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 = _CharT();
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 if (__is)
515 {
516 __is.putback(__ch);
517 if (__is >> __re_x)
518 __x = __re_x;
519 else
520 __is.setstate(ios_base::failbit);
521 }
522 return __is;
523 }
524
525 /// Insertion operator for complex values.
526 template<typename _Tp, typename _CharT, class _Traits>
527 basic_ostream<_CharT, _Traits>&
528 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
529 {
530 basic_ostringstream<_CharT, _Traits> __s;
531 __s.flags(__os.flags());
532 __s.imbue(__os.getloc());
533 __s.precision(__os.precision());
534 __s << '(' << __x.real() << ',' << __x.imag() << ')';
535 return __os << __s.str();
536 }
537
538 // Values
539#if __cplusplus >= 201103L
540 template<typename _Tp>
541 constexpr _Tp
542 real(const complex<_Tp>& __z)
543 { return __z.real(); }
544
545 template<typename _Tp>
546 constexpr _Tp
547 imag(const complex<_Tp>& __z)
548 { return __z.imag(); }
549#else
550 template<typename _Tp>
551 inline _Tp&
552 real(complex<_Tp>& __z)
553 { return __z.real(); }
554
555 template<typename _Tp>
556 inline const _Tp&
557 real(const complex<_Tp>& __z)
558 { return __z.real(); }
559
560 template<typename _Tp>
561 inline _Tp&
562 imag(complex<_Tp>& __z)
563 { return __z.imag(); }
564
565 template<typename _Tp>
566 inline const _Tp&
567 imag(const complex<_Tp>& __z)
568 { return __z.imag(); }
569#endif
570
571 // 26.2.7/3 abs(__z): Returns the magnitude of __z.
572 template<typename _Tp>
573 inline _Tp
574 __complex_abs(const complex<_Tp>& __z)
575 {
576 _Tp __x = __z.real();
577 _Tp __y = __z.imag();
578 const _Tp __s = std::max(abs(__x), abs(__y));
579 if (__s == _Tp()) // well ...
580 return __s;
581 __x /= __s;
582 __y /= __s;
583 return __s * sqrt(__x * __x + __y * __y);
584 }
585
586#if _GLIBCXX_USE_C99_COMPLEX
587 inline float
588 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
589
590 inline double
591 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
592
593 inline long double
594 __complex_abs(const __complex__ long double& __z)
595 { return __builtin_cabsl(__z); }
596
597 template<typename _Tp>
598 inline _Tp
599 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
600#else
601 template<typename _Tp>
602 inline _Tp
603 abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
604#endif
605
606
607 // 26.2.7/4: arg(__z): Returns the phase angle of __z.
608 template<typename _Tp>
609 inline _Tp
610 __complex_arg(const complex<_Tp>& __z)
611 { return atan2(__z.imag(), __z.real()); }
612
613#if _GLIBCXX_USE_C99_COMPLEX
614 inline float
615 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
616
617 inline double
618 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
619
620 inline long double
621 __complex_arg(const __complex__ long double& __z)
622 { return __builtin_cargl(__z); }
623
624 template<typename _Tp>
625 inline _Tp
626 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
627#else
628 template<typename _Tp>
629 inline _Tp
630 arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
631#endif
632
633 // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
634 // As defined, norm() is -not- a norm is the common mathematical
635 // sense used in numerics. The helper class _Norm_helper<> tries to
636 // distinguish between builtin floating point and the rest, so as
637 // to deliver an answer as close as possible to the real value.
