1 | // The template and inlines for the -*- C++ -*- complex number classes. |
2 | |
3 | // Copyright (C) 1997-2021 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 | /** @file include/complex |
26 | * This is a Standard C++ Library header. |
27 | */ |
28 | |
29 | // |
30 | // ISO C++ 14882: 26.2 Complex Numbers |
31 | // Note: this is not a conforming implementation. |
32 | // Initially implemented by Ulrich Drepper <drepper@cygnus.com> |
33 | // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr> |
34 | // |
35 | |
36 | #ifndef _GLIBCXX_COMPLEX |
37 | #define _GLIBCXX_COMPLEX 1 |
38 | |
39 | #pragma GCC system_header |
40 | |
41 | #include <bits/c++config.h> |
42 | #include <bits/cpp_type_traits.h> |
43 | #include <ext/type_traits.h> |
44 | #include <cmath> |
45 | #include <sstream> |
46 | |
47 | // Get rid of a macro possibly defined in <complex.h> |
48 | #undef complex |
49 | |
50 | #if __cplusplus > 201703L |
51 | # define __cpp_lib_constexpr_complex 201711L |
52 | #endif |
53 | |
54 | namespace std _GLIBCXX_VISIBILITY(default) |
55 | { |
56 | _GLIBCXX_BEGIN_NAMESPACE_VERSION |
57 | |
58 | /** |
59 | * @defgroup complex_numbers Complex Numbers |
60 | * @ingroup numerics |
61 | * |
62 | * Classes and functions for complex numbers. |
63 | * @{ |
64 | */ |
65 | |
66 | // Forward declarations. |
67 | template<typename _Tp> class complex; |
68 | template<> class complex<float>; |
69 | template<> class complex<double>; |
70 | template<> class complex<long double>; |
71 | |
72 | /// Return magnitude of @a z. |
73 | template<typename _Tp> _Tp abs(const complex<_Tp>&); |
74 | /// Return phase angle of @a z. |
75 | template<typename _Tp> _Tp arg(const complex<_Tp>&); |
76 | /// Return @a z magnitude squared. |
77 | template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&); |
78 | |
79 | /// Return complex conjugate of @a z. |
80 | template<typename _Tp> |
81 | _GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&); |
82 | /// Return complex with magnitude @a rho and angle @a theta. |
83 | template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); |
84 | |
85 | // Transcendentals: |
86 | /// Return complex cosine of @a z. |
87 | template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); |
88 | /// Return complex hyperbolic cosine of @a z. |
89 | template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); |
90 | /// Return complex base e exponential of @a z. |
91 | template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); |
92 | /// Return complex natural logarithm of @a z. |
93 | template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); |
94 | /// Return complex base 10 logarithm of @a z. |
95 | template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); |
96 | /// Return @a x to the @a y'th power. |
97 | template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); |
98 | /// Return @a x to the @a y'th power. |
99 | template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); |
100 | /// Return @a x to the @a y'th power. |
101 | template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, |
102 | const complex<_Tp>&); |
103 | /// Return @a x to the @a y'th power. |
104 | template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); |
105 | /// Return complex sine of @a z. |
106 | template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); |
107 | /// Return complex hyperbolic sine of @a z. |
108 | template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); |
109 | /// Return complex square root of @a z. |
110 | template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); |
111 | /// Return complex tangent of @a z. |
112 | template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); |
113 | /// Return complex hyperbolic tangent of @a z. |
114 | template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); |
115 | |
116 | |
117 | // 26.2.2 Primary template class complex |
118 | /** |
119 | * Template to represent complex numbers. |
120 | * |
121 | * Specializations for float, double, and long double are part of the |
122 | * library. Results with any other type are not guaranteed. |
123 | * |
124 | * @param Tp Type of real and imaginary values. |
125 | */ |
126 | template<typename _Tp> |
127 | class complex |
128 | { |
129 | public: |
130 | /// Value typedef. |
131 | typedef _Tp value_type; |
132 | |
133 | /// Default constructor. First parameter is x, second parameter is y. |
134 | /// Unspecified parameters default to 0. |
135 | _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) |
136 | : _M_real(__r), _M_imag(__i) { } |
137 | |
138 | // Let the compiler synthesize the copy constructor |
139 | #if __cplusplus >= 201103L |
140 | constexpr complex(const complex&) = default; |
141 | #endif |
142 | |
143 | /// Converting constructor. |
144 | template<typename _Up> |
145 | _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) |
146 | : _M_real(__z.real()), _M_imag(__z.imag()) { } |
147 | |
148 | #if __cplusplus >= 201103L |
149 | // _GLIBCXX_RESOLVE_LIB_DEFECTS |
150 | // DR 387. std::complex over-encapsulated. |
151 | _GLIBCXX_ABI_TAG_CXX11 |
152 | constexpr _Tp |
153 | real() const { return _M_real; } |
154 | |
155 | _GLIBCXX_ABI_TAG_CXX11 |
156 | constexpr _Tp |
157 | imag() const { return _M_imag; } |
158 | #else |
159 | /// Return real part of complex number. |
160 | _Tp& |
161 | real() { return _M_real; } |
162 | |
163 | /// Return real part of complex number. |
164 | const _Tp& |
165 | real() const { return _M_real; } |
166 | |
167 | /// Return imaginary part of complex number. |
168 | _Tp& |
169 | imag() { return _M_imag; } |
170 | |
171 | /// Return imaginary part of complex number. |
172 | const _Tp& |
173 | imag() const { return _M_imag; } |
174 | #endif |
175 | |
176 | // _GLIBCXX_RESOLVE_LIB_DEFECTS |
177 | // DR 387. std::complex over-encapsulated. |
178 | _GLIBCXX20_CONSTEXPR void |
179 | real(_Tp __val) { _M_real = __val; } |
180 | |
181 | _GLIBCXX20_CONSTEXPR void |
182 | imag(_Tp __val) { _M_imag = __val; } |
183 | |
184 | /// Assign a scalar to this complex number. |
185 | _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&); |
186 | |
187 | /// Add a scalar to this complex number. |
188 | // 26.2.5/1 |
189 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
190 | operator+=(const _Tp& __t) |
191 | { |
192 | _M_real += __t; |
193 | return *this; |
194 | } |
195 | |
196 | /// Subtract a scalar from this complex number. |
197 | // 26.2.5/3 |
198 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
199 | operator-=(const _Tp& __t) |
200 | { |
201 | _M_real -= __t; |
202 | return *this; |
203 | } |
204 | |
205 | /// Multiply this complex number by a scalar. |
206 | _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&); |
207 | /// Divide this complex number by a scalar. |
208 | _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&); |
209 | |
210 | // Let the compiler synthesize the copy assignment operator |
211 | #if __cplusplus >= 201103L |
212 | _GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default; |
213 | #endif |
214 | |
215 | /// Assign another complex number to this one. |
216 | template<typename _Up> |
217 | _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&); |
218 | /// Add another complex number to this one. |
219 | template<typename _Up> |
220 | _GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&); |
221 | /// Subtract another complex number from this one. |
222 | template<typename _Up> |
223 | _GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&); |
224 | /// Multiply this complex number by another. |
225 | template<typename _Up> |
226 | _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&); |
227 | /// Divide this complex number by another. |
228 | template<typename _Up> |
229 | _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&); |
230 | |
231 | _GLIBCXX_CONSTEXPR complex __rep() const |
232 | { return *this; } |
233 | |
234 | private: |
235 | _Tp _M_real; |
236 | _Tp _M_imag; |
237 | }; |
238 | |
239 | template<typename _Tp> |
240 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
241 | complex<_Tp>::operator=(const _Tp& __t) |
242 | { |
243 | _M_real = __t; |
