libstdc++
simd_math.h
1 // Math overloads for simd -*- C++ -*-
2 
3 // Copyright (C) 2020-2022 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 #ifndef _GLIBCXX_EXPERIMENTAL_SIMD_MATH_H_
26 #define _GLIBCXX_EXPERIMENTAL_SIMD_MATH_H_
27 
28 #if __cplusplus >= 201703L
29 
30 #include <utility>
31 #include <iomanip>
32 
33 _GLIBCXX_SIMD_BEGIN_NAMESPACE
34 template <typename _Tp, typename _V>
35  using _Samesize = fixed_size_simd<_Tp, _V::size()>;
36 
37 // _Math_return_type {{{
38 template <typename _DoubleR, typename _Tp, typename _Abi>
39  struct _Math_return_type;
40 
41 template <typename _DoubleR, typename _Tp, typename _Abi>
42  using _Math_return_type_t =
43  typename _Math_return_type<_DoubleR, _Tp, _Abi>::type;
44 
45 template <typename _Tp, typename _Abi>
46  struct _Math_return_type<double, _Tp, _Abi>
47  { using type = simd<_Tp, _Abi>; };
48 
49 template <typename _Tp, typename _Abi>
50  struct _Math_return_type<bool, _Tp, _Abi>
51  { using type = simd_mask<_Tp, _Abi>; };
52 
53 template <typename _DoubleR, typename _Tp, typename _Abi>
54  struct _Math_return_type
55  { using type = fixed_size_simd<_DoubleR, simd_size_v<_Tp, _Abi>>; };
56 
57 //}}}
58 // _GLIBCXX_SIMD_MATH_CALL_ {{{
59 #define _GLIBCXX_SIMD_MATH_CALL_(__name) \
60 template <typename _Tp, typename _Abi, typename..., \
61  typename _R = _Math_return_type_t< \
62  decltype(std::__name(declval<double>())), _Tp, _Abi>> \
63  _GLIBCXX_SIMD_ALWAYS_INLINE \
64  enable_if_t<is_floating_point_v<_Tp>, _R> \
65  __name(simd<_Tp, _Abi> __x) \
66  { return {__private_init, _Abi::_SimdImpl::_S_##__name(__data(__x))}; }
67 
68 // }}}
69 //_Extra_argument_type{{{
70 template <typename _Up, typename _Tp, typename _Abi>
71  struct _Extra_argument_type;
72 
73 template <typename _Tp, typename _Abi>
74  struct _Extra_argument_type<_Tp*, _Tp, _Abi>
75  {
76  using type = simd<_Tp, _Abi>*;
77  static constexpr double* declval();
78  static constexpr bool __needs_temporary_scalar = true;
79 
80  _GLIBCXX_SIMD_INTRINSIC static constexpr auto _S_data(type __x)
81  { return &__data(*__x); }
82  };
83 
84 template <typename _Up, typename _Tp, typename _Abi>
85  struct _Extra_argument_type<_Up*, _Tp, _Abi>
86  {
87  static_assert(is_integral_v<_Up>);
88  using type = fixed_size_simd<_Up, simd_size_v<_Tp, _Abi>>*;
89  static constexpr _Up* declval();
90  static constexpr bool __needs_temporary_scalar = true;
91 
92  _GLIBCXX_SIMD_INTRINSIC static constexpr auto _S_data(type __x)
93  { return &__data(*__x); }
94  };
95 
96 template <typename _Tp, typename _Abi>
97  struct _Extra_argument_type<_Tp, _Tp, _Abi>
98  {
99  using type = simd<_Tp, _Abi>;
100  static constexpr double declval();
101  static constexpr bool __needs_temporary_scalar = false;
102 
103  _GLIBCXX_SIMD_INTRINSIC static constexpr decltype(auto)
104  _S_data(const type& __x)
105  { return __data(__x); }
106  };
107 
108 template <typename _Up, typename _Tp, typename _Abi>
109  struct _Extra_argument_type
110  {
111  static_assert(is_integral_v<_Up>);
112  using type = fixed_size_simd<_Up, simd_size_v<_Tp, _Abi>>;
113  static constexpr _Up declval();
114  static constexpr bool __needs_temporary_scalar = false;
115 
116  _GLIBCXX_SIMD_INTRINSIC static constexpr decltype(auto)
117  _S_data(const type& __x)
118  { return __data(__x); }
119  };
120 
121 //}}}
122 // _GLIBCXX_SIMD_MATH_CALL2_ {{{
123 #define _GLIBCXX_SIMD_MATH_CALL2_(__name, __arg2) \
124 template < \
125  typename _Tp, typename _Abi, typename..., \
126  typename _Arg2 = _Extra_argument_type<__arg2, _Tp, _Abi>, \
127  typename _R = _Math_return_type_t< \
128  decltype(std::__name(declval<double>(), _Arg2::declval())), _Tp, _Abi>> \
129  _GLIBCXX_SIMD_ALWAYS_INLINE \
130  enable_if_t<is_floating_point_v<_Tp>, _R> \
131  __name(const simd<_Tp, _Abi>& __x, const typename _Arg2::type& __y) \
132  { \
133  return {__private_init, \
134  _Abi::_SimdImpl::_S_##__name(__data(__x), _Arg2::_S_data(__y))}; \
135  } \
136 template <typename _Up, typename _Tp, typename _Abi> \
137  _GLIBCXX_SIMD_INTRINSIC _Math_return_type_t< \
138  decltype(std::__name( \
139  declval<double>(), \
140  declval<enable_if_t< \
141  conjunction_v< \
142  is_same<__arg2, _Tp>, \
143  negation<is_same<__remove_cvref_t<_Up>, simd<_Tp, _Abi>>>, \
144  is_convertible<_Up, simd<_Tp, _Abi>>, is_floating_point<_Tp>>, \
145  double>>())), \
146  _Tp, _Abi> \
147  __name(_Up&& __xx, const simd<_Tp, _Abi>& __yy) \
148  { return __name(simd<_Tp, _Abi>(static_cast<_Up&&>(__xx)), __yy); }
149 
150 // }}}
151 // _GLIBCXX_SIMD_MATH_CALL3_ {{{
152 #define _GLIBCXX_SIMD_MATH_CALL3_(__name, __arg2, __arg3) \
153 template <typename _Tp, typename _Abi, typename..., \
154  typename _Arg2 = _Extra_argument_type<__arg2, _Tp, _Abi>, \
155  typename _Arg3 = _Extra_argument_type<__arg3, _Tp, _Abi>, \
156  typename _R = _Math_return_type_t< \
157  decltype(std::__name(declval<double>(), _Arg2::declval(), \
158  _Arg3::declval())), \
159  _Tp, _Abi>> \
160  _GLIBCXX_SIMD_ALWAYS_INLINE \
161  enable_if_t<is_floating_point_v<_Tp>, _R> \
162  __name(const simd<_Tp, _Abi>& __x, const typename _Arg2::type& __y, \
163  const typename _Arg3::type& __z) \
164  { \
165  return {__private_init, \
166  _Abi::_SimdImpl::_S_##__name(__data(__x), _Arg2::_S_data(__y), \
167  _Arg3::_S_data(__z))}; \
168  } \
169 template < \
170  typename _T0, typename _T1, typename _T2, typename..., \
171  typename _U0 = __remove_cvref_t<_T0>, \
172  typename _U1 = __remove_cvref_t<_T1>, \
173  typename _U2 = __remove_cvref_t<_T2>, \
174  typename _Simd = conditional_t<is_simd_v<_U1>, _U1, _U2>, \
175  typename = enable_if_t<conjunction_v< \
176  is_simd<_Simd>, is_convertible<_T0&&, _Simd>, \
177  is_convertible<_T1&&, _Simd>, is_convertible<_T2&&, _Simd>, \
178  negation<conjunction< \
179  is_simd<_U0>, is_floating_point<__value_type_or_identity_t<_U0>>>>>>> \
180  _GLIBCXX_SIMD_INTRINSIC decltype(__name(declval<const _Simd&>(), \
181  declval<const _Simd&>(), \
182  declval<const _Simd&>())) \
183  __name(_T0&& __xx, _T1&& __yy, _T2&& __zz) \
184  { \
185  return __name(_Simd(static_cast<_T0&&>(__xx)), \
186  _Simd(static_cast<_T1&&>(__yy)), \
187  _Simd(static_cast<_T2&&>(__zz))); \
188  }
189 
190 // }}}
191 // __cosSeries {{{
192 template <typename _Abi>
193  _GLIBCXX_SIMD_ALWAYS_INLINE static simd<float, _Abi>
194  __cosSeries(const simd<float, _Abi>& __x)
195  {
196  const simd<float, _Abi> __x2 = __x * __x;
197  simd<float, _Abi> __y;
198  __y = 0x1.ap-16f; // 1/8!
199  __y = __y * __x2 - 0x1.6c1p-10f; // -1/6!
200  __y = __y * __x2 + 0x1.555556p-5f; // 1/4!
201  return __y * (__x2 * __x2) - .5f * __x2 + 1.f;
202  }
203 
204 template <typename _Abi>
205  _GLIBCXX_SIMD_ALWAYS_INLINE static simd<double, _Abi>
206  __cosSeries(const simd<double, _Abi>& __x)
207  {
208  const simd<double, _Abi> __x2 = __x * __x;
209  simd<double, _Abi> __y;
210  __y = 0x1.AC00000000000p-45; // 1/16!
211  __y = __y * __x2 - 0x1.9394000000000p-37; // -1/14!
212  __y = __y * __x2 + 0x1.1EED8C0000000p-29; // 1/12!
213  __y = __y * __x2 - 0x1.27E4FB7400000p-22; // -1/10!
214  __y = __y * __x2 + 0x1.A01A01A018000p-16; // 1/8!
215  __y = __y * __x2 - 0x1.6C16C16C16C00p-10; // -1/6!
216  __y = __y * __x2 + 0x1.5555555555554p-5; // 1/4!