638 template<bool>
639 struct _Norm_helper
640 {
641 template<typename _Tp>
642 static inline _Tp _S_do_it(const complex<_Tp>& __z)
643 {
644 const _Tp __x = __z.real();
645 const _Tp __y = __z.imag();
646 return __x * __x + __y * __y;
647 }
648 };
649
650 template<>
651 struct _Norm_helper<true>
652 {
653 template<typename _Tp>
654 static inline _Tp _S_do_it(const complex<_Tp>& __z)
655 {
656 _Tp __res = std::abs(__z);
657 return __res * __res;
658 }
659 };
660
661 template<typename _Tp>
662 inline _Tp
663 norm(const complex<_Tp>& __z)
664 {
665 return _Norm_helper<__is_floating<_Tp>::__value
666 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
667 }
668
669 template<typename _Tp>
670 inline complex<_Tp>
671 polar(const _Tp& __rho, const _Tp& __theta)
672 {
673 __glibcxx_assert( __rho >= 0 );
674 return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
675 }
676
677 template<typename _Tp>
678 inline complex<_Tp>
679 conj(const complex<_Tp>& __z)
680 { return complex<_Tp>(__z.real(), -__z.imag()); }
681
682 // Transcendentals
683
684 // 26.2.8/1 cos(__z): Returns the cosine of __z.
685 template<typename _Tp>
686 inline complex<_Tp>
687 __complex_cos(const complex<_Tp>& __z)
688 {
689 const _Tp __x = __z.real();
690 const _Tp __y = __z.imag();
691 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
692 }
693
694#if _GLIBCXX_USE_C99_COMPLEX
695 inline __complex__ float
696 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
697
698 inline __complex__ double
699 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
700
701 inline __complex__ long double
702 __complex_cos(const __complex__ long double& __z)
703 { return __builtin_ccosl(__z); }
704
705 template<typename _Tp>
706 inline complex<_Tp>
707 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
708#else
709 template<typename _Tp>
710 inline complex<_Tp>
711 cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
712#endif
713
714 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
715 template<typename _Tp>
716 inline complex<_Tp>
717 __complex_cosh(const complex<_Tp>& __z)
718 {
719 const _Tp __x = __z.real();
720 const _Tp __y = __z.imag();
721 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
722 }
723
724#if _GLIBCXX_USE_C99_COMPLEX
725 inline __complex__ float
726 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
727
728 inline __complex__ double
729 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
730
731 inline __complex__ long double
732 __complex_cosh(const __complex__ long double& __z)
733 { return __builtin_ccoshl(__z); }
734
735 template<typename _Tp>
736 inline complex<_Tp>
737 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
738#else
739 template<typename _Tp>
740 inline complex<_Tp>
741 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
742#endif
743
744 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
745 template<typename _Tp>
746 inline complex<_Tp>
747 __complex_exp(const complex<_Tp>& __z)
748 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); }
749
750#if _GLIBCXX_USE_C99_COMPLEX
751 inline __complex__ float
752 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
753
754 inline __complex__ double
755 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
756
757 inline __complex__ long double
758 __complex_exp(const __complex__ long double& __z)
759 { return __builtin_cexpl(__z); }
760
761 template<typename _Tp>
762 inline complex<_Tp>
763 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
764#else
765 template<typename _Tp>
766 inline complex<_Tp>
767 exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
768#endif
769
770 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
771 // The branch cut is along the negative axis.
772 template<typename _Tp>
773 inline complex<_Tp>
774 __complex_log(const complex<_Tp>& __z)
775 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
776
777#if _GLIBCXX_USE_C99_COMPLEX
778 inline __complex__ float
779 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
780
781 inline __complex__ double
782 __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
783
784 inline __complex__ long double
785 __complex_log(const __complex__ long double& __z)
786 { return __builtin_clogl(__z); }
787
788 template<typename _Tp>
789 inline complex<_Tp>
790 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
791#else
792 template<typename _Tp>
793 inline complex<_Tp>
794 log(const complex<_Tp>& __z) { return __complex_log(__z); }
795#endif
796
797 template<typename _Tp>
798 inline complex<_Tp>
799 log10(const complex<_Tp>& __z)
800 { return std::log(__z) / log(_Tp(10.0)); }
801
802 // 26.2.8/10 sin(__z): Returns the sine of __z.