244 | _M_imag = _Tp(); |
245 | return *this; |
246 | } |
247 | |
248 | // 26.2.5/5 |
249 | template<typename _Tp> |
250 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
251 | complex<_Tp>::operator*=(const _Tp& __t) |
252 | { |
253 | _M_real *= __t; |
254 | _M_imag *= __t; |
255 | return *this; |
256 | } |
257 | |
258 | // 26.2.5/7 |
259 | template<typename _Tp> |
260 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
261 | complex<_Tp>::operator/=(const _Tp& __t) |
262 | { |
263 | _M_real /= __t; |
264 | _M_imag /= __t; |
265 | return *this; |
266 | } |
267 | |
268 | template<typename _Tp> |
269 | template<typename _Up> |
270 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
271 | complex<_Tp>::operator=(const complex<_Up>& __z) |
272 | { |
273 | _M_real = __z.real(); |
274 | _M_imag = __z.imag(); |
275 | return *this; |
276 | } |
277 | |
278 | // 26.2.5/9 |
279 | template<typename _Tp> |
280 | template<typename _Up> |
281 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
282 | complex<_Tp>::operator+=(const complex<_Up>& __z) |
283 | { |
284 | _M_real += __z.real(); |
285 | _M_imag += __z.imag(); |
286 | return *this; |
287 | } |
288 | |
289 | // 26.2.5/11 |
290 | template<typename _Tp> |
291 | template<typename _Up> |
292 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
293 | complex<_Tp>::operator-=(const complex<_Up>& __z) |
294 | { |
295 | _M_real -= __z.real(); |
296 | _M_imag -= __z.imag(); |
297 | return *this; |
298 | } |
299 | |
300 | // 26.2.5/13 |
301 | // XXX: This is a grammar school implementation. |
302 | template<typename _Tp> |
303 | template<typename _Up> |
304 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
305 | complex<_Tp>::operator*=(const complex<_Up>& __z) |
306 | { |
307 | const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); |
308 | _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); |
309 | _M_real = __r; |
310 | return *this; |
311 | } |
312 | |
313 | // 26.2.5/15 |
314 | // XXX: This is a grammar school implementation. |
315 | template<typename _Tp> |
316 | template<typename _Up> |
317 | _GLIBCXX20_CONSTEXPR complex<_Tp>& |
318 | complex<_Tp>::operator/=(const complex<_Up>& __z) |
319 | { |
320 | const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); |
321 | const _Tp __n = std::norm(__z); |
322 | _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; |
323 | _M_real = __r / __n; |
324 | return *this; |
325 | } |
326 | |
327 | // Operators: |
328 | ///@{ |
329 | /// Return new complex value @a x plus @a y. |
330 | template<typename _Tp> |
331 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
332 | operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) |
333 | { |
334 | complex<_Tp> __r = __x; |
335 | __r += __y; |
336 | return __r; |
337 | } |
338 | |
339 | template<typename _Tp> |
340 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
341 | operator+(const complex<_Tp>& __x, const _Tp& __y) |
342 | { |
343 | complex<_Tp> __r = __x; |
344 | __r += __y; |
345 | return __r; |
346 | } |
347 | |
348 | template<typename _Tp> |
349 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
350 | operator+(const _Tp& __x, const complex<_Tp>& __y) |
351 | { |
352 | complex<_Tp> __r = __y; |
353 | __r += __x; |
354 | return __r; |
355 | } |
356 | ///@} |
357 | |
358 | ///@{ |
359 | /// Return new complex value @a x minus @a y. |
360 | template<typename _Tp> |
361 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
362 | operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) |
363 | { |
364 | complex<_Tp> __r = __x; |
365 | __r -= __y; |
366 | return __r; |
367 | } |
368 | |
369 | template<typename _Tp> |
370 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
371 | operator-(const complex<_Tp>& __x, const _Tp& __y) |
372 | { |
373 | complex<_Tp> __r = __x; |
374 | __r -= __y; |
375 | return __r; |
376 | } |
377 | |
378 | template<typename _Tp> |
379 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
380 | operator-(const _Tp& __x, const complex<_Tp>& __y) |
381 | { |
382 | complex<_Tp> __r = -__y; |
383 | __r += __x; |
384 | return __r; |
385 | } |
386 | ///@} |
387 | |
388 | ///@{ |
389 | /// Return new complex value @a x times @a y. |
390 | template<typename _Tp> |
391 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
392 | operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) |
393 | { |
394 | complex<_Tp> __r = __x; |
395 | __r *= __y; |
396 | return __r; |
397 | } |
398 | |
399 | template<typename _Tp> |
400 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
401 | operator*(const complex<_Tp>& __x, const _Tp& __y) |
402 | { |
403 | complex<_Tp> __r = __x; |
404 | __r *= __y; |
405 | return __r; |
406 | } |
407 | |
408 | template<typename _Tp> |
409 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
410 | operator*(const _Tp& __x, const complex<_Tp>& __y) |
411 | { |
412 | complex<_Tp> __r = __y; |
413 | __r *= __x; |
414 | return __r; |
415 | } |
416 | ///@} |
417 | |
418 | ///@{ |
419 | /// Return new complex value @a x divided by @a y. |
420 | template<typename _Tp> |
421 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
422 | operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) |
423 | { |
424 | complex<_Tp> __r = __x; |
425 | __r /= __y; |
426 | return __r; |
427 | } |
428 | |
429 | template<typename _Tp> |
430 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
431 | operator/(const complex<_Tp>& __x, const _Tp& __y) |
432 | { |
433 | complex<_Tp> __r = __x; |
434 | __r /= __y; |
435 | return __r; |
436 | } |
437 | |
438 | template<typename _Tp> |
439 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
440 | operator/(const _Tp& __x, const complex<_Tp>& __y) |
441 | { |
442 | complex<_Tp> __r = __x; |
443 | __r /= __y; |
444 | return __r; |
445 | } |
446 | ///@} |
447 | |
448 | /// Return @a x. |
449 | template<typename _Tp> |
450 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
451 | operator+(const complex<_Tp>& __x) |
452 | { return __x; } |
453 | |
454 | /// Return complex negation of @a x. |
455 | template<typename _Tp> |
456 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
457 | operator-(const complex<_Tp>& __x) |
458 | { return complex<_Tp>(-__x.real(), -__x.imag()); } |
459 | |
460 | ///@{ |
461 | /// Return true if @a x is equal to @a y. |
462 | template<typename _Tp> |
463 | inline _GLIBCXX_CONSTEXPR bool |
464 | operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) |
465 | { return __x.real() == __y.real() && __x.imag() == __y.imag(); } |
466 | |
467 | template<typename _Tp> |
468 | inline _GLIBCXX_CONSTEXPR bool |
469 | operator==(const complex<_Tp>& __x, const _Tp& __y) |
470 | { return __x.real() == __y && __x.imag() == _Tp(); } |
471 | |
472 | #if !(__cpp_impl_three_way_comparison >= 201907L) |
473 | template<typename _Tp> |
474 | inline _GLIBCXX_CONSTEXPR bool |
475 | operator==(const _Tp& __x, const complex<_Tp>& __y) |
476 | { return __x == __y.real() && _Tp() == __y.imag(); } |
477 | ///@} |
478 | |
479 | ///@{ |
480 | /// Return false if @a x is equal to @a y. |
481 | template<typename _Tp> |
482 | inline _GLIBCXX_CONSTEXPR bool |
483 | operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) |
484 | { return __x.real() != __y.real() || __x.imag() != __y.imag(); } |
485 | |
486 | template<typename _Tp> |
487 | inline _GLIBCXX_CONSTEXPR bool |
488 | operator!=(const complex<_Tp>& __x, const _Tp& __y) |
489 | { return __x.real() != __y || __x.imag() != _Tp(); } |
490 | |
491 | template<typename _Tp> |
492 | inline _GLIBCXX_CONSTEXPR bool |
493 | operator!=(const _Tp& __x, const complex<_Tp>& __y) |
494 | { return __x != __y.real() || _Tp() != __y.imag(); } |
495 | #endif |
496 | ///@} |
497 | |
498 | /// Extraction operator for complex values. |
499 | template<typename _Tp, typename _CharT, class _Traits> |
500 | basic_istream<_CharT, _Traits>& |
501 | operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) |
502 | { |
503 | bool __fail = true; |
504 | _CharT __ch; |
505 | if (__is >> __ch) |
506 | { |
507 | if (_Traits::eq(__ch, __is.widen('('))) |
508 | { |
509 | _Tp __u; |
510 | if (__is >> __u >> __ch) |
511 | { |
