1795 	    __meta._S_masked_assign(__meta._S_make_mask(__bits), __native_lhs,
1796 				    __rhs);
1797 	  });
1798       }
1799 
1800     // _S_masked_cassign {{{2
1801     template <typename _Op, typename _Tp, typename... _As>
1802       static inline void _S_masked_cassign(const _MaskMember __bits,
1803 					   _SimdTuple<_Tp, _As...>& __lhs,
1804 					   const _SimdTuple<_Tp, _As...>& __rhs,
1805 					   _Op __op)
1806       {
1807 	__for_each(
1808 	  __lhs, __rhs,
1809 	  [&](auto __meta, auto& __native_lhs, auto __native_rhs) constexpr {
1810 	    __meta.template _S_masked_cassign(__meta._S_make_mask(__bits),
1811 					      __native_lhs, __native_rhs, __op);
1812 	  });
1813       }
1814 
1815     // Optimization for the case where the RHS is a scalar. No need to broadcast
1816     // the scalar to a simd first.
1817     template <typename _Op, typename _Tp, typename... _As>
1818       static inline void _S_masked_cassign(const _MaskMember __bits,
1819 					   _SimdTuple<_Tp, _As...>& __lhs,
1820 					   const _Tp& __rhs, _Op __op)
1821       {
1822 	__for_each(
1823 	  __lhs, [&](auto __meta, auto& __native_lhs) constexpr {
1824 	    __meta.template _S_masked_cassign(__meta._S_make_mask(__bits),
1825 					      __native_lhs, __rhs, __op);
1826 	  });
1827       }
1828 
1829     // _S_masked_unary {{{2
1830     template <template <typename> class _Op, typename _Tp, typename... _As>
1831       static inline _SimdTuple<_Tp, _As...>
1832       _S_masked_unary(const _MaskMember __bits,
1833 		      const _SimdTuple<_Tp, _As...> __v) // TODO: const-ref __v?
1834       {
1835 	return __v._M_apply_wrapped([&__bits](auto __meta,
1836 					      auto __native) constexpr {
1837 	  return __meta.template _S_masked_unary<_Op>(__meta._S_make_mask(
1838 							__bits),
1839 						      __native);
1840 	});
1841       }
1842 
1843     // }}}2
1844   };
1845 
1846 // _MaskImplFixedSize {{{1
1847 template <int _Np>
1848   struct _MaskImplFixedSize
1849   {
1850     static_assert(
1851       sizeof(_ULLong) * __CHAR_BIT__ >= _Np,
1852       "The fixed_size implementation relies on one _ULLong being able to store "
1853       "all boolean elements."); // required in load & store
1854 
1855     // member types {{{
1856     using _Abi = simd_abi::fixed_size<_Np>;
1857 
1858     using _MaskMember = _SanitizedBitMask<_Np>;
1859 
1860     template <typename _Tp>
1861       using _FirstAbi = typename __fixed_size_storage_t<_Tp, _Np>::_FirstAbi;
1862 
1863     template <typename _Tp>
1864       using _TypeTag = _Tp*;
1865 
1866     // }}}
1867     // _S_broadcast {{{
1868     template <typename>
1869       _GLIBCXX_SIMD_INTRINSIC static constexpr _MaskMember
1870       _S_broadcast(bool __x)
1871       { return __x ? ~_MaskMember() : _MaskMember(); }
1872 
1873     // }}}
1874     // _S_load {{{
1875     template <typename>
1876       _GLIBCXX_SIMD_INTRINSIC static constexpr _MaskMember
1877       _S_load(const bool* __mem)
1878       {
1879 	using _Ip = __int_for_sizeof_t<bool>;
1880 	// the following load uses element_aligned and relies on __mem already
1881 	// carrying alignment information from when this load function was
1882 	// called.