803 template<typename _Tp>
804 inline complex<_Tp>
805 __complex_sin(const complex<_Tp>& __z)
806 {
807 const _Tp __x = __z.real();
808 const _Tp __y = __z.imag();
809 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
810 }
811
812#if _GLIBCXX_USE_C99_COMPLEX
813 inline __complex__ float
814 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
815
816 inline __complex__ double
817 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
818
819 inline __complex__ long double
820 __complex_sin(const __complex__ long double& __z)
821 { return __builtin_csinl(__z); }
822
823 template<typename _Tp>
824 inline complex<_Tp>
825 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
826#else
827 template<typename _Tp>
828 inline complex<_Tp>
829 sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
830#endif
831
832 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
833 template<typename _Tp>
834 inline complex<_Tp>
835 __complex_sinh(const complex<_Tp>& __z)
836 {
837 const _Tp __x = __z.real();
838 const _Tp __y = __z.imag();
839 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
840 }
841
842#if _GLIBCXX_USE_C99_COMPLEX
843 inline __complex__ float
844 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
845
846 inline __complex__ double
847 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
848
849 inline __complex__ long double
850 __complex_sinh(const __complex__ long double& __z)
851 { return __builtin_csinhl(__z); }
852
853 template<typename _Tp>
854 inline complex<_Tp>
855 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
856#else
857 template<typename _Tp>
858 inline complex<_Tp>
859 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
860#endif
861
862 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
863 // The branch cut is on the negative axis.
864 template<typename _Tp>
865 complex<_Tp>
866 __complex_sqrt(const complex<_Tp>& __z)
867 {
868 _Tp __x = __z.real();
869 _Tp __y = __z.imag();
870
871 if (__x == _Tp())
872 {
873 _Tp __t = sqrt(abs(__y) / 2);
874 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
875 }
876 else
877 {
878 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
879 _Tp __u = __t / 2;
880 return __x > _Tp()
881 ? complex<_Tp>(__u, __y / __t)
882 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
883 }
884 }
885
886#if _GLIBCXX_USE_C99_COMPLEX
887 inline __complex__ float
888 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
889
890 inline __complex__ double
891 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
892
893 inline __complex__ long double
894 __complex_sqrt(const __complex__ long double& __z)
895 { return __builtin_csqrtl(__z); }
896
897 template<typename _Tp>
898 inline complex<_Tp>
899 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
900#else
901 template<typename _Tp>
902 inline complex<_Tp>
903 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
904#endif
905
906 // 26.2.8/14 tan(__z): Return the complex tangent of __z.
907
908 template<typename _Tp>
909 inline complex<_Tp>
910 __complex_tan(const complex<_Tp>& __z)
911 { return std::sin(__z) / std::cos(__z); }
912
913#if _GLIBCXX_USE_C99_COMPLEX
914 inline __complex__ float
915 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
916
917 inline __complex__ double
918 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
919
920 inline __complex__ long double
921 __complex_tan(const __complex__ long double& __z)
922 { return __builtin_ctanl(__z); }
923
924 template<typename _Tp>
925 inline complex<_Tp>
926 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
927#else
928 template<typename _Tp>
929 inline complex<_Tp>
930 tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
931#endif
932
933
934 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
935
936 template<typename _Tp>
937 inline complex<_Tp>
938 __complex_tanh(const complex<_Tp>& __z)
939 { return std::sinh(__z) / std::cosh(__z); }
940
941#if _GLIBCXX_USE_C99_COMPLEX
942 inline __complex__ float
943 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
944
945 inline __complex__ double
946 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
947
948 inline __complex__ long double
949 __complex_tanh(const __complex__ long double& __z)
950 { return __builtin_ctanhl(__z); }
951
952 template<typename _Tp>
953 inline complex<_Tp>
954 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
955#else
956 template<typename _Tp>
957 inline complex<_Tp>
958 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
959#endif
960
961
962 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
963 // raised to the __y-th power. The branch
964 // cut is on the negative axis.
965 template<typename _Tp>
966 complex<_Tp>
967 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
968 {
969 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
970
971 while (__n >>= 1)
972 {
973 __x *= __x;
974 if (__n % 2)
975 __y *= __x;
976 }
977
978 return __y;
979 }
980
981 // In C++11 mode we used to implement the resolution of
982 // DR 844. complex pow return type is ambiguous.