512 | const _CharT __rparen = __is.widen(')'); |
513 | if (_Traits::eq(__ch, __rparen)) |
514 | { |
515 | __x = __u; |
516 | __fail = false; |
517 | } |
518 | else if (_Traits::eq(__ch, __is.widen(','))) |
519 | { |
520 | _Tp __v; |
521 | if (__is >> __v >> __ch) |
522 | { |
523 | if (_Traits::eq(__ch, __rparen)) |
524 | { |
525 | __x = complex<_Tp>(__u, __v); |
526 | __fail = false; |
527 | } |
528 | else |
529 | __is.putback(__ch); |
530 | } |
531 | } |
532 | else |
533 | __is.putback(__ch); |
534 | } |
535 | } |
536 | else |
537 | { |
538 | __is.putback(__ch); |
539 | _Tp __u; |
540 | if (__is >> __u) |
541 | { |
542 | __x = __u; |
543 | __fail = false; |
544 | } |
545 | } |
546 | } |
547 | if (__fail) |
548 | __is.setstate(ios_base::failbit); |
549 | return __is; |
550 | } |
551 | |
552 | /// Insertion operator for complex values. |
553 | template<typename _Tp, typename _CharT, class _Traits> |
554 | basic_ostream<_CharT, _Traits>& |
555 | operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) |
556 | { |
557 | basic_ostringstream<_CharT, _Traits> __s; |
558 | __s.flags(__os.flags()); |
559 | __s.imbue(__os.getloc()); |
560 | __s.precision(__os.precision()); |
561 | __s << '(' << __x.real() << ',' << __x.imag() << ')'; |
562 | return __os << __s.str(); |
563 | } |
564 | |
565 | // Values |
566 | #if __cplusplus >= 201103L |
567 | template<typename _Tp> |
568 | constexpr _Tp |
569 | real(const complex<_Tp>& __z) |
570 | { return __z.real(); } |
571 | |
572 | template<typename _Tp> |
573 | constexpr _Tp |
574 | imag(const complex<_Tp>& __z) |
575 | { return __z.imag(); } |
576 | #else |
577 | template<typename _Tp> |
578 | inline _Tp& |
579 | real(complex<_Tp>& __z) |
580 | { return __z.real(); } |
581 | |
582 | template<typename _Tp> |
583 | inline const _Tp& |
584 | real(const complex<_Tp>& __z) |
585 | { return __z.real(); } |
586 | |
587 | template<typename _Tp> |
588 | inline _Tp& |
589 | imag(complex<_Tp>& __z) |
590 | { return __z.imag(); } |
591 | |
592 | template<typename _Tp> |
593 | inline const _Tp& |
594 | imag(const complex<_Tp>& __z) |
595 | { return __z.imag(); } |
596 | #endif |
597 | |
598 | // 26.2.7/3 abs(__z): Returns the magnitude of __z. |
599 | template<typename _Tp> |
600 | inline _Tp |
601 | __complex_abs(const complex<_Tp>& __z) |
602 | { |
603 | _Tp __x = __z.real(); |
604 | _Tp __y = __z.imag(); |
605 | const _Tp __s = std::max(abs(__x), abs(__y)); |
606 | if (__s == _Tp()) // well ... |
607 | return __s; |
608 | __x /= __s; |
609 | __y /= __s; |
610 | return __s * sqrt(__x * __x + __y * __y); |
611 | } |
612 | |
613 | #if _GLIBCXX_USE_C99_COMPLEX |
614 | inline float |
615 | __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } |
616 | |
617 | inline double |
618 | __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } |
619 | |
620 | inline long double |
621 | __complex_abs(const __complex__ long double& __z) |
622 | { return __builtin_cabsl(__z); } |
623 | |
624 | template<typename _Tp> |
625 | inline _Tp |
626 | abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } |
627 | #else |
628 | template<typename _Tp> |
629 | inline _Tp |
630 | abs(const complex<_Tp>& __z) { return __complex_abs(__z); } |
631 | #endif |
632 | |
633 | |
634 | // 26.2.7/4: arg(__z): Returns the phase angle of __z. |
635 | template<typename _Tp> |
636 | inline _Tp |
637 | __complex_arg(const complex<_Tp>& __z) |
638 | { return atan2(__z.imag(), __z.real()); } |
639 | |
640 | #if _GLIBCXX_USE_C99_COMPLEX |
641 | inline float |
642 | __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } |
643 | |
644 | inline double |
645 | __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } |
646 | |
647 | inline long double |
648 | __complex_arg(const __complex__ long double& __z) |
649 | { return __builtin_cargl(__z); } |
650 | |
651 | template<typename _Tp> |
652 | inline _Tp |
653 | arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } |
654 | #else |
655 | template<typename _Tp> |
656 | inline _Tp |
657 | arg(const complex<_Tp>& __z) { return __complex_arg(__z); } |
658 | #endif |
659 | |
660 | // 26.2.7/5: norm(__z) returns the squared magnitude of __z. |
661 | // As defined, norm() is -not- a norm is the common mathematical |
662 | // sense used in numerics. The helper class _Norm_helper<> tries to |
663 | // distinguish between builtin floating point and the rest, so as |
664 | // to deliver an answer as close as possible to the real value. |
665 | template<bool> |
666 | struct _Norm_helper |
667 | { |
668 | template<typename _Tp> |
669 | static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) |
670 | { |
671 | const _Tp __x = __z.real(); |
672 | const _Tp __y = __z.imag(); |
673 | return __x * __x + __y * __y; |
674 | } |
675 | }; |
676 | |
677 | template<> |
678 | struct _Norm_helper<true> |
679 | { |
680 | template<typename _Tp> |
681 | static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) |
682 | { |
683 | //_Tp __res = std::abs(__z); |
684 | //return __res * __res; |
685 | const _Tp __x = __z.real(); |
686 | const _Tp __y = __z.imag(); |
687 | return __x * __x + __y * __y; |
688 | } |
689 | }; |
690 | |
691 | template<typename _Tp> |
692 | inline _GLIBCXX20_CONSTEXPR _Tp |
693 | norm(const complex<_Tp>& __z) |
694 | { |
695 | return _Norm_helper<__is_floating<_Tp>::__value |
696 | && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); |
697 | } |
698 | |
699 | template<typename _Tp> |
700 | inline complex<_Tp> |
701 | polar(const _Tp& __rho, const _Tp& __theta) |
702 | { |
703 | __glibcxx_assert( __rho >= 0 ); |
704 | return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); |
705 | } |
706 | |
707 | template<typename _Tp> |
708 | inline _GLIBCXX20_CONSTEXPR complex<_Tp> |
709 | conj(const complex<_Tp>& __z) |
710 | { return complex<_Tp>(__z.real(), -__z.imag()); } |
711 | |
712 | // Transcendentals |
713 | |
714 | // 26.2.8/1 cos(__z): Returns the cosine of __z. |
715 | template<typename _Tp> |
716 | inline complex<_Tp> |
717 | __complex_cos(const complex<_Tp>& __z) |
718 | { |
719 | const _Tp __x = __z.real(); |
720 | const _Tp __y = __z.imag(); |
721 | return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); |
722 | } |
723 | |
724 | #if _GLIBCXX_USE_C99_COMPLEX |
725 | inline __complex__ float |
726 | __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } |
727 | |
728 | inline __complex__ double |
729 | __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } |
730 | |
731 | inline __complex__ long double |
732 | __complex_cos(const __complex__ long double& __z) |
733 | { return __builtin_ccosl(__z); } |
734 | |
735 | template<typename _Tp> |
736 | inline complex<_Tp> |
737 | cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } |
738 | #else |
739 | template<typename _Tp> |
740 | inline complex<_Tp> |
741 | cos(const complex<_Tp>& __z) { return __complex_cos(__z); } |
742 | #endif |
743 | |
744 | // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. |
745 | template<typename _Tp> |
746 | inline complex<_Tp> |
747 | __complex_cosh(const complex<_Tp>& __z) |
748 | { |
749 | const _Tp __x = __z.real(); |
750 | const _Tp __y = __z.imag(); |
751 | return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); |
752 | } |
753 | |
754 | #if _GLIBCXX_USE_C99_COMPLEX |
755 | inline __complex__ float |
756 | __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } |
757 | |
758 | inline __complex__ double |
759 | __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } |
760 | |
761 | inline __complex__ long double |
762 | __complex_cosh(const __complex__ long double& __z) |
763 | { return __builtin_ccoshl(__z); } |
764 | |
765 | template<typename _Tp> |
766 | inline complex<_Tp> |
767 | cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } |
768 | #else |
769 | template<typename _Tp> |
770 | inline complex<_Tp> |
771 | cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } |
772 | #endif |
773 | |
774 | // 26.2.8/3 exp(__z): Returns the complex base e exponential of x |
775 | template<typename _Tp> |
776 | inline complex<_Tp> |
777 | __complex_exp(const complex<_Tp>& __z) |
778 | { return std::polar<_Tp>(exp(__z.real()), __z.imag()); } |
779 | |