217  return (__y * __x2 - .5f) * __x2 + 1.f;
218  }
219 
220 // }}}
221 // __sinSeries {{{
222 template <typename _Abi>
223  _GLIBCXX_SIMD_ALWAYS_INLINE static simd<float, _Abi>
224  __sinSeries(const simd<float, _Abi>& __x)
225  {
226  const simd<float, _Abi> __x2 = __x * __x;
227  simd<float, _Abi> __y;
228  __y = -0x1.9CC000p-13f; // -1/7!
229  __y = __y * __x2 + 0x1.111100p-7f; // 1/5!
230  __y = __y * __x2 - 0x1.555556p-3f; // -1/3!
231  return __y * (__x2 * __x) + __x;
232  }
233 
234 template <typename _Abi>
235  _GLIBCXX_SIMD_ALWAYS_INLINE static simd<double, _Abi>
236  __sinSeries(const simd<double, _Abi>& __x)
237  {
238  // __x = [0, 0.7854 = pi/4]
239  // __x² = [0, 0.6169 = pi²/8]
240  const simd<double, _Abi> __x2 = __x * __x;
241  simd<double, _Abi> __y;
242  __y = -0x1.ACF0000000000p-41; // -1/15!
243  __y = __y * __x2 + 0x1.6124400000000p-33; // 1/13!
244  __y = __y * __x2 - 0x1.AE64567000000p-26; // -1/11!
245  __y = __y * __x2 + 0x1.71DE3A5540000p-19; // 1/9!
246  __y = __y * __x2 - 0x1.A01A01A01A000p-13; // -1/7!
247  __y = __y * __x2 + 0x1.1111111111110p-7; // 1/5!
248  __y = __y * __x2 - 0x1.5555555555555p-3; // -1/3!
249  return __y * (__x2 * __x) + __x;
250  }
251 
252 // }}}
253 // __zero_low_bits {{{
254 template <int _Bits, typename _Tp, typename _Abi>
255  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi>
256  __zero_low_bits(simd<_Tp, _Abi> __x)
257  {
258  const simd<_Tp, _Abi> __bitmask
259  = __bit_cast<_Tp>(~make_unsigned_t<__int_for_sizeof_t<_Tp>>() << _Bits);
260  return {__private_init,
261  _Abi::_SimdImpl::_S_bit_and(__data(__x), __data(__bitmask))};
262  }
263 
264 // }}}
265 // __fold_input {{{
266 
267 /**@internal
268  * Fold @p x into [-¼π, ¼π] and remember the quadrant it came from:
269  * quadrant 0: [-¼π, ¼π]
270  * quadrant 1: [ ¼π, ¾π]
271  * quadrant 2: [ ¾π, 1¼π]
272  * quadrant 3: [1¼π, 1¾π]
273  *
274  * The algorithm determines `y` as the multiple `x - y * ¼π = [-¼π, ¼π]`. Using
275  * a bitmask, `y` is reduced to `quadrant`. `y` can be calculated as
276  * ```
277  * y = trunc(x / ¼π);
278  * y += fmod(y, 2);
279  * ```
280  * This can be simplified by moving the (implicit) division by 2 into the
281  * truncation expression. The `+= fmod` effect can the be achieved by using
282  * rounding instead of truncation: `y = round(x / ½π) * 2`. If precision allows,
283  * `2/π * x` is better (faster).
284  */
285 template <typename _Tp, typename _Abi>
286  struct _Folded
287  {
288  simd<_Tp, _Abi> _M_x;
289  rebind_simd_t<int, simd<_Tp, _Abi>> _M_quadrant;
290  };
291 
292 namespace __math_float {
293 inline constexpr float __pi_over_4 = 0x1.921FB6p-1f; // π/4
294 inline constexpr float __2_over_pi = 0x1.45F306p-1f; // 2/π
295 inline constexpr float __pi_2_5bits0
296  = 0x1.921fc0p0f; // π/2, 5 0-bits (least significant)
297 inline constexpr float __pi_2_5bits0_rem
298  = -0x1.5777a6p-21f; // π/2 - __pi_2_5bits0
299 } // namespace __math_float
300 namespace __math_double {
301 inline constexpr double __pi_over_4 = 0x1.921fb54442d18p-1; // π/4
302 inline constexpr double __2_over_pi = 0x1.45F306DC9C883p-1; // 2/π
303 inline constexpr double __pi_2 = 0x1.921fb54442d18p0; // π/2
304 } // namespace __math_double
305 
306 template <typename _Abi>
307  _GLIBCXX_SIMD_ALWAYS_INLINE _Folded<float, _Abi>
308  __fold_input(const simd<float, _Abi>& __x)
309  {
310  using _V = simd<float, _Abi>;
311  using _IV = rebind_simd_t<int, _V>;
312  using namespace __math_float;
313  _Folded<float, _Abi> __r;
314  __r._M_x = abs(__x);
315 #if 0
316  // zero most mantissa bits:
317  constexpr float __1_over_pi = 0x1.45F306p-2f; // 1/π
318  const auto __y = (__r._M_x * __1_over_pi + 0x1.8p23f) - 0x1.8p23f;
319  // split π into 4 parts, the first three with 13 trailing zeros (to make the
320  // following multiplications precise):
321  constexpr float __pi0 = 0x1.920000p1f;
322  constexpr float __pi1 = 0x1.fb4000p-11f;
323  constexpr float __pi2 = 0x1.444000p-23f;
324  constexpr float __pi3 = 0x1.68c234p-38f;
325  __r._M_x - __y*__pi0 - __y*__pi1 - __y*__pi2 - __y*__pi3
326 #else
327  if (_GLIBCXX_SIMD_IS_UNLIKELY(all_of(__r._M_x < __pi_over_4)))
328  __r._M_quadrant = 0;
329  else if (_GLIBCXX_SIMD_IS_LIKELY(all_of(__r._M_x < 6 * __pi_over_4)))
330  {
331  const _V __y = nearbyint(__r._M_x * __2_over_pi);
332  __r._M_quadrant = static_simd_cast<_IV>(__y) & 3; // __y mod 4
333  __r._M_x -= __y * __pi_2_5bits0;
334  __r._M_x -= __y * __pi_2_5bits0_rem;
335  }
336  else
337  {
338  using __math_double::__2_over_pi;
339  using __math_double::__pi_2;
340  using _VD = rebind_simd_t<double, _V>;
341  _VD __xd = static_simd_cast<_VD>(__r._M_x);
342  _VD __y = nearbyint(__xd * __2_over_pi);
343  __r._M_quadrant = static_simd_cast<_IV>(__y) & 3; // = __y mod 4
344  __r._M_x = static_simd_cast<_V>(__xd - __y * __pi_2);
345  }
346 #endif
347  return __r;
348  }
349 
350 template <typename _Abi>
351  _GLIBCXX_SIMD_ALWAYS_INLINE _Folded<double, _Abi>
352  __fold_input(const simd<double, _Abi>& __x)
353  {
354  using _V = simd<double, _Abi>;
355  using _IV = rebind_simd_t<int, _V>;
356  using namespace __math_double;
357 
358  _Folded<double, _Abi> __r;
359  __r._M_x = abs(__x);
360  if (_GLIBCXX_SIMD_IS_UNLIKELY(all_of(__r._M_x < __pi_over_4)))
361  {
362  __r._M_quadrant = 0;
363  return __r;
364  }
365  const _V __y = nearbyint(__r._M_x / (2 * __pi_over_4));
366  __r._M_quadrant = static_simd_cast<_IV>(__y) & 3;
367 
368  if (_GLIBCXX_SIMD_IS_LIKELY(all_of(__r._M_x < 1025 * __pi_over_4)))
369  {
370  // x - y * pi/2, y uses no more than 11 mantissa bits
371  __r._M_x -= __y * 0x1.921FB54443000p0;
372  __r._M_x -= __y * -0x1.73DCB3B39A000p-43;
373  __r._M_x -= __y * 0x1.45C06E0E68948p-86;
374  }
375  else if (_GLIBCXX_SIMD_IS_LIKELY(all_of(__y <= 0x1.0p30)))
376  {
377  // x - y * pi/2, y uses no more than 29 mantissa bits
378  __r._M_x -= __y * 0x1.921FB40000000p0;
379  __r._M_x -= __y * 0x1.4442D00000000p-24;
380  __r._M_x -= __y * 0x1.8469898CC5170p-48;
381  }
382  else
383  {
384  // x - y * pi/2, y may require all mantissa bits
385  const _V __y_hi = __zero_low_bits<26>(__y);
386  const _V __y_lo = __y - __y_hi;
387  const auto __pi_2_1 = 0x1.921FB50000000p0;
388  const auto __pi_2_2 = 0x1.110B460000000p-26;
389  const auto __pi_2_3 = 0x1.1A62630000000p-54;
390  const auto __pi_2_4 = 0x1.8A2E03707344Ap-81;
391  __r._M_x = __r._M_x - __y_hi * __pi_2_1
392  - max(__y_hi * __pi_2_2, __y_lo * __pi_2_1)
393  - min(__y_hi * __pi_2_2, __y_lo * __pi_2_1)
394  - max(__y_hi * __pi_2_3, __y_lo * __pi_2_2)
395  - min(__y_hi * __pi_2_3, __y_lo * __pi_2_2)
396  - max(__y * __pi_2_4, __y_lo * __pi_2_3)
397  - min(__y * __pi_2_4, __y_lo * __pi_2_3);
398  }
399  return __r;
400  }
401 
402 // }}}
403 // __extract_exponent_as_int {{{
404 template <typename _Tp, typename _Abi>
405  _GLIBCXX_SIMD_INTRINSIC
406  rebind_simd_t<int, simd<_Tp, _Abi>>
407  __extract_exponent_as_int(const simd<_Tp, _Abi>& __v)
408  {
409  using _Vp = simd<_Tp, _Abi>;
410  using _Up = make_unsigned_t<__int_for_sizeof_t<_Tp>>;
411  using namespace std::experimental::__float_bitwise_operators;
412  using namespace std::experimental::__proposed;
413  const _Vp __exponent_mask
414  = __infinity_v<_Tp>; // 0x7f800000 or 0x7ff0000000000000
415  return static_simd_cast<rebind_simd_t<int, _Vp>>(
416  simd_bit_cast<rebind_simd_t<_Up, _Vp>>(__v & __exponent_mask)
417  >> (__digits_v<_Tp> - 1));
418  }
419 
420 // }}}
421 // __impl_or_fallback {{{
422 template <typename ImplFun, typename FallbackFun, typename... _Args>
423  _GLIBCXX_SIMD_INTRINSIC auto
424  __impl_or_fallback_dispatch(int, ImplFun&& __impl_fun, FallbackFun&&,
425  _Args&&... __args)
426  -> decltype(__impl_fun(static_cast<_Args&&>(__args)...))