1883 	const simd<_Ip, _Abi> __bools(reinterpret_cast<const __may_alias<_Ip>*>(
1884 					__mem),
1885 				      element_aligned);
1886 	return __data(__bools != 0);
1887       }
1888 
1889     // }}}
1890     // _S_to_bits {{{
1891     template <bool _Sanitized>
1892       _GLIBCXX_SIMD_INTRINSIC static constexpr _SanitizedBitMask<_Np>
1893       _S_to_bits(_BitMask<_Np, _Sanitized> __x)
1894       {
1895 	if constexpr (_Sanitized)
1896 	  return __x;
1897 	else
1898 	  return __x._M_sanitized();
1899       }
1900 
1901     // }}}
1902     // _S_convert {{{
1903     template <typename _Tp, typename _Up, typename _UAbi>
1904       _GLIBCXX_SIMD_INTRINSIC static constexpr _MaskMember
1905       _S_convert(simd_mask<_Up, _UAbi> __x)
1906       {
1907 	return _UAbi::_MaskImpl::_S_to_bits(__data(__x))
1908 	  .template _M_extract<0, _Np>();
1909       }
1910 
1911     // }}}
1912     // _S_from_bitmask {{{2
1913     template <typename _Tp>
1914       _GLIBCXX_SIMD_INTRINSIC static _MaskMember
1915       _S_from_bitmask(_MaskMember __bits, _TypeTag<_Tp>) noexcept
1916       { return __bits; }
1917 
1918     // _S_load {{{2
1919     static inline _MaskMember _S_load(const bool* __mem) noexcept
1920     {
1921       // TODO: _UChar is not necessarily the best type to use here. For smaller
1922       // _Np _UShort, _UInt, _ULLong, float, and double can be more efficient.
1923       _ULLong __r = 0;
1924       using _Vs = __fixed_size_storage_t<_UChar, _Np>;
1925       __for_each(_Vs{}, [&](auto __meta, auto) {
1926 	__r |= __meta._S_mask_to_shifted_ullong(
1927 	  __meta._S_mask_impl._S_load(&__mem[__meta._S_offset],
1928 				      _SizeConstant<__meta._S_size()>()));
1929       });
1930       return __r;
1931     }
1932 
1933     // _S_masked_load {{{2
1934     static inline _MaskMember _S_masked_load(_MaskMember __merge,
1935 					     _MaskMember __mask,
1936 					     const bool* __mem) noexcept
1937     {
1938       _BitOps::_S_bit_iteration(__mask.to_ullong(), [&](auto __i) {
1939 	__merge.set(__i, __mem[__i]);
1940       });
1941       return __merge;
1942     }
1943 
1944     // _S_store {{{2
1945     static inline void _S_store(const _MaskMember __bitmask,
1946 				bool* __mem) noexcept
1947     {
1948       if constexpr (_Np == 1)
1949 	__mem[0] = __bitmask[0];
1950       else
1951 	_FirstAbi<_UChar>::_CommonImpl::_S_store_bool_array(__bitmask, __mem);
1952     }
1953 
1954     // _S_masked_store {{{2
1955     static inline void _S_masked_store(const _MaskMember __v, bool* __mem,
1956 				       const _MaskMember __k) noexcept
1957     {
1958       _BitOps::_S_bit_iteration(__k, [&](auto __i) { __mem[__i] = __v[__i]; });
1959     }
1960 
1961     // logical and bitwise operators {{{2
1962     _GLIBCXX_SIMD_INTRINSIC static _MaskMember
1963     _S_logical_and(const _MaskMember& __x, const _MaskMember& __y) noexcept
1964     { return __x & __y; }
1965 
1966     _GLIBCXX_SIMD_INTRINSIC static _MaskMember
1967     _S_logical_or(const _MaskMember& __x, const _MaskMember& __y) noexcept
1968     { return __x | __y; }
1969 
1970     _GLIBCXX_SIMD_INTRINSIC static constexpr _MaskMember
1971     _S_bit_not(const _MaskMember& __x) noexcept
1972     { return ~__x; }
1973 
1974     _GLIBCXX_SIMD_INTRINSIC static _MaskMember
1975     _S_bit_and(const _MaskMember& __x, const _MaskMember& __y) noexcept
1976     { return __x & __y; }
1977 
1978     _GLIBCXX_SIMD_INTRINSIC static _MaskMember
1979     _S_bit_or(const _MaskMember& __x, const _MaskMember& __y) noexcept
1980     { return __x | __y; }
1981 
1982     _GLIBCXX_SIMD_INTRINSIC static _MaskMember
1983     _S_bit_xor(const _MaskMember& __x, const _MaskMember& __y) noexcept
1984     { return __x ^ __y; }
1985 
1986     // smart_reference access {{{2
1987     _GLIBCXX_SIMD_INTRINSIC static void _S_set(_MaskMember& __k, int __i,
1988 					       bool __x) noexcept
1989     { __k.set(__i, __x); }
1990 
1991     // _S_masked_assign {{{2
1992     _GLIBCXX_SIMD_INTRINSIC static void
1993     _S_masked_assign(const _MaskMember __k, _MaskMember& __lhs,
1994 		     const _MaskMember __rhs)
1995     { __lhs = (__lhs & ~__k) | (__rhs & __k); }
1996 
1997     // Optimization for the case where the RHS is a scalar.