780 | #if _GLIBCXX_USE_C99_COMPLEX |
781 | inline __complex__ float |
782 | __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } |
783 | |
784 | inline __complex__ double |
785 | __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } |
786 | |
787 | inline __complex__ long double |
788 | __complex_exp(const __complex__ long double& __z) |
789 | { return __builtin_cexpl(__z); } |
790 | |
791 | template<typename _Tp> |
792 | inline complex<_Tp> |
793 | exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } |
794 | #else |
795 | template<typename _Tp> |
796 | inline complex<_Tp> |
797 | exp(const complex<_Tp>& __z) { return __complex_exp(__z); } |
798 | #endif |
799 | |
800 | // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. |
801 | // The branch cut is along the negative axis. |
802 | template<typename _Tp> |
803 | inline complex<_Tp> |
804 | __complex_log(const complex<_Tp>& __z) |
805 | { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } |
806 | |
807 | #if _GLIBCXX_USE_C99_COMPLEX |
808 | inline __complex__ float |
809 | __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } |
810 | |
811 | inline __complex__ double |
812 | __complex_log(__complex__ double __z) { return __builtin_clog(__z); } |
813 | |
814 | inline __complex__ long double |
815 | __complex_log(const __complex__ long double& __z) |
816 | { return __builtin_clogl(__z); } |
817 | |
818 | template<typename _Tp> |
819 | inline complex<_Tp> |
820 | log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } |
821 | #else |
822 | template<typename _Tp> |
823 | inline complex<_Tp> |
824 | log(const complex<_Tp>& __z) { return __complex_log(__z); } |
825 | #endif |
826 | |
827 | template<typename _Tp> |
828 | inline complex<_Tp> |
829 | log10(const complex<_Tp>& __z) |
830 | { return std::log(__z) / log(_Tp(10.0)); } |
831 | |
832 | // 26.2.8/10 sin(__z): Returns the sine of __z. |
833 | template<typename _Tp> |
834 | inline complex<_Tp> |
835 | __complex_sin(const complex<_Tp>& __z) |
836 | { |
837 | const _Tp __x = __z.real(); |
838 | const _Tp __y = __z.imag(); |
839 | return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); |
840 | } |
841 | |
842 | #if _GLIBCXX_USE_C99_COMPLEX |
843 | inline __complex__ float |
844 | __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } |
845 | |
846 | inline __complex__ double |
847 | __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } |
848 | |
849 | inline __complex__ long double |
850 | __complex_sin(const __complex__ long double& __z) |
851 | { return __builtin_csinl(__z); } |
852 | |
853 | template<typename _Tp> |
854 | inline complex<_Tp> |
855 | sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } |
856 | #else |
857 | template<typename _Tp> |
858 | inline complex<_Tp> |
859 | sin(const complex<_Tp>& __z) { return __complex_sin(__z); } |
860 | #endif |
861 | |
862 | // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. |
863 | template<typename _Tp> |
864 | inline complex<_Tp> |
865 | __complex_sinh(const complex<_Tp>& __z) |
866 | { |
867 | const _Tp __x = __z.real(); |
868 | const _Tp __y = __z.imag(); |
869 | return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); |
870 | } |
871 | |
872 | #if _GLIBCXX_USE_C99_COMPLEX |
873 | inline __complex__ float |
874 | __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } |
875 | |
876 | inline __complex__ double |
877 | __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } |
878 | |
879 | inline __complex__ long double |
880 | __complex_sinh(const __complex__ long double& __z) |
881 | { return __builtin_csinhl(__z); } |
882 | |
883 | template<typename _Tp> |
884 | inline complex<_Tp> |
885 | sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } |
886 | #else |
887 | template<typename _Tp> |
888 | inline complex<_Tp> |
889 | sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } |
890 | #endif |
891 | |
892 | // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. |
893 | // The branch cut is on the negative axis. |
894 | template<typename _Tp> |
895 | complex<_Tp> |
896 | __complex_sqrt(const complex<_Tp>& __z) |
897 | { |
898 | _Tp __x = __z.real(); |
899 | _Tp __y = __z.imag(); |
900 | |
901 | if (__x == _Tp()) |
902 | { |
903 | _Tp __t = sqrt(abs(__y) / 2); |
904 | return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); |
905 | } |
906 | else |
907 | { |
908 | _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); |
909 | _Tp __u = __t / 2; |
910 | return __x > _Tp() |
911 | ? complex<_Tp>(__u, __y / __t) |
912 | : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); |
913 | } |
914 | } |
915 | |
916 | #if _GLIBCXX_USE_C99_COMPLEX |
917 | inline __complex__ float |
918 | __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } |
919 | |
920 | inline __complex__ double |
921 | __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } |
922 | |
923 | inline __complex__ long double |
924 | __complex_sqrt(const __complex__ long double& __z) |
925 | { return __builtin_csqrtl(__z); } |
926 | |
927 | template<typename _Tp> |
928 | inline complex<_Tp> |
929 | sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } |
930 | #else |
931 | template<typename _Tp> |
932 | inline complex<_Tp> |
933 | sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } |
934 | #endif |
935 | |
936 | // 26.2.8/14 tan(__z): Return the complex tangent of __z. |
937 | |
938 | template<typename _Tp> |
939 | inline complex<_Tp> |
940 | __complex_tan(const complex<_Tp>& __z) |
941 | { return std::sin(__z) / std::cos(__z); } |
942 | |
943 | #if _GLIBCXX_USE_C99_COMPLEX |
944 | inline __complex__ float |
945 | __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } |
946 | |
947 | inline __complex__ double |
948 | __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } |
949 | |
950 | inline __complex__ long double |
951 | __complex_tan(const __complex__ long double& __z) |
952 | { return __builtin_ctanl(__z); } |
953 | |
954 | template<typename _Tp> |
955 | inline complex<_Tp> |
956 | tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } |
957 | #else |
958 | template<typename _Tp> |
959 | inline complex<_Tp> |
960 | tan(const complex<_Tp>& __z) { return __complex_tan(__z); } |
961 | #endif |
962 | |
963 | |
964 | // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. |
965 | |
966 | template<typename _Tp> |
967 | inline complex<_Tp> |
968 | __complex_tanh(const complex<_Tp>& __z) |
969 | { return std::sinh(__z) / std::cosh(__z); } |
970 | |
971 | #if _GLIBCXX_USE_C99_COMPLEX |
972 | inline __complex__ float |
973 | __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } |
974 | |
975 | inline __complex__ double |
976 | __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } |
977 | |
978 | inline __complex__ long double |
979 | __complex_tanh(const __complex__ long double& __z) |
980 | { return __builtin_ctanhl(__z); } |
981 | |
982 | template<typename _Tp> |
983 | inline complex<_Tp> |
984 | tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } |
985 | #else |
986 | template<typename _Tp> |
987 | inline complex<_Tp> |
988 | tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } |
989 | #endif |
990 | |
991 | |
992 | // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x |
993 | // raised to the __y-th power. The branch |
994 | // cut is on the negative axis. |
995 | template<typename _Tp> |
996 | complex<_Tp> |
997 | __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) |
998 | { |
999 | complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); |
1000 | |
1001 | while (__n >>= 1) |
1002 | { |
1003 | __x *= __x; |
1004 | if (__n % 2) |
1005 | __y *= __x; |
1006 | } |
1007 | |
1008 | return __y; |
1009 | } |
1010 | |
1011 | // In C++11 mode we used to implement the resolution of |
1012 | // DR 844. complex pow return type is ambiguous. |
1013 | // thus the following overload was disabled in that mode. However, doing |
1014 | // that causes all sorts of issues, see, for example: |
1015 | // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html |
1016 | // and also PR57974. |
1017 | template<typename _Tp> |
1018 | inline complex<_Tp> |
1019 | pow(const complex<_Tp>& __z, int __n) |
1020 | { |
1021 | return __n < 0 |