427  { return __impl_fun(static_cast<_Args&&>(__args)...); }
428 
429 template <typename ImplFun, typename FallbackFun, typename... _Args,
430  typename = __detail::__odr_helper>
431  inline auto
432  __impl_or_fallback_dispatch(float, ImplFun&&, FallbackFun&& __fallback_fun,
433  _Args&&... __args)
434  -> decltype(__fallback_fun(static_cast<_Args&&>(__args)...))
435  { return __fallback_fun(static_cast<_Args&&>(__args)...); }
436 
437 template <typename... _Args>
438  _GLIBCXX_SIMD_INTRINSIC auto
439  __impl_or_fallback(_Args&&... __args)
440  {
441  return __impl_or_fallback_dispatch(int(), static_cast<_Args&&>(__args)...);
442  }
443 //}}}
444 
445 // trigonometric functions {{{
446 _GLIBCXX_SIMD_MATH_CALL_(acos)
447 _GLIBCXX_SIMD_MATH_CALL_(asin)
448 _GLIBCXX_SIMD_MATH_CALL_(atan)
449 _GLIBCXX_SIMD_MATH_CALL2_(atan2, _Tp)
450 
451 /*
452  * algorithm for sine and cosine:
453  *
454  * The result can be calculated with sine or cosine depending on the π/4 section
455  * the input is in. sine ≈ __x + __x³ cosine ≈ 1 - __x²
456  *
457  * sine:
458  * Map -__x to __x and invert the output
459  * Extend precision of __x - n * π/4 by calculating
460  * ((__x - n * p1) - n * p2) - n * p3 (p1 + p2 + p3 = π/4)
461  *
462  * Calculate Taylor series with tuned coefficients.
463  * Fix sign.
464  */
465 // cos{{{
466 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
467  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
468  cos(const simd<_Tp, _Abi>& __x)
469  {
470  using _V = simd<_Tp, _Abi>;
471  if constexpr (__is_scalar_abi<_Abi>() || __is_fixed_size_abi_v<_Abi>)
472  return {__private_init, _Abi::_SimdImpl::_S_cos(__data(__x))};
473  else
474  {
475  if constexpr (is_same_v<_Tp, float>)
476  if (_GLIBCXX_SIMD_IS_UNLIKELY(any_of(abs(__x) >= 393382)))
477  return static_simd_cast<_V>(
478  cos(static_simd_cast<rebind_simd_t<double, _V>>(__x)));
479 
480  const auto __f = __fold_input(__x);
481  // quadrant | effect
482  // 0 | cosSeries, +
483  // 1 | sinSeries, -
484  // 2 | cosSeries, -
485  // 3 | sinSeries, +
486  using namespace std::experimental::__float_bitwise_operators;
487  const _V __sign_flip
488  = _V(-0.f) & static_simd_cast<_V>((1 + __f._M_quadrant) << 30);
489 
490  const auto __need_cos = (__f._M_quadrant & 1) == 0;
491  if (_GLIBCXX_SIMD_IS_UNLIKELY(all_of(__need_cos)))
492  return __sign_flip ^ __cosSeries(__f._M_x);
493  else if (_GLIBCXX_SIMD_IS_UNLIKELY(none_of(__need_cos)))
494  return __sign_flip ^ __sinSeries(__f._M_x);
495  else // some_of(__need_cos)
496  {
497  _V __r = __sinSeries(__f._M_x);
498  where(__need_cos.__cvt(), __r) = __cosSeries(__f._M_x);
499  return __r ^ __sign_flip;
500  }
501  }
502  }
503 
504 template <typename _Tp>
505  _GLIBCXX_SIMD_ALWAYS_INLINE
506  enable_if_t<is_floating_point<_Tp>::value, simd<_Tp, simd_abi::scalar>>
507  cos(simd<_Tp, simd_abi::scalar> __x)
508  { return std::cos(__data(__x)); }
509 
510 //}}}
511 // sin{{{
512 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
513  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
514  sin(const simd<_Tp, _Abi>& __x)
515  {
516  using _V = simd<_Tp, _Abi>;
517  if constexpr (__is_scalar_abi<_Abi>() || __is_fixed_size_abi_v<_Abi>)
518  return {__private_init, _Abi::_SimdImpl::_S_sin(__data(__x))};
519  else
520  {
521  if constexpr (is_same_v<_Tp, float>)
522  if (_GLIBCXX_SIMD_IS_UNLIKELY(any_of(abs(__x) >= 527449)))
523  return static_simd_cast<_V>(
524  sin(static_simd_cast<rebind_simd_t<double, _V>>(__x)));
525 
526  const auto __f = __fold_input(__x);
527  // quadrant | effect
528  // 0 | sinSeries
529  // 1 | cosSeries
530  // 2 | sinSeries, sign flip
531  // 3 | cosSeries, sign flip
532  using namespace std::experimental::__float_bitwise_operators;
533  const auto __sign_flip
534  = (__x ^ static_simd_cast<_V>(1 - __f._M_quadrant)) & _V(_Tp(-0.));
535 
536  const auto __need_sin = (__f._M_quadrant & 1) == 0;
537  if (_GLIBCXX_SIMD_IS_UNLIKELY(all_of(__need_sin)))
538  return __sign_flip ^ __sinSeries(__f._M_x);
539  else if (_GLIBCXX_SIMD_IS_UNLIKELY(none_of(__need_sin)))
540  return __sign_flip ^ __cosSeries(__f._M_x);
541  else // some_of(__need_sin)
542  {
543  _V __r = __cosSeries(__f._M_x);
544  where(__need_sin.__cvt(), __r) = __sinSeries(__f._M_x);
545  return __sign_flip ^ __r;
546  }
547  }
548  }
549 
550 template <typename _Tp>
551  _GLIBCXX_SIMD_ALWAYS_INLINE
552  enable_if_t<is_floating_point<_Tp>::value, simd<_Tp, simd_abi::scalar>>
553  sin(simd<_Tp, simd_abi::scalar> __x)
554  { return std::sin(__data(__x)); }
555 
556 //}}}
557 _GLIBCXX_SIMD_MATH_CALL_(tan)
558 _GLIBCXX_SIMD_MATH_CALL_(acosh)
559 _GLIBCXX_SIMD_MATH_CALL_(asinh)
560 _GLIBCXX_SIMD_MATH_CALL_(atanh)
561 _GLIBCXX_SIMD_MATH_CALL_(cosh)
562 _GLIBCXX_SIMD_MATH_CALL_(sinh)
563 _GLIBCXX_SIMD_MATH_CALL_(tanh)
564 // }}}
565 // exponential functions {{{
566 _GLIBCXX_SIMD_MATH_CALL_(exp)
567 _GLIBCXX_SIMD_MATH_CALL_(exp2)
568 _GLIBCXX_SIMD_MATH_CALL_(expm1)
569 
570 // }}}
571 // frexp {{{
572 #if _GLIBCXX_SIMD_X86INTRIN
573 template <typename _Tp, size_t _Np>
574  _GLIBCXX_SIMD_INTRINSIC
575  _SimdWrapper<_Tp, _Np>
576  __getexp(_SimdWrapper<_Tp, _Np> __x)
577  {
578  if constexpr (__have_avx512vl && __is_sse_ps<_Tp, _Np>())
579  return __auto_bitcast(_mm_getexp_ps(__to_intrin(__x)));
580  else if constexpr (__have_avx512f && __is_sse_ps<_Tp, _Np>())
581  return __auto_bitcast(_mm512_getexp_ps(__auto_bitcast(__to_intrin(__x))));
582  else if constexpr (__have_avx512vl && __is_sse_pd<_Tp, _Np>())
583  return _mm_getexp_pd(__x);
584  else if constexpr (__have_avx512f && __is_sse_pd<_Tp, _Np>())
585  return __lo128(_mm512_getexp_pd(__auto_bitcast(__x)));
586  else if constexpr (__have_avx512vl && __is_avx_ps<_Tp, _Np>())
587  return _mm256_getexp_ps(__x);
588  else if constexpr (__have_avx512f && __is_avx_ps<_Tp, _Np>())
589  return __lo256(_mm512_getexp_ps(__auto_bitcast(__x)));
590  else if constexpr (__have_avx512vl && __is_avx_pd<_Tp, _Np>())
591  return _mm256_getexp_pd(__x);
592  else if constexpr (__have_avx512f && __is_avx_pd<_Tp, _Np>())
593  return __lo256(_mm512_getexp_pd(__auto_bitcast(__x)));
594  else if constexpr (__is_avx512_ps<_Tp, _Np>())
595  return _mm512_getexp_ps(__x);
596  else if constexpr (__is_avx512_pd<_Tp, _Np>())
597  return _mm512_getexp_pd(__x);
598  else
599  __assert_unreachable<_Tp>();
600  }
601 
602 template <typename _Tp, size_t _Np>
603  _GLIBCXX_SIMD_INTRINSIC
604  _SimdWrapper<_Tp, _Np>
605  __getmant_avx512(_SimdWrapper<_Tp, _Np> __x)
606  {
607  if constexpr (__have_avx512vl && __is_sse_ps<_Tp, _Np>())
608  return __auto_bitcast(_mm_getmant_ps(__to_intrin(__x), _MM_MANT_NORM_p5_1,
609  _MM_MANT_SIGN_src));
610  else if constexpr (__have_avx512f && __is_sse_ps<_Tp, _Np>())
611  return __auto_bitcast(_mm512_getmant_ps(__auto_bitcast(__to_intrin(__x)),
612  _MM_MANT_NORM_p5_1,
613  _MM_MANT_SIGN_src));
614  else if constexpr (__have_avx512vl && __is_sse_pd<_Tp, _Np>())
615  return _mm_getmant_pd(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src);
616  else if constexpr (__have_avx512f && __is_sse_pd<_Tp, _Np>())
617  return __lo128(_mm512_getmant_pd(__auto_bitcast(__x), _MM_MANT_NORM_p5_1,
618  _MM_MANT_SIGN_src));
619  else if constexpr (__have_avx512vl && __is_avx_ps<_Tp, _Np>())
620  return _mm256_getmant_ps(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src);
621  else if constexpr (__have_avx512f && __is_avx_ps<_Tp, _Np>())
622  return __lo256(_mm512_getmant_ps(__auto_bitcast(__x), _MM_MANT_NORM_p5_1,
623  _MM_MANT_SIGN_src));
624  else if constexpr (__have_avx512vl && __is_avx_pd<_Tp, _Np>())