1998     _GLIBCXX_SIMD_INTRINSIC static void _S_masked_assign(const _MaskMember __k,
1999 							 _MaskMember& __lhs,
2000 							 const bool __rhs)
2001     {
2002       if (__rhs)
2003 	__lhs |= __k;
2004       else
2005 	__lhs &= ~__k;
2006     }
2007 
2008     // }}}2
2009     // _S_all_of {{{
2010     template <typename _Tp>
2011       _GLIBCXX_SIMD_INTRINSIC static bool _S_all_of(simd_mask<_Tp, _Abi> __k)
2012       { return __data(__k).all(); }
2013 
2014     // }}}
2015     // _S_any_of {{{
2016     template <typename _Tp>
2017       _GLIBCXX_SIMD_INTRINSIC static bool _S_any_of(simd_mask<_Tp, _Abi> __k)
2018       { return __data(__k).any(); }
2019 
2020     // }}}
2021     // _S_none_of {{{
2022     template <typename _Tp>
2023       _GLIBCXX_SIMD_INTRINSIC static bool _S_none_of(simd_mask<_Tp, _Abi> __k)
2024       { return __data(__k).none(); }
2025 
2026     // }}}
2027     // _S_some_of {{{
2028     template <typename _Tp>
2029       _GLIBCXX_SIMD_INTRINSIC static bool
2030       _S_some_of([[maybe_unused]] simd_mask<_Tp, _Abi> __k)
2031       {
2032 	if constexpr (_Np == 1)
2033 	  return false;
2034 	else
2035 	  return __data(__k).any() && !__data(__k).all();
2036       }
2037 
2038     // }}}
2039     // _S_popcount {{{
2040     template <typename _Tp>
2041       _GLIBCXX_SIMD_INTRINSIC static int _S_popcount(simd_mask<_Tp, _Abi> __k)
2042       { return __data(__k).count(); }
2043 
2044     // }}}
2045     // _S_find_first_set {{{
2046     template <typename _Tp>
2047       _GLIBCXX_SIMD_INTRINSIC static int
2048       _S_find_first_set(simd_mask<_Tp, _Abi> __k)
2049       { return std::__countr_zero(__data(__k).to_ullong()); }
2050 
2051     // }}}
2052     // _S_find_last_set {{{
2053     template <typename _Tp>
2054       _GLIBCXX_SIMD_INTRINSIC static int
2055       _S_find_last_set(simd_mask<_Tp, _Abi> __k)
2056       { return std::__bit_width(__data(__k).to_ullong()) - 1; }
2057 
2058     // }}}
2059   };
2060 // }}}1
2061 
2062 _GLIBCXX_SIMD_END_NAMESPACE
2063 #endif // __cplusplus >= 201703L
2064 #endif // _GLIBCXX_EXPERIMENTAL_SIMD_FIXED_SIZE_H_
2065 
2066 // vim: foldmethod=marker sw=2 noet ts=8 sts=2 tw=80
2067