1022 | ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) |
1023 | : std::__complex_pow_unsigned(__z, __n); |
1024 | } |
1025 | |
1026 | template<typename _Tp> |
1027 | complex<_Tp> |
1028 | pow(const complex<_Tp>& __x, const _Tp& __y) |
1029 | { |
1030 | #if ! _GLIBCXX_USE_C99_COMPLEX |
1031 | if (__x == _Tp()) |
1032 | return _Tp(); |
1033 | #endif |
1034 | if (__x.imag() == _Tp() && __x.real() > _Tp()) |
1035 | return pow(__x.real(), __y); |
1036 | |
1037 | complex<_Tp> __t = std::log(__x); |
1038 | return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag()); |
1039 | } |
1040 | |
1041 | template<typename _Tp> |
1042 | inline complex<_Tp> |
1043 | __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
1044 | { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } |
1045 | |
1046 | #if _GLIBCXX_USE_C99_COMPLEX |
1047 | inline __complex__ float |
1048 | __complex_pow(__complex__ float __x, __complex__ float __y) |
1049 | { return __builtin_cpowf(__x, __y); } |
1050 | |
1051 | inline __complex__ double |
1052 | __complex_pow(__complex__ double __x, __complex__ double __y) |
1053 | { return __builtin_cpow(__x, __y); } |
1054 | |
1055 | inline __complex__ long double |
1056 | __complex_pow(const __complex__ long double& __x, |
1057 | const __complex__ long double& __y) |
1058 | { return __builtin_cpowl(__x, __y); } |
1059 | |
1060 | template<typename _Tp> |
1061 | inline complex<_Tp> |
1062 | pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
1063 | { return __complex_pow(__x.__rep(), __y.__rep()); } |
1064 | #else |
1065 | template<typename _Tp> |
1066 | inline complex<_Tp> |
1067 | pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
1068 | { return __complex_pow(__x, __y); } |
1069 | #endif |
1070 | |
1071 | template<typename _Tp> |
1072 | inline complex<_Tp> |
1073 | pow(const _Tp& __x, const complex<_Tp>& __y) |
1074 | { |
1075 | return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()), |
1076 | __y.imag() * log(__x)) |
1077 | : std::pow(complex<_Tp>(__x), __y); |
1078 | } |
1079 | |
1080 | /// 26.2.3 complex specializations |
1081 | /// complex<float> specialization |
1082 | template<> |
1083 | class complex<float> |
1084 | { |
1085 | public: |
1086 | typedef float value_type; |
1087 | typedef __complex__ float _ComplexT; |
1088 | |
1089 | _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } |
1090 | |
1091 | _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) |
1092 | #if __cplusplus >= 201103L |
1093 | : _M_value{ __r, __i } { } |
1094 | #else |
1095 | { |
1096 | __real__ _M_value = __r; |
1097 | __imag__ _M_value = __i; |
1098 | } |
1099 | #endif |
1100 | |
1101 | explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); |
1102 | explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); |
1103 | |
1104 | #if __cplusplus >= 201103L |
1105 | // _GLIBCXX_RESOLVE_LIB_DEFECTS |
1106 | // DR 387. std::complex over-encapsulated. |
1107 | __attribute ((__abi_tag__ ("cxx11" ))) |
1108 | constexpr float |
1109 | real() const { return __real__ _M_value; } |
1110 | |
1111 | __attribute ((__abi_tag__ ("cxx11" ))) |
1112 | constexpr float |
1113 | imag() const { return __imag__ _M_value; } |
1114 | #else |
1115 | float& |
1116 | real() { return __real__ _M_value; } |
1117 | |
1118 | const float& |
1119 | real() const { return __real__ _M_value; } |
1120 | |
1121 | float& |
1122 | imag() { return __imag__ _M_value; } |
1123 | |
1124 | const float& |
1125 | imag() const { return __imag__ _M_value; } |
1126 | #endif |
1127 | |
1128 | // _GLIBCXX_RESOLVE_LIB_DEFECTS |
1129 | // DR 387. std::complex over-encapsulated. |
1130 | _GLIBCXX20_CONSTEXPR void |
1131 | real(float __val) { __real__ _M_value = __val; } |
1132 | |
1133 | _GLIBCXX20_CONSTEXPR void |
1134 | imag(float __val) { __imag__ _M_value = __val; } |
1135 | |
1136 | _GLIBCXX20_CONSTEXPR complex& |
1137 | operator=(float __f) |
1138 | { |
1139 | _M_value = __f; |
1140 | return *this; |
1141 | } |
1142 | |
1143 | _GLIBCXX20_CONSTEXPR complex& |
1144 | operator+=(float __f) |
1145 | { |
1146 | _M_value += __f; |
1147 | return *this; |
1148 | } |
1149 | |
1150 | _GLIBCXX20_CONSTEXPR complex& |
1151 | operator-=(float __f) |
1152 | { |
1153 | _M_value -= __f; |
1154 | return *this; |
1155 | } |
1156 | |
1157 | _GLIBCXX20_CONSTEXPR complex& |
1158 | operator*=(float __f) |
1159 | { |
1160 | _M_value *= __f; |
1161 | return *this; |
1162 | } |
1163 | |
1164 | _GLIBCXX20_CONSTEXPR complex& |
1165 | operator/=(float __f) |
1166 | { |
1167 | _M_value /= __f; |
1168 | return *this; |
1169 | } |
1170 | |
1171 | // Let the compiler synthesize the copy and assignment |
1172 | // operator. It always does a pretty good job. |
1173 | #if __cplusplus >= 201103L |
1174 | _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; |
1175 | #endif |
1176 | |
1177 | template<typename _Tp> |
1178 | _GLIBCXX20_CONSTEXPR complex& |
1179 | operator=(const complex<_Tp>& __z) |
1180 | { |
1181 | __real__ _M_value = __z.real(); |
1182 | __imag__ _M_value = __z.imag(); |
1183 | return *this; |
1184 | } |
1185 | |
1186 | template<typename _Tp> |
1187 | _GLIBCXX20_CONSTEXPR complex& |
1188 | operator+=(const complex<_Tp>& __z) |
1189 | { |
1190 | _M_value += __z.__rep(); |
1191 | return *this; |
1192 | } |
1193 | |
1194 | template<class _Tp> |
1195 | _GLIBCXX20_CONSTEXPR complex& |
1196 | operator-=(const complex<_Tp>& __z) |
1197 | { |
1198 | _M_value -= __z.__rep(); |
1199 | return *this; |
1200 | } |
1201 | |
1202 | template<class _Tp> |
1203 | _GLIBCXX20_CONSTEXPR complex& |
1204 | operator*=(const complex<_Tp>& __z) |
1205 | { |
1206 | const _ComplexT __t = __z.__rep(); |
1207 | _M_value *= __t; |
1208 | return *this; |
1209 | } |
1210 | |
1211 | template<class _Tp> |
1212 | _GLIBCXX20_CONSTEXPR complex& |
1213 | operator/=(const complex<_Tp>& __z) |
1214 | { |
1215 | const _ComplexT __t = __z.__rep(); |
1216 | _M_value /= __t; |
1217 | return *this; |
1218 | } |
1219 | |
1220 | _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } |
1221 | |
1222 | private: |
1223 | _ComplexT _M_value; |
1224 | }; |
1225 | |
1226 | /// 26.2.3 complex specializations |
1227 | /// complex<double> specialization |
1228 | template<> |
1229 | class complex<double> |
1230 | { |
1231 | public: |
1232 | typedef double value_type; |
1233 | typedef __complex__ double _ComplexT; |
1234 | |
1235 | _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } |
1236 | |
1237 | _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) |
1238 | #if __cplusplus >= 201103L |
1239 | : _M_value{ __r, __i } { } |
1240 | #else |
1241 | { |
1242 | __real__ _M_value = __r; |
1243 | __imag__ _M_value = __i; |
1244 | } |
1245 | #endif |
1246 | |
1247 | _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) |
1248 | : _M_value(__z.__rep()) { } |
1249 | |
1250 | explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); |
1251 | |
1252 | #if __cplusplus >= 201103L |
1253 | // _GLIBCXX_RESOLVE_LIB_DEFECTS |
1254 | // DR 387. std::complex over-encapsulated. |
1255 | __attribute ((__abi_tag__ ("cxx11" ))) |
1256 | constexpr double |
1257 | real() const { return __real__ _M_value; } |
1258 | |
1259 | __attribute ((__abi_tag__ ("cxx11" ))) |
1260 | constexpr double |
1261 | imag() const { return __imag__ _M_value; } |
1262 | #else |
1263 | double& |
1264 | real() { return __real__ _M_value; } |
1265 | |
1266 | const double& |
1267 | real() const { return __real__ _M_value; } |
1268 | |
1269 | double& |
1270 | imag() { return __imag__ _M_value; } |
1271 | |
1272 | const double& |
1273 | imag() const { return __imag__ _M_value; } |
1274 | #endif |
1275 | |
1276 | // _GLIBCXX_RESOLVE_LIB_DEFECTS |
1277 | // DR 387. std::complex over-encapsulated. |
1278 | _GLIBCXX20_CONSTEXPR void |
1279 | real(double __val) { __real__ _M_value = __val; } |
1280 | |
1281 | _GLIBCXX20_CONSTEXPR void |
1282 | imag(double __val) { __imag__ _M_value = __val; } |
1283 | |
1284 | _GLIBCXX20_CONSTEXPR complex& |
1285 | operator=(double __d) |
1286 | { |
1287 | _M_value = __d; |
1288 | return *this; |
1289 | } |
1290 | |
1291 | _GLIBCXX20_CONSTEXPR complex& |
1292 | operator+=(double __d) |
1293 | { |
1294 | _M_value += __d; |