625  return _mm256_getmant_pd(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src);
626  else if constexpr (__have_avx512f && __is_avx_pd<_Tp, _Np>())
627  return __lo256(_mm512_getmant_pd(__auto_bitcast(__x), _MM_MANT_NORM_p5_1,
628  _MM_MANT_SIGN_src));
629  else if constexpr (__is_avx512_ps<_Tp, _Np>())
630  return _mm512_getmant_ps(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src);
631  else if constexpr (__is_avx512_pd<_Tp, _Np>())
632  return _mm512_getmant_pd(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src);
633  else
634  __assert_unreachable<_Tp>();
635  }
636 #endif // _GLIBCXX_SIMD_X86INTRIN
637 
638 /**
639  * splits @p __v into exponent and mantissa, the sign is kept with the mantissa
640  *
641  * The return value will be in the range [0.5, 1.0[
642  * The @p __e value will be an integer defining the power-of-two exponent
643  */
644 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
645  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
646  frexp(const simd<_Tp, _Abi>& __x, _Samesize<int, simd<_Tp, _Abi>>* __exp)
647  {
648  if constexpr (simd_size_v<_Tp, _Abi> == 1)
649  {
650  int __tmp;
651  const auto __r = std::frexp(__x[0], &__tmp);
652  (*__exp)[0] = __tmp;
653  return __r;
654  }
655  else if constexpr (__is_fixed_size_abi_v<_Abi>)
656  return {__private_init, _Abi::_SimdImpl::_S_frexp(__data(__x), __data(*__exp))};
657 #if _GLIBCXX_SIMD_X86INTRIN
658  else if constexpr (__have_avx512f)
659  {
660  constexpr size_t _Np = simd_size_v<_Tp, _Abi>;
661  constexpr size_t _NI = _Np < 4 ? 4 : _Np;
662  const auto __v = __data(__x);
663  const auto __isnonzero
664  = _Abi::_SimdImpl::_S_isnonzerovalue_mask(__v._M_data);
665  const _SimdWrapper<int, _NI> __exp_plus1
666  = 1 + __convert<_SimdWrapper<int, _NI>>(__getexp(__v))._M_data;
667  const _SimdWrapper<int, _Np> __e = __wrapper_bitcast<int, _Np>(
668  _Abi::_CommonImpl::_S_blend(_SimdWrapper<bool, _NI>(__isnonzero),
669  _SimdWrapper<int, _NI>(), __exp_plus1));
670  simd_abi::deduce_t<int, _Np>::_CommonImpl::_S_store(__e, __exp);
671  return {__private_init,
672  _Abi::_CommonImpl::_S_blend(_SimdWrapper<bool, _Np>(
673  __isnonzero),
674  __v, __getmant_avx512(__v))};
675  }
676 #endif // _GLIBCXX_SIMD_X86INTRIN
677  else
678  {
679  // fallback implementation
680  static_assert(sizeof(_Tp) == 4 || sizeof(_Tp) == 8);
681  using _V = simd<_Tp, _Abi>;
682  using _IV = rebind_simd_t<int, _V>;
683  using namespace std::experimental::__proposed;
684  using namespace std::experimental::__float_bitwise_operators;
685 
686  constexpr int __exp_adjust = sizeof(_Tp) == 4 ? 0x7e : 0x3fe;
687  constexpr int __exp_offset = sizeof(_Tp) == 4 ? 0x70 : 0x200;
688  constexpr _Tp __subnorm_scale = sizeof(_Tp) == 4 ? 0x1p112 : 0x1p512;
689  _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __exponent_mask
690  = __infinity_v<_Tp>; // 0x7f800000 or 0x7ff0000000000000
691  _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __p5_1_exponent
692  = -(2 - __epsilon_v<_Tp>) / 2; // 0xbf7fffff or 0xbfefffffffffffff
693 
694  _V __mant = __p5_1_exponent & (__exponent_mask | __x); // +/-[.5, 1)
695  const _IV __exponent_bits = __extract_exponent_as_int(__x);
696  if (_GLIBCXX_SIMD_IS_LIKELY(all_of(isnormal(__x))))
697  {
698  *__exp
699  = simd_cast<_Samesize<int, _V>>(__exponent_bits - __exp_adjust);
700  return __mant;
701  }
702 
703 #if __FINITE_MATH_ONLY__
704  // at least one element of __x is 0 or subnormal, the rest is normal
705  // (inf and NaN are excluded by -ffinite-math-only)
706  const auto __iszero_inf_nan = __x == 0;
707 #else
708  using _Ip = __int_for_sizeof_t<_Tp>;
709  const auto __as_int = simd_bit_cast<rebind_simd_t<_Ip, _V>>(abs(__x));
710  const auto __inf = simd_bit_cast<rebind_simd_t<_Ip, _V>>(_V(__infinity_v<_Tp>));
711  const auto __iszero_inf_nan = static_simd_cast<typename _V::mask_type>(
712  __as_int == 0 || __as_int >= __inf);
713 #endif
714 
715  const _V __scaled_subnormal = __x * __subnorm_scale;
716  const _V __mant_subnormal
717  = __p5_1_exponent & (__exponent_mask | __scaled_subnormal);
718  where(!isnormal(__x), __mant) = __mant_subnormal;
719  where(__iszero_inf_nan, __mant) = __x;
720  _IV __e = __extract_exponent_as_int(__scaled_subnormal);
721  using _MaskType =
722  typename conditional_t<sizeof(typename _V::value_type) == sizeof(int),
723  _V, _IV>::mask_type;
724  const _MaskType __value_isnormal = isnormal(__x).__cvt();
725  where(__value_isnormal.__cvt(), __e) = __exponent_bits;
726  static_assert(sizeof(_IV) == sizeof(__value_isnormal));
727  const _IV __offset
728  = (simd_bit_cast<_IV>(__value_isnormal) & _IV(__exp_adjust))
729  | (simd_bit_cast<_IV>(static_simd_cast<_MaskType>(__exponent_bits == 0)
730  & static_simd_cast<_MaskType>(__x != 0))
731  & _IV(__exp_adjust + __exp_offset));
732  *__exp = simd_cast<_Samesize<int, _V>>(__e - __offset);
733  return __mant;
734  }
735  }
736 
737 // }}}
738 _GLIBCXX_SIMD_MATH_CALL2_(ldexp, int)
739 _GLIBCXX_SIMD_MATH_CALL_(ilogb)
740 
741 // logarithms {{{
742 _GLIBCXX_SIMD_MATH_CALL_(log)
743 _GLIBCXX_SIMD_MATH_CALL_(log10)
744 _GLIBCXX_SIMD_MATH_CALL_(log1p)
745 _GLIBCXX_SIMD_MATH_CALL_(log2)
746 
747 //}}}
748 // logb{{{
749 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
750  enable_if_t<is_floating_point<_Tp>::value, simd<_Tp, _Abi>>
751  logb(const simd<_Tp, _Abi>& __x)
752  {
753  constexpr size_t _Np = simd_size_v<_Tp, _Abi>;
754  if constexpr (_Np == 1)
755  return std::logb(__x[0]);
756  else if constexpr (__is_fixed_size_abi_v<_Abi>)
757  return {__private_init, _Abi::_SimdImpl::_S_logb(__data(__x))};
758 #if _GLIBCXX_SIMD_X86INTRIN // {{{
759  else if constexpr (__have_avx512vl && __is_sse_ps<_Tp, _Np>())
760  return {__private_init,
761  __auto_bitcast(_mm_getexp_ps(__to_intrin(__as_vector(__x))))};
762  else if constexpr (__have_avx512vl && __is_sse_pd<_Tp, _Np>())
763  return {__private_init, _mm_getexp_pd(__data(__x))};
764  else if constexpr (__have_avx512vl && __is_avx_ps<_Tp, _Np>())
765  return {__private_init, _mm256_getexp_ps(__data(__x))};
766  else if constexpr (__have_avx512vl && __is_avx_pd<_Tp, _Np>())
767  return {__private_init, _mm256_getexp_pd(__data(__x))};
768  else if constexpr (__have_avx512f && __is_avx_ps<_Tp, _Np>())
769  return {__private_init,
770  __lo256(_mm512_getexp_ps(__auto_bitcast(__data(__x))))};
771  else if constexpr (__have_avx512f && __is_avx_pd<_Tp, _Np>())
772  return {__private_init,
773  __lo256(_mm512_getexp_pd(__auto_bitcast(__data(__x))))};
774  else if constexpr (__is_avx512_ps<_Tp, _Np>())
775  return {__private_init, _mm512_getexp_ps(__data(__x))};
776  else if constexpr (__is_avx512_pd<_Tp, _Np>())
777  return {__private_init, _mm512_getexp_pd(__data(__x))};
778 #endif // _GLIBCXX_SIMD_X86INTRIN }}}
779  else
780  {
781  using _V = simd<_Tp, _Abi>;
782  using namespace std::experimental::__proposed;
783  auto __is_normal = isnormal(__x);
784 
785  // work on abs(__x) to reflect the return value on Linux for negative
786  // inputs (domain-error => implementation-defined value is returned)
787  const _V abs_x = abs(__x);
788 
789  // __exponent(__x) returns the exponent value (bias removed) as
790  // simd<_Up> with integral _Up
791  auto&& __exponent = [](const _V& __v) {
792  using namespace std::experimental::__proposed;
793  using _IV = rebind_simd_t<
794  conditional_t<sizeof(_Tp) == sizeof(_LLong), _LLong, int>, _V>;
795  return (simd_bit_cast<_IV>(__v) >> (__digits_v<_Tp> - 1))
796  - (__max_exponent_v<_Tp> - 1);
797  };
798  _V __r = static_simd_cast<_V>(__exponent(abs_x));
799  if (_GLIBCXX_SIMD_IS_LIKELY(all_of(__is_normal)))