983 // thus the following overload was disabled in that mode. However, doing
984 // that causes all sorts of issues, see, for example:
985 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html
986 // and also PR57974.
987 template<typename _Tp>
988 inline complex<_Tp>
989 pow(const complex<_Tp>& __z, int __n)
990 {
991 return __n < 0
992 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
993 : std::__complex_pow_unsigned(__z, __n);
994 }
995
996 template<typename _Tp>
997 complex<_Tp>
998 pow(const complex<_Tp>& __x, const _Tp& __y)
999 {
1000#if ! _GLIBCXX_USE_C99_COMPLEX
1001 if (__x == _Tp())
1002 return _Tp();
1003#endif
1004 if (__x.imag() == _Tp() && __x.real() > _Tp())
1005 return pow(__x.real(), __y);
1006
1007 complex<_Tp> __t = std::log(__x);
1008 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
1009 }
1010
1011 template<typename _Tp>
1012 inline complex<_Tp>
1013 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1014 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
1015
1016#if _GLIBCXX_USE_C99_COMPLEX
1017 inline __complex__ float
1018 __complex_pow(__complex__ float __x, __complex__ float __y)
1019 { return __builtin_cpowf(__x, __y); }
1020
1021 inline __complex__ double
1022 __complex_pow(__complex__ double __x, __complex__ double __y)
1023 { return __builtin_cpow(__x, __y); }
1024
1025 inline __complex__ long double
1026 __complex_pow(const __complex__ long double& __x,
1027 const __complex__ long double& __y)
1028 { return __builtin_cpowl(__x, __y); }
1029
1030 template<typename _Tp>
1031 inline complex<_Tp>
1032 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1033 { return __complex_pow(__x.__rep(), __y.__rep()); }
1034#else
1035 template<typename _Tp>
1036 inline complex<_Tp>
1037 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1038 { return __complex_pow(__x, __y); }
1039#endif
1040
1041 template<typename _Tp>
1042 inline complex<_Tp>
1043 pow(const _Tp& __x, const complex<_Tp>& __y)
1044 {
1045 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
1046 __y.imag() * log(__x))
1047 : std::pow(complex<_Tp>(__x), __y);
1048 }
1049
1050 /// 26.2.3 complex specializations
1051 /// complex<float> specialization
1052 template<>
1053 struct complex<float>
1054 {
1055 typedef float value_type;
1056 typedef __complex__ float _ComplexT;
1057
1058 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1059
1060 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
1061#if __cplusplus >= 201103L
1062 : _M_value{ __r, __i } { }
1063#else
1064 {
1065 __real__ _M_value = __r;
1066 __imag__ _M_value = __i;
1067 }
1068#endif
1069
1070 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
1071 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1072
1073#if __cplusplus >= 201103L
1074 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1075 // DR 387. std::complex over-encapsulated.
1076 __attribute ((__abi_tag__ ("cxx11")))
1077 constexpr float
1078 real() const { return __real__ _M_value; }
1079
1080 __attribute ((__abi_tag__ ("cxx11")))
1081 constexpr float
1082 imag() const { return __imag__ _M_value; }
1083#else
1084 float&
1085 real() { return __real__ _M_value; }
1086
1087 const float&
1088 real() const { return __real__ _M_value; }
1089
1090 float&
1091 imag() { return __imag__ _M_value; }
1092
1093 const float&
1094 imag() const { return __imag__ _M_value; }
1095#endif
1096
1097 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1098 // DR 387. std::complex over-encapsulated.
1099 void
1100 real(float __val) { __real__ _M_value = __val; }
1101
1102 void
1103 imag(float __val) { __imag__ _M_value = __val; }
1104
1105 complex&
1106 operator=(float __f)
1107 {
1108 _M_value = __f;
1109 return *this;
1110 }
1111
1112 complex&
1113 operator+=(float __f)
1114 {
1115 _M_value += __f;
1116 return *this;
1117 }
1118
1119 complex&
1120 operator-=(float __f)
1121 {
1122 _M_value -= __f;
1123 return *this;
1124 }
1125
1126 complex&
1127 operator*=(float __f)
1128 {
1129 _M_value *= __f;
1130 return *this;
1131 }
1132
1133 complex&
1134 operator/=(float __f)
1135 {
1136 _M_value /= __f;
1137 return *this;
1138 }
1139
1140 // Let the compiler synthesize the copy and assignment
1141 // operator. It always does a pretty good job.