1295 | return *this; |
1296 | } |
1297 | |
1298 | _GLIBCXX20_CONSTEXPR complex& |
1299 | operator-=(double __d) |
1300 | { |
1301 | _M_value -= __d; |
1302 | return *this; |
1303 | } |
1304 | |
1305 | _GLIBCXX20_CONSTEXPR complex& |
1306 | operator*=(double __d) |
1307 | { |
1308 | _M_value *= __d; |
1309 | return *this; |
1310 | } |
1311 | |
1312 | _GLIBCXX20_CONSTEXPR complex& |
1313 | operator/=(double __d) |
1314 | { |
1315 | _M_value /= __d; |
1316 | return *this; |
1317 | } |
1318 | |
1319 | // The compiler will synthesize this, efficiently. |
1320 | #if __cplusplus >= 201103L |
1321 | _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; |
1322 | #endif |
1323 | |
1324 | template<typename _Tp> |
1325 | _GLIBCXX20_CONSTEXPR complex& |
1326 | operator=(const complex<_Tp>& __z) |
1327 | { |
1328 | _M_value = __z.__rep(); |
1329 | return *this; |
1330 | } |
1331 | |
1332 | template<typename _Tp> |
1333 | _GLIBCXX20_CONSTEXPR complex& |
1334 | operator+=(const complex<_Tp>& __z) |
1335 | { |
1336 | _M_value += __z.__rep(); |
1337 | return *this; |
1338 | } |
1339 | |
1340 | template<typename _Tp> |
1341 | _GLIBCXX20_CONSTEXPR complex& |
1342 | operator-=(const complex<_Tp>& __z) |
1343 | { |
1344 | _M_value -= __z.__rep(); |
1345 | return *this; |
1346 | } |
1347 | |
1348 | template<typename _Tp> |
1349 | _GLIBCXX20_CONSTEXPR complex& |
1350 | operator*=(const complex<_Tp>& __z) |
1351 | { |
1352 | const _ComplexT __t = __z.__rep(); |
1353 | _M_value *= __t; |
1354 | return *this; |
1355 | } |
1356 | |
1357 | template<typename _Tp> |
1358 | _GLIBCXX20_CONSTEXPR complex& |
1359 | operator/=(const complex<_Tp>& __z) |
1360 | { |
1361 | const _ComplexT __t = __z.__rep(); |
1362 | _M_value /= __t; |
1363 | return *this; |
1364 | } |
1365 | |
1366 | _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } |
1367 | |
1368 | private: |
1369 | _ComplexT _M_value; |
1370 | }; |
1371 | |
1372 | /// 26.2.3 complex specializations |
1373 | /// complex<long double> specialization |
1374 | template<> |
1375 | class complex<long double> |
1376 | { |
1377 | public: |
1378 | typedef long double value_type; |
1379 | typedef __complex__ long double _ComplexT; |
1380 | |
1381 | _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } |
1382 | |
1383 | _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, |
1384 | long double __i = 0.0L) |
1385 | #if __cplusplus >= 201103L |
1386 | : _M_value{ __r, __i } { } |
1387 | #else |
1388 | { |
1389 | __real__ _M_value = __r; |
1390 | __imag__ _M_value = __i; |
1391 | } |
1392 | #endif |
1393 | |
1394 | _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) |
1395 | : _M_value(__z.__rep()) { } |
1396 | |
1397 | _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) |
1398 | : _M_value(__z.__rep()) { } |
1399 | |
1400 | #if __cplusplus >= 201103L |
1401 | // _GLIBCXX_RESOLVE_LIB_DEFECTS |
1402 | // DR 387. std::complex over-encapsulated. |
1403 | __attribute ((__abi_tag__ ("cxx11" ))) |
1404 | constexpr long double |
1405 | real() const { return __real__ _M_value; } |
1406 | |
1407 | __attribute ((__abi_tag__ ("cxx11" ))) |
1408 | constexpr long double |
1409 | imag() const { return __imag__ _M_value; } |
1410 | #else |
1411 | long double& |
1412 | real() { return __real__ _M_value; } |
1413 | |
1414 | const long double& |
1415 | real() const { return __real__ _M_value; } |
1416 | |
1417 | long double& |
1418 | imag() { return __imag__ _M_value; } |
1419 | |
1420 | const long double& |
1421 | imag() const { return __imag__ _M_value; } |
1422 | #endif |
1423 | |
1424 | // _GLIBCXX_RESOLVE_LIB_DEFECTS |
1425 | // DR 387. std::complex over-encapsulated. |
1426 | _GLIBCXX20_CONSTEXPR void |
1427 | real(long double __val) { __real__ _M_value = __val; } |
1428 | |
1429 | _GLIBCXX20_CONSTEXPR void |
1430 | imag(long double __val) { __imag__ _M_value = __val; } |
1431 | |
1432 | _GLIBCXX20_CONSTEXPR complex& |
1433 | operator=(long double __r) |
1434 | { |
1435 | _M_value = __r; |
1436 | return *this; |
1437 | } |
1438 | |
1439 | _GLIBCXX20_CONSTEXPR complex& |
1440 | operator+=(long double __r) |
1441 | { |
1442 | _M_value += __r; |
1443 | return *this; |
1444 | } |
1445 | |
1446 | _GLIBCXX20_CONSTEXPR complex& |
1447 | operator-=(long double __r) |
1448 | { |
1449 | _M_value -= __r; |
1450 | return *this; |
1451 | } |
1452 | |
1453 | _GLIBCXX20_CONSTEXPR complex& |
1454 | operator*=(long double __r) |
1455 | { |
1456 | _M_value *= __r; |
1457 | return *this; |
1458 | } |
1459 | |
1460 | _GLIBCXX20_CONSTEXPR complex& |
1461 | operator/=(long double __r) |
1462 | { |
1463 | _M_value /= __r; |
1464 | return *this; |
1465 | } |
1466 | |
1467 | // The compiler knows how to do this efficiently |
1468 | #if __cplusplus >= 201103L |
1469 | _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; |
1470 | #endif |
1471 | |
1472 | template<typename _Tp> |
1473 | _GLIBCXX20_CONSTEXPR complex& |
1474 | operator=(const complex<_Tp>& __z) |
1475 | { |
1476 | _M_value = __z.__rep(); |
1477 | return *this; |
1478 | } |
1479 | |
1480 | template<typename _Tp> |
1481 | _GLIBCXX20_CONSTEXPR complex& |
1482 | operator+=(const complex<_Tp>& __z) |
1483 | { |
1484 | _M_value += __z.__rep(); |
1485 | return *this; |
1486 | } |
1487 | |
1488 | template<typename _Tp> |
1489 | _GLIBCXX20_CONSTEXPR complex& |
1490 | operator-=(const complex<_Tp>& __z) |
1491 | { |
1492 | _M_value -= __z.__rep(); |
1493 | return *this; |
1494 | } |
1495 | |
1496 | template<typename _Tp> |
1497 | _GLIBCXX20_CONSTEXPR complex& |
1498 | operator*=(const complex<_Tp>& __z) |
1499 | { |
1500 | const _ComplexT __t = __z.__rep(); |
1501 | _M_value *= __t; |
1502 | return *this; |
1503 | } |
1504 | |
1505 | template<typename _Tp> |
1506 | _GLIBCXX20_CONSTEXPR complex& |
1507 | operator/=(const complex<_Tp>& __z) |
1508 | { |
1509 | const _ComplexT __t = __z.__rep(); |
1510 | _M_value /= __t; |
1511 | return *this; |
1512 | } |
1513 | |
1514 | _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } |
1515 | |
1516 | private: |
1517 | _ComplexT _M_value; |
1518 | }; |
1519 | |
1520 | // These bits have to be at the end of this file, so that the |
1521 | // specializations have all been defined. |
1522 | inline _GLIBCXX_CONSTEXPR |
1523 | complex<float>::complex(const complex<double>& __z) |
1524 | : _M_value(__z.__rep()) { } |
1525 | |
1526 | inline _GLIBCXX_CONSTEXPR |
1527 | complex<float>::complex(const complex<long double>& __z) |
1528 | : _M_value(__z.__rep()) { } |
1529 | |
1530 | inline _GLIBCXX_CONSTEXPR |
1531 | complex<double>::complex(const complex<long double>& __z) |
1532 | : _M_value(__z.__rep()) { } |
1533 | |
1534 | // Inhibit implicit instantiations for required instantiations, |
1535 | // which are defined via explicit instantiations elsewhere. |
1536 | // NB: This syntax is a GNU extension. |
1537 | #if _GLIBCXX_EXTERN_TEMPLATE |
1538 | extern template istream& operator>>(istream&, complex<float>&); |
1539 | extern template ostream& operator<<(ostream&, const complex<float>&); |
1540 | extern template istream& operator>>(istream&, complex<double>&); |
1541 | extern template ostream& operator<<(ostream&, const complex<double>&); |
1542 | extern template istream& operator>>(istream&, complex<long double>&); |
1543 | extern template ostream& operator<<(ostream&, const complex<long double>&); |
1544 | |
1545 | #ifdef _GLIBCXX_USE_WCHAR_T |
1546 | extern template wistream& operator>>(wistream&, complex<float>&); |
1547 | extern template wostream& operator<<(wostream&, const complex<float>&); |
1548 | extern template wistream& operator>>(wistream&, complex<double>&); |
1549 | extern template wostream& operator<<(wostream&, const complex<double>&); |
1550 | extern template wistream& operator>>(wistream&, complex<long double>&); |
1551 | extern template wostream& operator<<(wostream&, const complex<long double>&); |
1552 | #endif |
1553 | #endif |
1554 | |
1555 | /// @} group complex_numbers |
1556 | |
1557 | _GLIBCXX_END_NAMESPACE_VERSION |
1558 | } // namespace |
1559 | |
1560 | namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) |
1561 | { |
1562 | _GLIBCXX_BEGIN_NAMESPACE_VERSION |
1563 | |