800  // without corner cases (nan, inf, subnormal, zero) we have our
801  // answer:
802  return __r;
803  const auto __is_zero = __x == 0;
804  const auto __is_nan = isnan(__x);
805  const auto __is_inf = isinf(__x);
806  where(__is_zero, __r) = -__infinity_v<_Tp>;
807  where(__is_nan, __r) = __x;
808  where(__is_inf, __r) = __infinity_v<_Tp>;
809  __is_normal |= __is_zero || __is_nan || __is_inf;
810  if (all_of(__is_normal))
811  // at this point everything but subnormals is handled
812  return __r;
813  // subnormals repeat the exponent extraction after multiplication of the
814  // input with __a floating point value that has 112 (0x70) in its exponent
815  // (not too big for sp and large enough for dp)
816  const _V __scaled = abs_x * _Tp(0x1p112);
817  _V __scaled_exp = static_simd_cast<_V>(__exponent(__scaled) - 112);
818  where(__is_normal, __scaled_exp) = __r;
819  return __scaled_exp;
820  }
821  }
822 
823 //}}}
824 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
825  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
826  modf(const simd<_Tp, _Abi>& __x, simd<_Tp, _Abi>* __iptr)
827  {
828  if constexpr (simd_size_v<_Tp, _Abi> == 1)
829  {
830  _Tp __tmp;
831  _Tp __r = std::modf(__x[0], &__tmp);
832  __iptr[0] = __tmp;
833  return __r;
834  }
835  else
836  {
837  const auto __integral = trunc(__x);
838  *__iptr = __integral;
839  auto __r = __x - __integral;
840 #if !__FINITE_MATH_ONLY__
841  where(isinf(__x), __r) = _Tp();
842 #endif
843  return copysign(__r, __x);
844  }
845  }
846 
847 _GLIBCXX_SIMD_MATH_CALL2_(scalbn, int)
848 _GLIBCXX_SIMD_MATH_CALL2_(scalbln, long)
849 
850 _GLIBCXX_SIMD_MATH_CALL_(cbrt)
851 
852 _GLIBCXX_SIMD_MATH_CALL_(abs)
853 _GLIBCXX_SIMD_MATH_CALL_(fabs)
854 
855 // [parallel.simd.math] only asks for is_floating_point_v<_Tp> and forgot to
856 // allow signed integral _Tp
857 template <typename _Tp, typename _Abi>
858  _GLIBCXX_SIMD_ALWAYS_INLINE
859  enable_if_t<!is_floating_point_v<_Tp> && is_signed_v<_Tp>, simd<_Tp, _Abi>>
860  abs(const simd<_Tp, _Abi>& __x)
861  { return {__private_init, _Abi::_SimdImpl::_S_abs(__data(__x))}; }
862 
863 #define _GLIBCXX_SIMD_CVTING2(_NAME) \
864 template <typename _Tp, typename _Abi> \
865  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \
866  const simd<_Tp, _Abi>& __x, const __type_identity_t<simd<_Tp, _Abi>>& __y) \
867  { \
868  return _NAME(__x, __y); \
869  } \
870  \
871 template <typename _Tp, typename _Abi> \
872  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \
873  const __type_identity_t<simd<_Tp, _Abi>>& __x, const simd<_Tp, _Abi>& __y) \
874  { \
875  return _NAME(__x, __y); \
876  }
877 
878 #define _GLIBCXX_SIMD_CVTING3(_NAME) \
879 template <typename _Tp, typename _Abi> \
880  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \
881  const __type_identity_t<simd<_Tp, _Abi>>& __x, const simd<_Tp, _Abi>& __y, \
882  const simd<_Tp, _Abi>& __z) \
883  { \
884  return _NAME(__x, __y, __z); \
885  } \
886  \
887 template <typename _Tp, typename _Abi> \
888  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \
889  const simd<_Tp, _Abi>& __x, const __type_identity_t<simd<_Tp, _Abi>>& __y, \
890  const simd<_Tp, _Abi>& __z) \
891  { \
892  return _NAME(__x, __y, __z); \
893  } \
894  \
895 template <typename _Tp, typename _Abi> \
896  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \
897  const simd<_Tp, _Abi>& __x, const simd<_Tp, _Abi>& __y, \
898  const __type_identity_t<simd<_Tp, _Abi>>& __z) \
899  { \
900  return _NAME(__x, __y, __z); \
901  } \
902  \
903 template <typename _Tp, typename _Abi> \
904  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \
905  const simd<_Tp, _Abi>& __x, const __type_identity_t<simd<_Tp, _Abi>>& __y, \
906  const __type_identity_t<simd<_Tp, _Abi>>& __z) \
907  { \
908  return _NAME(__x, __y, __z); \
909  } \
910  \
911 template <typename _Tp, typename _Abi> \
912  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \
913  const __type_identity_t<simd<_Tp, _Abi>>& __x, const simd<_Tp, _Abi>& __y, \
914  const __type_identity_t<simd<_Tp, _Abi>>& __z) \
915  { \
916  return _NAME(__x, __y, __z); \
917  } \
918  \
919 template <typename _Tp, typename _Abi> \
920  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \
921  const __type_identity_t<simd<_Tp, _Abi>>& __x, \
922  const __type_identity_t<simd<_Tp, _Abi>>& __y, const simd<_Tp, _Abi>& __z) \
923  { \
924  return _NAME(__x, __y, __z); \
925  }
926 
927 template <typename _R, typename _ToApply, typename _Tp, typename... _Tps>
928  _GLIBCXX_SIMD_INTRINSIC _R
929  __fixed_size_apply(_ToApply&& __apply, const _Tp& __arg0,
930  const _Tps&... __args)
931  {
932  return {__private_init,
933  __data(__arg0)._M_apply_per_chunk(
934  [&](auto __impl, const auto&... __inner) {
935  using _V = typename decltype(__impl)::simd_type;
936  return __data(__apply(_V(__private_init, __inner)...));
937  },
938  __data(__args)...)};
939  }
940 
941 template <typename _VV, typename = __detail::__odr_helper>
942  __remove_cvref_t<_VV>
943  __hypot(_VV __x, _VV __y)
944  {
945  using _V = __remove_cvref_t<_VV>;
946  using _Tp = typename _V::value_type;
947  if constexpr (_V::size() == 1)
948  return std::hypot(_Tp(__x[0]), _Tp(__y[0]));
949  else if constexpr (__is_fixed_size_abi_v<typename _V::abi_type>)
950  {
951  return __fixed_size_apply<_V>([](auto __a,
952  auto __b) { return hypot(__a, __b); },
953  __x, __y);
954  }
955  else
956  {
957  // A simple solution for _Tp == float would be to cast to double and
958  // simply calculate sqrt(x²+y²) as it can't over-/underflow anymore with
959  // dp. It still needs the Annex F fixups though and isn't faster on
960  // Skylake-AVX512 (not even for SSE and AVX vectors, and really bad for
961  // AVX-512).
962  using namespace __float_bitwise_operators;
963  using namespace __proposed;
964  _V __absx = abs(__x); // no error
965  _V __absy = abs(__y); // no error
966  _V __hi = max(__absx, __absy); // no error
967  _V __lo = min(__absy, __absx); // no error
968 
969  // round __hi down to the next power-of-2:
970  _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __inf(__infinity_v<_Tp>);
971 
972 #ifndef __FAST_MATH__
973  if constexpr (__have_neon && !__have_neon_a32)
974  { // With ARMv7 NEON, we have no subnormals and must use slightly
975  // different strategy
976  const _V __hi_exp = __hi & __inf;
977  _V __scale_back = __hi_exp;
978  // For large exponents (max & max/2) the inversion comes too close
979  // to subnormals. Subtract 3 from the exponent:
980  where(__hi_exp > 1, __scale_back) = __hi_exp * _Tp(0.125);
981  // Invert and adjust for the off-by-one error of inversion via xor:
982  const _V __scale = (__scale_back ^ __inf) * _Tp(.5);
983  const _V __h1 = __hi * __scale;
984  const _V __l1 = __lo * __scale;
985  _V __r = __scale_back * sqrt(__h1 * __h1 + __l1 * __l1);
986  // Fix up hypot(0, 0) to not be NaN:
987  where(__hi == 0, __r) = 0;
988  return __r;
989  }
990 #endif
991 
992 #ifdef __FAST_MATH__
993  // With fast-math, ignore precision of subnormals and inputs from
994  // __finite_max_v/2 to __finite_max_v. This removes all
995  // branching/masking.
996  if constexpr (true)
997 #else
998  if (_GLIBCXX_SIMD_IS_LIKELY(all_of(isnormal(__x))
999  && all_of(isnormal(__y))))
1000 #endif
1001  {
1002  const _V __hi_exp = __hi & __inf;
1003  //((__hi + __hi) & __inf) ^ __inf almost works for computing
1004  //__scale,
1005  // except when (__hi + __hi) & __inf == __inf, in which case __scale
1006  // becomes 0 (should be min/2 instead) and thus loses the
1007  // information from __lo.