1142 // complex& operator=(const complex&);
1143
1144 template<typename _Tp>
1145 complex&
1146 operator=(const complex<_Tp>& __z)
1147 {
1148 __real__ _M_value = __z.real();
1149 __imag__ _M_value = __z.imag();
1150 return *this;
1151 }
1152
1153 template<typename _Tp>
1154 complex&
1155 operator+=(const complex<_Tp>& __z)
1156 {
1157 __real__ _M_value += __z.real();
1158 __imag__ _M_value += __z.imag();
1159 return *this;
1160 }
1161
1162 template<class _Tp>
1163 complex&
1164 operator-=(const complex<_Tp>& __z)
1165 {
1166 __real__ _M_value -= __z.real();
1167 __imag__ _M_value -= __z.imag();
1168 return *this;
1169 }
1170
1171 template<class _Tp>
1172 complex&
1173 operator*=(const complex<_Tp>& __z)
1174 {
1175 _ComplexT __t;
1176 __real__ __t = __z.real();
1177 __imag__ __t = __z.imag();
1178 _M_value *= __t;
1179 return *this;
1180 }
1181
1182 template<class _Tp>
1183 complex&
1184 operator/=(const complex<_Tp>& __z)
1185 {
1186 _ComplexT __t;
1187 __real__ __t = __z.real();
1188 __imag__ __t = __z.imag();
1189 _M_value /= __t;
1190 return *this;
1191 }
1192
1193 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1194
1195 private:
1196 _ComplexT _M_value;
1197 };
1198
1199 /// 26.2.3 complex specializations
1200 /// complex<double> specialization
1201 template<>
1202 struct complex<double>
1203 {
1204 typedef double value_type;
1205 typedef __complex__ double _ComplexT;
1206
1207 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1208
1209 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
1210#if __cplusplus >= 201103L
1211 : _M_value{ __r, __i } { }
1212#else
1213 {
1214 __real__ _M_value = __r;
1215 __imag__ _M_value = __i;
1216 }
1217#endif
1218
1219 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1220 : _M_value(__z.__rep()) { }
1221
1222 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1223
1224#if __cplusplus >= 201103L
1225 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1226 // DR 387. std::complex over-encapsulated.
1227 __attribute ((__abi_tag__ ("cxx11")))
1228 constexpr double
1229 real() const { return __real__ _M_value; }
1230
1231 __attribute ((__abi_tag__ ("cxx11")))
1232 constexpr double
1233 imag() const { return __imag__ _M_value; }
1234#else
1235 double&
1236 real() { return __real__ _M_value; }
1237
1238 const double&
1239 real() const { return __real__ _M_value; }
1240
1241 double&
1242 imag() { return __imag__ _M_value; }
1243
1244 const double&
1245 imag() const { return __imag__ _M_value; }
1246#endif
1247
1248 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1249 // DR 387. std::complex over-encapsulated.
1250 void
1251 real(double __val) { __real__ _M_value = __val; }
1252
1253 void
1254 imag(double __val) { __imag__ _M_value = __val; }
1255
1256 complex&
1257 operator=(double __d)
1258 {
1259 _M_value = __d;
1260 return *this;
1261 }
1262
1263 complex&
1264 operator+=(double __d)
1265 {
1266 _M_value += __d;
1267 return *this;
1268 }
1269
1270 complex&
1271 operator-=(double __d)
1272 {
1273 _M_value -= __d;
1274 return *this;
1275 }
1276
1277 complex&
1278 operator*=(double __d)
1279 {
1280 _M_value *= __d;
1281 return *this;
1282 }
1283
1284 complex&
1285 operator/=(double __d)
1286 {
1287 _M_value /= __d;
1288 return *this;
1289 }
1290
1291 // The compiler will synthesize this, efficiently.