1564 | // See ext/type_traits.h for the primary template. |
1565 | template<typename _Tp, typename _Up> |
1566 | struct __promote_2<std::complex<_Tp>, _Up> |
1567 | { |
1568 | public: |
1569 | typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; |
1570 | }; |
1571 | |
1572 | template<typename _Tp, typename _Up> |
1573 | struct __promote_2<_Tp, std::complex<_Up> > |
1574 | { |
1575 | public: |
1576 | typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; |
1577 | }; |
1578 | |
1579 | template<typename _Tp, typename _Up> |
1580 | struct __promote_2<std::complex<_Tp>, std::complex<_Up> > |
1581 | { |
1582 | public: |
1583 | typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; |
1584 | }; |
1585 | |
1586 | _GLIBCXX_END_NAMESPACE_VERSION |
1587 | } // namespace |
1588 | |
1589 | #if __cplusplus >= 201103L |
1590 | |
1591 | namespace std _GLIBCXX_VISIBILITY(default) |
1592 | { |
1593 | _GLIBCXX_BEGIN_NAMESPACE_VERSION |
1594 | |
1595 | // Forward declarations. |
1596 | template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); |
1597 | template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); |
1598 | template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); |
1599 | |
1600 | template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); |
1601 | template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); |
1602 | template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); |
1603 | // DR 595. |
1604 | template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); |
1605 | |
1606 | template<typename _Tp> |
1607 | inline std::complex<_Tp> |
1608 | __complex_acos(const std::complex<_Tp>& __z) |
1609 | { |
1610 | const std::complex<_Tp> __t = std::asin(__z); |
1611 | const _Tp __pi_2 = 1.5707963267948966192313216916397514L; |
1612 | return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); |
1613 | } |
1614 | |
1615 | #if _GLIBCXX_USE_C99_COMPLEX_TR1 |
1616 | inline __complex__ float |
1617 | __complex_acos(__complex__ float __z) |
1618 | { return __builtin_cacosf(__z); } |
1619 | |
1620 | inline __complex__ double |
1621 | __complex_acos(__complex__ double __z) |
1622 | { return __builtin_cacos(__z); } |
1623 | |
1624 | inline __complex__ long double |
1625 | __complex_acos(const __complex__ long double& __z) |
1626 | { return __builtin_cacosl(__z); } |
1627 | |
1628 | template<typename _Tp> |
1629 | inline std::complex<_Tp> |
1630 | acos(const std::complex<_Tp>& __z) |
1631 | { return __complex_acos(__z.__rep()); } |
1632 | #else |
1633 | /// acos(__z) [8.1.2]. |
1634 | // Effects: Behaves the same as C99 function cacos, defined |
1635 | // in subclause 7.3.5.1. |
1636 | template<typename _Tp> |
1637 | inline std::complex<_Tp> |
1638 | acos(const std::complex<_Tp>& __z) |
1639 | { return __complex_acos(__z); } |
1640 | #endif |
1641 | |
1642 | template<typename _Tp> |
1643 | inline std::complex<_Tp> |
1644 | __complex_asin(const std::complex<_Tp>& __z) |
1645 | { |
1646 | std::complex<_Tp> __t(-__z.imag(), __z.real()); |
1647 | __t = std::asinh(__t); |
1648 | return std::complex<_Tp>(__t.imag(), -__t.real()); |
1649 | } |
1650 | |
1651 | #if _GLIBCXX_USE_C99_COMPLEX_TR1 |
1652 | inline __complex__ float |
1653 | __complex_asin(__complex__ float __z) |
1654 | { return __builtin_casinf(__z); } |
1655 | |
1656 | inline __complex__ double |
1657 | __complex_asin(__complex__ double __z) |
1658 | { return __builtin_casin(__z); } |
1659 | |
1660 | inline __complex__ long double |
1661 | __complex_asin(const __complex__ long double& __z) |
1662 | { return __builtin_casinl(__z); } |
1663 | |
1664 | template<typename _Tp> |
1665 | inline std::complex<_Tp> |
1666 | asin(const std::complex<_Tp>& __z) |
1667 | { return __complex_asin(__z.__rep()); } |
1668 | #else |
1669 | /// asin(__z) [8.1.3]. |
1670 | // Effects: Behaves the same as C99 function casin, defined |
1671 | // in subclause 7.3.5.2. |
1672 | template<typename _Tp> |
1673 | inline std::complex<_Tp> |
1674 | asin(const std::complex<_Tp>& __z) |
1675 | { return __complex_asin(__z); } |
1676 | #endif |
1677 | |
1678 | template<typename _Tp> |
1679 | std::complex<_Tp> |
1680 | __complex_atan(const std::complex<_Tp>& __z) |
1681 | { |
1682 | const _Tp __r2 = __z.real() * __z.real(); |
1683 | const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); |
1684 | |
1685 | _Tp __num = __z.imag() + _Tp(1.0); |
1686 | _Tp __den = __z.imag() - _Tp(1.0); |
1687 | |
1688 | __num = __r2 + __num * __num; |
1689 | __den = __r2 + __den * __den; |
1690 | |
1691 | return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), |
1692 | _Tp(0.25) * log(__num / __den)); |
1693 | } |
1694 | |
1695 | #if _GLIBCXX_USE_C99_COMPLEX_TR1 |
1696 | inline __complex__ float |
1697 | __complex_atan(__complex__ float __z) |
1698 | { return __builtin_catanf(__z); } |
1699 | |
1700 | inline __complex__ double |
1701 | __complex_atan(__complex__ double __z) |
1702 | { return __builtin_catan(__z); } |
1703 | |
1704 | inline __complex__ long double |
1705 | __complex_atan(const __complex__ long double& __z) |
1706 | { return __builtin_catanl(__z); } |
1707 | |
1708 | template<typename _Tp> |
1709 | inline std::complex<_Tp> |
1710 | atan(const std::complex<_Tp>& __z) |
1711 | { return __complex_atan(__z.__rep()); } |
1712 | #else |
1713 | /// atan(__z) [8.1.4]. |
1714 | // Effects: Behaves the same as C99 function catan, defined |
1715 | // in subclause 7.3.5.3. |
1716 | template<typename _Tp> |
1717 | inline std::complex<_Tp> |
1718 | atan(const std::complex<_Tp>& __z) |
1719 | { return __complex_atan(__z); } |
1720 | #endif |
1721 | |
1722 | template<typename _Tp> |
1723 | std::complex<_Tp> |
1724 | __complex_acosh(const std::complex<_Tp>& __z) |
1725 | { |
1726 | // Kahan's formula. |
1727 | return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) |
1728 | + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); |
1729 | } |
1730 | |
1731 | #if _GLIBCXX_USE_C99_COMPLEX_TR1 |
1732 | inline __complex__ float |
1733 | __complex_acosh(__complex__ float __z) |
1734 | { return __builtin_cacoshf(__z); } |
1735 | |
1736 | inline __complex__ double |
1737 | __complex_acosh(__complex__ double __z) |
1738 | { return __builtin_cacosh(__z); } |
1739 | |
1740 | inline __complex__ long double |
1741 | __complex_acosh(const __complex__ long double& __z) |
1742 | { return __builtin_cacoshl(__z); } |
1743 | |
1744 | template<typename _Tp> |
1745 | inline std::complex<_Tp> |
1746 | acosh(const std::complex<_Tp>& __z) |
1747 | { return __complex_acosh(__z.__rep()); } |
1748 | #else |
1749 | /// acosh(__z) [8.1.5]. |
1750 | // Effects: Behaves the same as C99 function cacosh, defined |
1751 | // in subclause 7.3.6.1. |
1752 | template<typename _Tp> |
1753 | inline std::complex<_Tp> |
1754 | acosh(const std::complex<_Tp>& __z) |
1755 | { return __complex_acosh(__z); } |
1756 | #endif |
1757 | |
1758 | template<typename _Tp> |
1759 | std::complex<_Tp> |
1760 | __complex_asinh(const std::complex<_Tp>& __z) |
1761 | { |
1762 | std::complex<_Tp> __t((__z.real() - __z.imag()) |
1763 | * (__z.real() + __z.imag()) + _Tp(1.0), |
1764 | _Tp(2.0) * __z.real() * __z.imag()); |
1765 | __t = std::sqrt(__t); |
1766 | |
1767 | return std::log(__t + __z); |
1768 | } |
1769 | |
1770 | #if _GLIBCXX_USE_C99_COMPLEX_TR1 |
1771 | inline __complex__ float |
1772 | __complex_asinh(__complex__ float __z) |
1773 | { return __builtin_casinhf(__z); } |
1774 | |
1775 | inline __complex__ double |
1776 | __complex_asinh(__complex__ double __z) |
1777 | { return __builtin_casinh(__z); } |
1778 | |
1779 | inline __complex__ long double |
1780 | __complex_asinh(const __complex__ long double& __z) |
1781 | { return __builtin_casinhl(__z); } |
1782 | |
1783 | template<typename _Tp> |
1784 | inline std::complex<_Tp> |
1785 | asinh(const std::complex<_Tp>& __z) |
1786 | { return __complex_asinh(__z.__rep()); } |
1787 | #else |
1788 | /// asinh(__z) [8.1.6]. |
1789 | // Effects: Behaves the same as C99 function casin, defined |
1790 | // in subclause 7.3.6.2. |
1791 | template<typename _Tp> |
1792 | inline std::complex<_Tp> |
1793 | asinh(const std::complex<_Tp>& __z) |
1794 | { return __complex_asinh(__z); } |
1795 | #endif |
1796 | |