1008 #ifdef __FAST_MATH__
1009  using _Ip = __int_for_sizeof_t<_Tp>;
1010  using _IV = rebind_simd_t<_Ip, _V>;
1011  const auto __as_int = simd_bit_cast<_IV>(__hi_exp);
1012  const _V __scale
1013  = simd_bit_cast<_V>(2 * simd_bit_cast<_Ip>(_Tp(1)) - __as_int);
1014 #else
1015  const _V __scale = (__hi_exp ^ __inf) * _Tp(.5);
1016 #endif
1017  _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __mant_mask
1018  = __norm_min_v<_Tp> - __denorm_min_v<_Tp>;
1019  const _V __h1 = (__hi & __mant_mask) | _V(1);
1020  const _V __l1 = __lo * __scale;
1021  return __hi_exp * sqrt(__h1 * __h1 + __l1 * __l1);
1022  }
1023  else
1024  {
1025  // slower path to support subnormals
1026  // if __hi is subnormal, avoid scaling by inf & final mul by 0
1027  // (which yields NaN) by using min()
1028  _V __scale = _V(1 / __norm_min_v<_Tp>);
1029  // invert exponent w/o error and w/o using the slow divider unit:
1030  // xor inverts the exponent but off by 1. Multiplication with .5
1031  // adjusts for the discrepancy.
1032  where(__hi >= __norm_min_v<_Tp>, __scale)
1033  = ((__hi & __inf) ^ __inf) * _Tp(.5);
1034  // adjust final exponent for subnormal inputs
1035  _V __hi_exp = __norm_min_v<_Tp>;
1036  where(__hi >= __norm_min_v<_Tp>, __hi_exp)
1037  = __hi & __inf; // no error
1038  _V __h1 = __hi * __scale; // no error
1039  _V __l1 = __lo * __scale; // no error
1040 
1041  // sqrt(x²+y²) = e*sqrt((x/e)²+(y/e)²):
1042  // this ensures no overflow in the argument to sqrt
1043  _V __r = __hi_exp * sqrt(__h1 * __h1 + __l1 * __l1);
1044 #ifdef __STDC_IEC_559__
1045  // fixup for Annex F requirements
1046  // the naive fixup goes like this:
1047  //
1048  // where(__l1 == 0, __r) = __hi;
1049  // where(isunordered(__x, __y), __r) = __quiet_NaN_v<_Tp>;
1050  // where(isinf(__absx) || isinf(__absy), __r) = __inf;
1051  //
1052  // The fixup can be prepared in parallel with the sqrt, requiring a
1053  // single blend step after hi_exp * sqrt, reducing latency and
1054  // throughput:
1055  _V __fixup = __hi; // __lo == 0
1056  where(isunordered(__x, __y), __fixup) = __quiet_NaN_v<_Tp>;
1057  where(isinf(__absx) || isinf(__absy), __fixup) = __inf;
1058  where(!(__lo == 0 || isunordered(__x, __y)
1059  || (isinf(__absx) || isinf(__absy))),
1060  __fixup)
1061  = __r;
1062  __r = __fixup;
1063 #endif
1064  return __r;
1065  }
1066  }
1067  }
1068 
1069 template <typename _Tp, typename _Abi>
1070  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi>
1071  hypot(const simd<_Tp, _Abi>& __x, const simd<_Tp, _Abi>& __y)
1072  {
1073  return __hypot<conditional_t<__is_fixed_size_abi_v<_Abi>,
1074  const simd<_Tp, _Abi>&, simd<_Tp, _Abi>>>(__x,
1075  __y);
1076  }
1077 
1078 _GLIBCXX_SIMD_CVTING2(hypot)
1079 
1080  template <typename _VV, typename = __detail::__odr_helper>
1081  __remove_cvref_t<_VV>
1082  __hypot(_VV __x, _VV __y, _VV __z)
1083  {
1084  using _V = __remove_cvref_t<_VV>;
1085  using _Abi = typename _V::abi_type;
1086  using _Tp = typename _V::value_type;
1087  /* FIXME: enable after PR77776 is resolved
1088  if constexpr (_V::size() == 1)
1089  return std::hypot(_Tp(__x[0]), _Tp(__y[0]), _Tp(__z[0]));
1090  else
1091  */
1092  if constexpr (__is_fixed_size_abi_v<_Abi> && _V::size() > 1)
1093  {
1094  return __fixed_size_apply<simd<_Tp, _Abi>>(
1095  [](auto __a, auto __b, auto __c) { return hypot(__a, __b, __c); },
1096  __x, __y, __z);
1097  }
1098  else
1099  {
1100  using namespace __float_bitwise_operators;
1101  using namespace __proposed;
1102  const _V __absx = abs(__x); // no error
1103  const _V __absy = abs(__y); // no error
1104  const _V __absz = abs(__z); // no error
1105  _V __hi = max(max(__absx, __absy), __absz); // no error
1106  _V __l0 = min(__absz, max(__absx, __absy)); // no error
1107  _V __l1 = min(__absy, __absx); // no error
1108  if constexpr (__digits_v<_Tp> == 64 && __max_exponent_v<_Tp> == 0x4000
1109  && __min_exponent_v<_Tp> == -0x3FFD && _V::size() == 1)
1110  { // Seems like x87 fp80, where bit 63 is always 1 unless subnormal or
1111  // NaN. In this case the bit-tricks don't work, they require IEC559
1112  // binary32 or binary64 format.
1113 #ifdef __STDC_IEC_559__
1114  // fixup for Annex F requirements
1115  if (isinf(__absx[0]) || isinf(__absy[0]) || isinf(__absz[0]))
1116  return __infinity_v<_Tp>;
1117  else if (isunordered(__absx[0], __absy[0] + __absz[0]))
1118  return __quiet_NaN_v<_Tp>;
1119  else if (__l0[0] == 0 && __l1[0] == 0)
1120  return __hi;
1121 #endif
1122  _V __hi_exp = __hi;
1123  const _ULLong __tmp = 0x8000'0000'0000'0000ull;
1124  __builtin_memcpy(&__data(__hi_exp), &__tmp, 8);
1125  const _V __scale = 1 / __hi_exp;
1126  __hi *= __scale;
1127  __l0 *= __scale;
1128  __l1 *= __scale;
1129  return __hi_exp * sqrt((__l0 * __l0 + __l1 * __l1) + __hi * __hi);
1130  }
1131  else
1132  {
1133  // round __hi down to the next power-of-2:
1134  _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __inf(__infinity_v<_Tp>);
1135 
1136 #ifndef __FAST_MATH__
1137  if constexpr (_V::size() > 1 && __have_neon && !__have_neon_a32)
1138  { // With ARMv7 NEON, we have no subnormals and must use slightly
1139  // different strategy
1140  const _V __hi_exp = __hi & __inf;
1141  _V __scale_back = __hi_exp;
1142  // For large exponents (max & max/2) the inversion comes too
1143  // close to subnormals. Subtract 3 from the exponent:
1144  where(__hi_exp > 1, __scale_back) = __hi_exp * _Tp(0.125);
1145  // Invert and adjust for the off-by-one error of inversion via
1146  // xor:
1147  const _V __scale = (__scale_back ^ __inf) * _Tp(.5);
1148  const _V __h1 = __hi * __scale;
1149  __l0 *= __scale;
1150  __l1 *= __scale;
1151  _V __lo = __l0 * __l0
1152  + __l1 * __l1; // add the two smaller values first
1153  asm("" : "+m"(__lo));
1154  _V __r = __scale_back * sqrt(__h1 * __h1 + __lo);
1155  // Fix up hypot(0, 0, 0) to not be NaN:
1156  where(__hi == 0, __r) = 0;
1157  return __r;
1158  }
1159 #endif
1160 
1161 #ifdef __FAST_MATH__
1162  // With fast-math, ignore precision of subnormals and inputs from
1163  // __finite_max_v/2 to __finite_max_v. This removes all
1164  // branching/masking.
1165  if constexpr (true)
1166 #else
1167  if (_GLIBCXX_SIMD_IS_LIKELY(all_of(isnormal(__x))
1168  && all_of(isnormal(__y))
1169  && all_of(isnormal(__z))))
1170 #endif
1171  {
1172  const _V __hi_exp = __hi & __inf;
1173  //((__hi + __hi) & __inf) ^ __inf almost works for computing
1174  //__scale, except when (__hi + __hi) & __inf == __inf, in which
1175  // case __scale
1176  // becomes 0 (should be min/2 instead) and thus loses the
1177  // information from __lo.
1178 #ifdef __FAST_MATH__
1179  using _Ip = __int_for_sizeof_t<_Tp>;
1180  using _IV = rebind_simd_t<_Ip, _V>;
1181  const auto __as_int = simd_bit_cast<_IV>(__hi_exp);
1182  const _V __scale
1183  = simd_bit_cast<_V>(2 * simd_bit_cast<_Ip>(_Tp(1)) - __as_int);
1184 #else
1185  const _V __scale = (__hi_exp ^ __inf) * _Tp(.5);
1186 #endif
1187  constexpr _Tp __mant_mask
1188  = __norm_min_v<_Tp> - __denorm_min_v<_Tp>;
1189  const _V __h1 = (__hi & _V(__mant_mask)) | _V(1);
1190  __l0 *= __scale;
1191  __l1 *= __scale;
1192  const _V __lo
1193  = __l0 * __l0
1194  + __l1 * __l1; // add the two smaller values first
1195  return __hi_exp * sqrt(__lo + __h1 * __h1);
1196  }
1197  else
1198  {
1199  // slower path to support subnormals
1200  // if __hi is subnormal, avoid scaling by inf & final mul by 0
1201  // (which yields NaN) by using min()
1202  _V __scale = _V(1 / __norm_min_v<_Tp>);
1203  // invert exponent w/o error and w/o using the slow divider
1204  // unit: xor inverts the exponent but off by 1. Multiplication
1205  // with .5 adjusts for the discrepancy.
