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