1797 | template<typename _Tp> |
1798 | std::complex<_Tp> |
1799 | __complex_atanh(const std::complex<_Tp>& __z) |
1800 | { |
1801 | const _Tp __i2 = __z.imag() * __z.imag(); |
1802 | const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); |
1803 | |
1804 | _Tp __num = _Tp(1.0) + __z.real(); |
1805 | _Tp __den = _Tp(1.0) - __z.real(); |
1806 | |
1807 | __num = __i2 + __num * __num; |
1808 | __den = __i2 + __den * __den; |
1809 | |
1810 | return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), |
1811 | _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); |
1812 | } |
1813 | |
1814 | #if _GLIBCXX_USE_C99_COMPLEX_TR1 |
1815 | inline __complex__ float |
1816 | __complex_atanh(__complex__ float __z) |
1817 | { return __builtin_catanhf(__z); } |
1818 | |
1819 | inline __complex__ double |
1820 | __complex_atanh(__complex__ double __z) |
1821 | { return __builtin_catanh(__z); } |
1822 | |
1823 | inline __complex__ long double |
1824 | __complex_atanh(const __complex__ long double& __z) |
1825 | { return __builtin_catanhl(__z); } |
1826 | |
1827 | template<typename _Tp> |
1828 | inline std::complex<_Tp> |
1829 | atanh(const std::complex<_Tp>& __z) |
1830 | { return __complex_atanh(__z.__rep()); } |
1831 | #else |
1832 | /// atanh(__z) [8.1.7]. |
1833 | // Effects: Behaves the same as C99 function catanh, defined |
1834 | // in subclause 7.3.6.3. |
1835 | template<typename _Tp> |
1836 | inline std::complex<_Tp> |
1837 | atanh(const std::complex<_Tp>& __z) |
1838 | { return __complex_atanh(__z); } |
1839 | #endif |
1840 | |
1841 | template<typename _Tp> |
1842 | inline _Tp |
1843 | /// fabs(__z) [8.1.8]. |
1844 | // Effects: Behaves the same as C99 function cabs, defined |
1845 | // in subclause 7.3.8.1. |
1846 | fabs(const std::complex<_Tp>& __z) |
1847 | { return std::abs(__z); } |
1848 | |
1849 | /// Additional overloads [8.1.9]. |
1850 | template<typename _Tp> |
1851 | inline typename __gnu_cxx::__promote<_Tp>::__type |
1852 | arg(_Tp __x) |
1853 | { |
1854 | typedef typename __gnu_cxx::__promote<_Tp>::__type __type; |
1855 | #if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) |
1856 | return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) |
1857 | : __type(); |
1858 | #else |
1859 | return std::arg(std::complex<__type>(__x)); |
1860 | #endif |
1861 | } |
1862 | |
1863 | template<typename _Tp> |
1864 | _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type |
1865 | imag(_Tp) |
1866 | { return _Tp(); } |
1867 | |
1868 | template<typename _Tp> |
1869 | _GLIBCXX20_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type |
1870 | norm(_Tp __x) |
1871 | { |
1872 | typedef typename __gnu_cxx::__promote<_Tp>::__type __type; |
1873 | return __type(__x) * __type(__x); |
1874 | } |
1875 | |
1876 | template<typename _Tp> |
1877 | _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type |
1878 | real(_Tp __x) |
1879 | { return __x; } |
1880 | |
1881 | template<typename _Tp, typename _Up> |
1882 | inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> |
1883 | pow(const std::complex<_Tp>& __x, const _Up& __y) |
1884 | { |
1885 | typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; |
1886 | return std::pow(std::complex<__type>(__x), __type(__y)); |
1887 | } |
1888 | |
1889 | template<typename _Tp, typename _Up> |
1890 | inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> |
1891 | pow(const _Tp& __x, const std::complex<_Up>& __y) |
1892 | { |
1893 | typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; |
1894 | return std::pow(__type(__x), std::complex<__type>(__y)); |
1895 | } |
1896 | |
1897 | template<typename _Tp, typename _Up> |
1898 | inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> |
1899 | pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) |
1900 | { |
1901 | typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; |
1902 | return std::pow(std::complex<__type>(__x), |
1903 | std::complex<__type>(__y)); |
1904 | } |
1905 | |
1906 | // Forward declarations. |
1907 | // DR 781. |
1908 | template<typename _Tp> |
1909 | std::complex<_Tp> proj(const std::complex<_Tp>&); |
1910 | |
1911 | // Generic implementation of std::proj, does not work for infinities. |
1912 | template<typename _Tp> |
1913 | inline std::complex<_Tp> |
1914 | __complex_proj(const std::complex<_Tp>& __z) |
1915 | { return __z; } |
1916 | |
1917 | #if _GLIBCXX_USE_C99_COMPLEX |
1918 | inline complex<float> |
1919 | __complex_proj(const complex<float>& __z) |
1920 | { return __builtin_cprojf(__z.__rep()); } |
1921 | |
1922 | inline complex<double> |
1923 | __complex_proj(const complex<double>& __z) |
1924 | { return __builtin_cproj(__z.__rep()); } |
1925 | |
1926 | inline complex<long double> |
1927 | __complex_proj(const complex<long double>& __z) |
1928 | { return __builtin_cprojl(__z.__rep()); } |
1929 | #elif defined _GLIBCXX_USE_C99_MATH_TR1 |
1930 | inline complex<float> |
1931 | __complex_proj(const complex<float>& __z) |
1932 | { |
1933 | if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) |
1934 | return complex<float>(__builtin_inff(), |
1935 | __builtin_copysignf(0.0f, __z.imag())); |
1936 | return __z; |
1937 | } |
1938 | |
1939 | inline complex<double> |
1940 | __complex_proj(const complex<double>& __z) |
1941 | { |
1942 | if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) |
1943 | return complex<double>(__builtin_inf(), |
1944 | __builtin_copysign(0.0, __z.imag())); |
1945 | return __z; |
1946 | } |
1947 | |
1948 | inline complex<long double> |
1949 | __complex_proj(const complex<long double>& __z) |
1950 | { |
1951 | if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) |
1952 | return complex<long double>(__builtin_infl(), |
1953 | __builtin_copysignl(0.0l, __z.imag())); |
1954 | return __z; |
1955 | } |
1956 | #endif |
1957 | |
1958 | template<typename _Tp> |
1959 | inline std::complex<_Tp> |
1960 | proj(const std::complex<_Tp>& __z) |
1961 | { return __complex_proj(__z); } |
1962 | |
1963 | // Overload for scalars |
1964 | template<typename _Tp> |
1965 | inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> |
1966 | proj(_Tp __x) |
1967 | { |
1968 | typedef typename __gnu_cxx::__promote<_Tp>::__type __type; |
1969 | return std::proj(std::complex<__type>(__x)); |
1970 | } |
1971 | |
1972 | template<typename _Tp> |
1973 | inline _GLIBCXX20_CONSTEXPR |
1974 | std::complex<typename __gnu_cxx::__promote<_Tp>::__type> |
1975 | conj(_Tp __x) |
1976 | { |
1977 | typedef typename __gnu_cxx::__promote<_Tp>::__type __type; |
1978 | return std::complex<__type>(__x, -__type()); |
1979 | } |
1980 | |
1981 | #if __cplusplus > 201103L |
1982 | |
1983 | inline namespace literals { |
1984 | inline namespace complex_literals { |
1985 | #pragma GCC diagnostic push |
1986 | #pragma GCC diagnostic ignored "-Wliteral-suffix" |
1987 | #define __cpp_lib_complex_udls 201309 |
1988 | |
1989 | constexpr std::complex<float> |
1990 | operator""if (long double __num) |
1991 | { return std::complex<float>{0.0F, static_cast<float>(__num)}; } |
1992 | |
1993 | constexpr std::complex<float> |
1994 | operator""if (unsigned long long __num) |
1995 | { return std::complex<float>{0.0F, static_cast<float>(__num)}; } |
1996 | |
1997 | constexpr std::complex<double> |
1998 | operator""i (long double __num) |
1999 | { return std::complex<double>{0.0, static_cast<double>(__num)}; } |
2000 | |
2001 | constexpr std::complex<double> |
2002 | operator""i (unsigned long long __num) |
2003 | { return std::complex<double>{0.0, static_cast<double>(__num)}; } |
2004 | |
2005 | constexpr std::complex<long double> |
2006 | operator""il (long double __num) |
2007 | { return std::complex<long double>{0.0L, __num}; } |
2008 | |
2009 | constexpr std::complex<long double> |
2010 | operator""il (unsigned long long __num) |
2011 | { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } |
2012 | |
2013 | #pragma GCC diagnostic pop |
2014 | } // inline namespace complex_literals |
2015 | } // inline namespace literals |
2016 | |
2017 | #endif // C++14 |
2018 | |
2019 | _GLIBCXX_END_NAMESPACE_VERSION |
2020 | } // namespace |
2021 | |
2022 | #endif // C++11 |
2023 | |
2024 | #endif /* _GLIBCXX_COMPLEX */ |
2025 | |