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