1206  where(__hi >= __norm_min_v<_Tp>, __scale)
1207  = ((__hi & __inf) ^ __inf) * _Tp(.5);
1208  // adjust final exponent for subnormal inputs
1209  _V __hi_exp = __norm_min_v<_Tp>;
1210  where(__hi >= __norm_min_v<_Tp>, __hi_exp)
1211  = __hi & __inf; // no error
1212  _V __h1 = __hi * __scale; // no error
1213  __l0 *= __scale; // no error
1214  __l1 *= __scale; // no error
1215  _V __lo = __l0 * __l0
1216  + __l1 * __l1; // add the two smaller values first
1217  _V __r = __hi_exp * sqrt(__lo + __h1 * __h1);
1218 #ifdef __STDC_IEC_559__
1219  // fixup for Annex F requirements
1220  _V __fixup = __hi; // __lo == 0
1221  // where(__lo == 0, __fixup) = __hi;
1222  where(isunordered(__x, __y + __z), __fixup)
1223  = __quiet_NaN_v<_Tp>;
1224  where(isinf(__absx) || isinf(__absy) || isinf(__absz), __fixup)
1225  = __inf;
1226  // Instead of __lo == 0, the following could depend on __h1² ==
1227  // __h1² + __lo (i.e. __hi is so much larger than the other two
1228  // inputs that the result is exactly __hi). While this may
1229  // improve precision, it is likely to reduce efficiency if the
1230  // ISA has FMAs (because __h1² + __lo is an FMA, but the
1231  // intermediate
1232  // __h1² must be kept)
1233  where(!(__lo == 0 || isunordered(__x, __y + __z)
1234  || isinf(__absx) || isinf(__absy) || isinf(__absz)),
1235  __fixup)
1236  = __r;
1237  __r = __fixup;
1238 #endif
1239  return __r;
1240  }
1241  }
1242  }
1243  }
1244 
1245  template <typename _Tp, typename _Abi>
1246  _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi>
1247  hypot(const simd<_Tp, _Abi>& __x, const simd<_Tp, _Abi>& __y,
1248  const simd<_Tp, _Abi>& __z)
1249  {
1250  return __hypot<conditional_t<__is_fixed_size_abi_v<_Abi>,
1251  const simd<_Tp, _Abi>&, simd<_Tp, _Abi>>>(__x,
1252  __y,
1253  __z);
1254  }
1255 
1256 _GLIBCXX_SIMD_CVTING3(hypot)
1257 
1258 _GLIBCXX_SIMD_MATH_CALL2_(pow, _Tp)
1259 
1260 _GLIBCXX_SIMD_MATH_CALL_(sqrt)
1261 _GLIBCXX_SIMD_MATH_CALL_(erf)
1262 _GLIBCXX_SIMD_MATH_CALL_(erfc)
1263 _GLIBCXX_SIMD_MATH_CALL_(lgamma)
1264 _GLIBCXX_SIMD_MATH_CALL_(tgamma)
1265 _GLIBCXX_SIMD_MATH_CALL_(ceil)
1266 _GLIBCXX_SIMD_MATH_CALL_(floor)
1267 _GLIBCXX_SIMD_MATH_CALL_(nearbyint)
1268 _GLIBCXX_SIMD_MATH_CALL_(rint)
1269 _GLIBCXX_SIMD_MATH_CALL_(lrint)
1270 _GLIBCXX_SIMD_MATH_CALL_(llrint)
1271 
1272 _GLIBCXX_SIMD_MATH_CALL_(round)
1273 _GLIBCXX_SIMD_MATH_CALL_(lround)
1274 _GLIBCXX_SIMD_MATH_CALL_(llround)
1275 
1276 _GLIBCXX_SIMD_MATH_CALL_(trunc)
1277 
1278 _GLIBCXX_SIMD_MATH_CALL2_(fmod, _Tp)
1279 _GLIBCXX_SIMD_MATH_CALL2_(remainder, _Tp)
1280 _GLIBCXX_SIMD_MATH_CALL3_(remquo, _Tp, int*)
1281 
1282 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1283  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1284  copysign(const simd<_Tp, _Abi>& __x, const simd<_Tp, _Abi>& __y)
1285  {
1286  if constexpr (simd_size_v<_Tp, _Abi> == 1)
1287  return std::copysign(__x[0], __y[0]);
1288  else if constexpr (__is_fixed_size_abi_v<_Abi>)
1289  return {__private_init, _Abi::_SimdImpl::_S_copysign(__data(__x), __data(__y))};
1290  else
1291  {
1292  using _V = simd<_Tp, _Abi>;
1293  using namespace std::experimental::__float_bitwise_operators;
1294  _GLIBCXX_SIMD_USE_CONSTEXPR_API auto __signmask = _V(1) ^ _V(-1);
1295  return (__x & ~__signmask) | (__y & __signmask);
1296  }
1297  }
1298 
1299 _GLIBCXX_SIMD_MATH_CALL2_(nextafter, _Tp)
1300 // not covered in [parallel.simd.math]:
1301 // _GLIBCXX_SIMD_MATH_CALL2_(nexttoward, long double)
1302 _GLIBCXX_SIMD_MATH_CALL2_(fdim, _Tp)
1303 _GLIBCXX_SIMD_MATH_CALL2_(fmax, _Tp)
1304 _GLIBCXX_SIMD_MATH_CALL2_(fmin, _Tp)
1305 
1306 _GLIBCXX_SIMD_MATH_CALL3_(fma, _Tp, _Tp)
1307 _GLIBCXX_SIMD_MATH_CALL_(fpclassify)
1308 _GLIBCXX_SIMD_MATH_CALL_(isfinite)
1309 
1310 // isnan and isinf require special treatment because old glibc may declare
1311 // `int isinf(double)`.
1312 template <typename _Tp, typename _Abi, typename...,
1313  typename _R = _Math_return_type_t<bool, _Tp, _Abi>>
1314  _GLIBCXX_SIMD_ALWAYS_INLINE
1315  enable_if_t<is_floating_point_v<_Tp>, _R>
1316  isinf(simd<_Tp, _Abi> __x)
1317  { return {__private_init, _Abi::_SimdImpl::_S_isinf(__data(__x))}; }
1318 
1319 template <typename _Tp, typename _Abi, typename...,
1320  typename _R = _Math_return_type_t<bool, _Tp, _Abi>>
1321  _GLIBCXX_SIMD_ALWAYS_INLINE
1322  enable_if_t<is_floating_point_v<_Tp>, _R>
1323  isnan(simd<_Tp, _Abi> __x)
1324  { return {__private_init, _Abi::_SimdImpl::_S_isnan(__data(__x))}; }
1325 
1326 _GLIBCXX_SIMD_MATH_CALL_(isnormal)
1327 
1328 template <typename..., typename _Tp, typename _Abi>
1329  _GLIBCXX_SIMD_ALWAYS_INLINE
1330  simd_mask<_Tp, _Abi>
1331  signbit(simd<_Tp, _Abi> __x)
1332  {
1333  if constexpr (is_integral_v<_Tp>)
1334  {
1335  if constexpr (is_unsigned_v<_Tp>)
1336  return simd_mask<_Tp, _Abi>{}; // false
1337  else
1338  return __x < 0;
1339  }
1340  else
1341  return {__private_init, _Abi::_SimdImpl::_S_signbit(__data(__x))};
1342  }
1343 
1344 _GLIBCXX_SIMD_MATH_CALL2_(isgreater, _Tp)
1345 _GLIBCXX_SIMD_MATH_CALL2_(isgreaterequal, _Tp)
1346 _GLIBCXX_SIMD_MATH_CALL2_(isless, _Tp)
1347 _GLIBCXX_SIMD_MATH_CALL2_(islessequal, _Tp)
1348 _GLIBCXX_SIMD_MATH_CALL2_(islessgreater, _Tp)
1349 _GLIBCXX_SIMD_MATH_CALL2_(isunordered, _Tp)
1350 
1351 /* not covered in [parallel.simd.math]
1352 template <typename _Abi> __doublev<_Abi> nan(const char* tagp);
1353 template <typename _Abi> __floatv<_Abi> nanf(const char* tagp);
1354 template <typename _Abi> __ldoublev<_Abi> nanl(const char* tagp);
1355 
1356 template <typename _V> struct simd_div_t {
1357  _V quot, rem;
1358 };
1359 
1360 template <typename _Abi>
1361 simd_div_t<_SCharv<_Abi>> div(_SCharv<_Abi> numer,
1362  _SCharv<_Abi> denom);
1363 template <typename _Abi>
1364 simd_div_t<__shortv<_Abi>> div(__shortv<_Abi> numer,
1365  __shortv<_Abi> denom);
1366 template <typename _Abi>
1367 simd_div_t<__intv<_Abi>> div(__intv<_Abi> numer, __intv<_Abi> denom);
1368 template <typename _Abi>
1369 simd_div_t<__longv<_Abi>> div(__longv<_Abi> numer,
1370  __longv<_Abi> denom);
1371 template <typename _Abi>
1372 simd_div_t<__llongv<_Abi>> div(__llongv<_Abi> numer,
1373  __llongv<_Abi> denom);
1374 */
1375 
1376 // special math {{{
1377 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1378  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1379  assoc_laguerre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n,
1380  const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __m,
1381  const simd<_Tp, _Abi>& __x)
1382  {
1383  return simd<_Tp, _Abi>([&](auto __i) {
1384  return std::assoc_laguerre(__n[__i], __m[__i], __x[__i]);
1385  });
1386  }
1387 
1388 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1389  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1390  assoc_legendre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n,
1391  const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __m,
1392  const simd<_Tp, _Abi>& __x)
1393  {
1394  return simd<_Tp, _Abi>([&](auto __i) {
1395  return std::assoc_legendre(__n[__i], __m[__i], __x[__i]);
1396  });
1397  }
1398 
1399 _GLIBCXX_SIMD_MATH_CALL2_(beta, _Tp)
1400 _GLIBCXX_SIMD_MATH_CALL_(comp_ellint_1)
1401 _GLIBCXX_SIMD_MATH_CALL_(comp_ellint_2)
1402 _GLIBCXX_SIMD_MATH_CALL2_(comp_ellint_3, _Tp)
1403 _GLIBCXX_SIMD_MATH_CALL2_(cyl_bessel_i, _Tp)
1404 _GLIBCXX_SIMD_MATH_CALL2_(cyl_bessel_j, _Tp)
1405 _GLIBCXX_SIMD_MATH_CALL2_(cyl_bessel_k, _Tp)
1406 _GLIBCXX_SIMD_MATH_CALL2_(cyl_neumann, _Tp)
1407 _GLIBCXX_SIMD_MATH_CALL2_(ellint_1, _Tp)
1408 _GLIBCXX_SIMD_MATH_CALL2_(ellint_2, _Tp)
1409 _GLIBCXX_SIMD_MATH_CALL3_(ellint_3, _Tp, _Tp)
1410 _GLIBCXX_SIMD_MATH_CALL_(expint)
1411 
1412 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1413  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1414  hermite(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n,
1415  const simd<_Tp, _Abi>& __x)
1416  {
1417  return simd<_Tp, _Abi>(
1418  [&](auto __i) { return std::hermite(__n[__i], __x[__i]); });
1419  }
1420 
1421 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1422  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1423  laguerre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n,
1424  const simd<_Tp, _Abi>& __x)
1425  {
1426  return simd<_Tp, _Abi>(
1427  [&](auto __i) { return std::laguerre(__n[__i], __x[__i]); });
1428  }
1429 
1430 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1431  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1432  legendre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n,
1433  const simd<_Tp, _Abi>& __x)
1434  {
1435  return simd<_Tp, _Abi>(
1436  [&](auto __i) { return std::legendre(__n[__i], __x[__i]); });
1437  }
1438 
1439 _GLIBCXX_SIMD_MATH_CALL_(riemann_zeta)
1440 
1441 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1442  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1443  sph_bessel(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n,
1444  const simd<_Tp, _Abi>& __x)
1445  {
1446  return simd<_Tp, _Abi>(
1447  [&](auto __i) { return std::sph_bessel(__n[__i], __x[__i]); });
1448  }
1449 
1450 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1451  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1452  sph_legendre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __l,
1453  const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __m,
1454  const simd<_Tp, _Abi>& theta)
1455  {
1456  return simd<_Tp, _Abi>([&](auto __i) {
1457  return std::assoc_legendre(__l[__i], __m[__i], theta[__i]);
1458  });
1459  }
1460 
1461 template <typename _Tp, typename _Abi, typename = __detail::__odr_helper>
1462  enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>>
1463  sph_neumann(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n,
1464  const simd<_Tp, _Abi>& __x)
1465  {
1466  return simd<_Tp, _Abi>(
1467  [&](auto __i) { return std::sph_neumann(__n[__i], __x[__i]); });
1468  }
1469 // }}}
1470 
1471 #undef _GLIBCXX_SIMD_CVTING2
1472 #undef _GLIBCXX_SIMD_CVTING3
1473 #undef _GLIBCXX_SIMD_MATH_CALL_
1474 #undef _GLIBCXX_SIMD_MATH_CALL2_
1475 #undef _GLIBCXX_SIMD_MATH_CALL3_
1476 
1477 _GLIBCXX_SIMD_END_NAMESPACE
1478 
1479 #endif // __cplusplus >= 201703L
1480 #endif // _GLIBCXX_EXPERIMENTAL_SIMD_MATH_H_
1481 
1482 // vim: foldmethod=marker sw=2 ts=8 noet sts=2
std::log10
complex< _Tp > log10(const complex< _Tp > &)
Return complex base 10 logarithm of z.
Definition: complex:829
std::sin
complex< _Tp > sin(const complex< _Tp > &)
Return complex sine of z.
Definition: complex:859
std::log
complex< _Tp > log(const complex< _Tp > &)
Return complex natural logarithm of z.
Definition: complex:824
std::tan
complex< _Tp > tan(const complex< _Tp > &)
Return complex tangent of z.
Definition: complex:960
std::abs
_Tp abs(const complex< _Tp > &)
Return magnitude of z.
Definition: complex:630
std::exp
complex< _Tp > exp(const complex< _Tp > &)
Return complex base e exponential of z.
Definition: complex:797
std::cosh
complex< _Tp > cosh(const complex< _Tp > &)
Return complex hyperbolic cosine of z.
Definition: complex:771
std::tanh
complex< _Tp > tanh(const complex< _Tp > &)
Return complex hyperbolic tangent of z.
Definition: complex:988
std::pow
complex< _Tp > pow(const complex< _Tp > &, int)
Return x to the y'th power.
Definition: complex:1019
std::sinh
complex< _Tp > sinh(const complex< _Tp > &)
Return complex hyperbolic sine of z.
Definition: complex:889
std::cos
complex< _Tp > cos(const complex< _Tp > &)
Return complex cosine of z.
Definition: complex:741
std::sqrt
complex< _Tp > sqrt(const complex< _Tp > &)
Return complex square root of z.
Definition: complex:933
std::make_unsigned_t
typename make_unsigned< _Tp >::type make_unsigned_t
Alias template for make_unsigned.
Definition: type_traits:2009
std::conditional_t
typename conditional< _Cond, _Iftrue, _Iffalse >::type conditional_t
Alias template for conditional.
Definition: type_traits:2618
std::declval
auto declval() noexcept -> decltype(__declval< _Tp >(0))
Definition: type_traits:2393
std::max
constexpr const _Tp & max(const _Tp &, const _Tp &)
This does what you think it does.
Definition: stl_algobase.h:254
std::min
constexpr const _Tp & min(const _Tp &, const _Tp &)
This does what you think it does.
Definition: stl_algobase.h:230
std::cyl_bessel_i
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_i(_Tpnu __nu, _Tp __x)
Definition: specfun.h:535
std::sph_neumann
__gnu_cxx::__promote< _Tp >::__type sph_neumann(unsigned int __n, _Tp __x)
Definition: specfun.h:1193
std::ellint_3
__gnu_cxx::__promote_3< _Tp, _Tpn, _Tpp >::__type ellint_3(_Tp __k, _Tpn __nu, _Tpp __phi)
Return the incomplete elliptic integral of the third kind .
Definition: specfun.h:830
std::comp_ellint_2
__gnu_cxx::__promote< _Tp >::__type comp_ellint_2(_Tp __k)
Definition: specfun.h:438
std::assoc_legendre
__gnu_cxx::__promote< _Tp >::__type assoc_legendre(unsigned int __l, unsigned int __m, _Tp __x)
Definition: specfun.h:298
std::assoc_laguerre
__gnu_cxx::__promote< _Tp >::__type assoc_laguerre(unsigned int __n, unsigned int __m, _Tp __x)
Definition: specfun.h:252
std::sph_bessel
__gnu_cxx::__promote< _Tp >::__type sph_bessel(unsigned int __n, _Tp __x)
Definition: specfun.h:1102
std::cyl_bessel_j
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_j(_Tpnu __nu, _Tp __x)
Definition: specfun.h:581
std::sph_legendre
__gnu_cxx::__promote< _Tp >::__type sph_legendre(unsigned int __l, unsigned int __m, _Tp __theta)
Definition: specfun.h:1149
std::cyl_neumann
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_neumann(_Tpnu __nu, _Tp __x)
Definition: specfun.h:681
std::riemann_zeta
__gnu_cxx::__promote< _Tp >::__type riemann_zeta(_Tp __s)
Definition: specfun.h:1058
std::beta
__gnu_cxx::__promote_2< _Tpa, _Tpb >::__type beta(_Tpa __a, _Tpb __b)
Definition: specfun.h:343
std::cyl_bessel_k
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type cyl_bessel_k(_Tpnu __nu, _Tp __x)
Definition: specfun.h:633
std::expint
__gnu_cxx::__promote< _Tp >::__type expint(_Tp __x)
Definition: specfun.h:870
std::hermite
__gnu_cxx::__promote< _Tp >::__type hermite(unsigned int __n, _Tp __x)
Definition: specfun.h:918
std::comp_ellint_1
__gnu_cxx::__promote< _Tp >::__type comp_ellint_1(_Tp __k)
Definition: specfun.h:391
std::laguerre
__gnu_cxx::__promote< _Tp >::__type laguerre(unsigned int __n, _Tp __x)
Definition: specfun.h:962
std::ellint_2
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type ellint_2(_Tp __k, _Tpp __phi)
Definition: specfun.h:777
std::comp_ellint_3
__gnu_cxx::__promote_2< _Tp, _Tpn >::__type comp_ellint_3(_Tp __k, _Tpn __nu)
Definition: specfun.h:489
std::ellint_1
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type ellint_1(_Tp __k, _Tpp __phi)
Definition: specfun.h:729
std::legendre
__gnu_cxx::__promote< _Tp >::__type legendre(unsigned int __l, _Tp __x)
Definition: specfun.h:1007
std
ISO C++ entities toplevel namespace is std.
std::fabs
_Tp fabs(const std::complex< _Tp > &)
fabs(__z) [8.1.8].
Definition: complex:1817
std::asinh
std::complex< _Tp > asinh(const std::complex< _Tp > &)
asinh(__z) [8.1.6].
Definition: complex:1764
std::atan
std::complex< _Tp > atan(const std::complex< _Tp > &)
atan(__z) [8.1.4].
Definition: complex:1689
std::atanh
std::complex< _Tp > atanh(const std::complex< _Tp > &)
atanh(__z) [8.1.7].
Definition: complex:1808
std::acosh
std::complex< _Tp > acosh(const std::complex< _Tp > &)
acosh(__z) [8.1.5].
Definition: complex:1725
std::acos
std::complex< _Tp > acos(const std::complex< _Tp > &)
acos(__z) [8.1.2].
Definition: complex:1609
std::asin
std::complex< _Tp > asin(const std::complex< _Tp > &)
asin(__z) [8.1.3].
Definition: complex:1645