1292 // complex& operator=(const complex&);
1293
1294 template<typename _Tp>
1295 complex&
1296 operator=(const complex<_Tp>& __z)
1297 {
1298 __real__ _M_value = __z.real();
1299 __imag__ _M_value = __z.imag();
1300 return *this;
1301 }
1302
1303 template<typename _Tp>
1304 complex&
1305 operator+=(const complex<_Tp>& __z)
1306 {
1307 __real__ _M_value += __z.real();
1308 __imag__ _M_value += __z.imag();
1309 return *this;
1310 }
1311
1312 template<typename _Tp>
1313 complex&
1314 operator-=(const complex<_Tp>& __z)
1315 {
1316 __real__ _M_value -= __z.real();
1317 __imag__ _M_value -= __z.imag();
1318 return *this;
1319 }
1320
1321 template<typename _Tp>
1322 complex&
1323 operator*=(const complex<_Tp>& __z)
1324 {
1325 _ComplexT __t;
1326 __real__ __t = __z.real();
1327 __imag__ __t = __z.imag();
1328 _M_value *= __t;
1329 return *this;
1330 }
1331
1332 template<typename _Tp>
1333 complex&
1334 operator/=(const complex<_Tp>& __z)
1335 {
1336 _ComplexT __t;
1337 __real__ __t = __z.real();
1338 __imag__ __t = __z.imag();
1339 _M_value /= __t;
1340 return *this;
1341 }
1342
1343 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1344
1345 private:
1346 _ComplexT _M_value;
1347 };
1348
1349 /// 26.2.3 complex specializations
1350 /// complex<long double> specialization
1351 template<>
1352 struct complex<long double>
1353 {
1354 typedef long double value_type;
1355 typedef __complex__ long double _ComplexT;
1356
1357 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1358
1359 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
1360 long double __i = 0.0L)
1361#if __cplusplus >= 201103L
1362 : _M_value{ __r, __i } { }
1363#else
1364 {
1365 __real__ _M_value = __r;
1366 __imag__ _M_value = __i;
1367 }
1368#endif
1369
1370 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1371 : _M_value(__z.__rep()) { }
1372
1373 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
1374 : _M_value(__z.__rep()) { }
1375
1376#if __cplusplus >= 201103L
1377 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1378 // DR 387. std::complex over-encapsulated.
1379 __attribute ((__abi_tag__ ("cxx11")))
1380 constexpr long double
1381 real() const { return __real__ _M_value; }
1382
1383 __attribute ((__abi_tag__ ("cxx11")))
1384 constexpr long double
1385 imag() const { return __imag__ _M_value; }
1386#else
1387 long double&
1388 real() { return __real__ _M_value; }
1389
1390 const long double&
1391 real() const { return __real__ _M_value; }
1392
1393 long double&
1394 imag() { return __imag__ _M_value; }
1395
1396 const long double&
1397 imag() const { return __imag__ _M_value; }
1398#endif
1399
1400 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1401 // DR 387. std::complex over-encapsulated.
1402 void
1403 real(long double __val) { __real__ _M_value = __val; }
1404
1405 void
1406 imag(long double __val) { __imag__ _M_value = __val; }
1407
1408 complex&
1409 operator=(long double __r)
1410 {
1411 _M_value = __r;
1412 return *this;
1413 }
1414
1415 complex&
1416 operator+=(long double __r)
1417 {
1418 _M_value += __r;
1419 return *this;
1420 }
1421
1422 complex&
1423 operator-=(long double __r)
1424 {
1425 _M_value -= __r;
1426 return *this;
1427 }
1428
1429 complex&
1430 operator*=(long double __r)
1431 {
1432 _M_value *= __r;
1433 return *this;
1434 }
1435
1436 complex&
1437 operator/=(long double __r)
1438 {
1439 _M_value /= __r;
1440 return *this;
1441 }
1442
1443 // The compiler knows how to do this efficiently
1444 // complex& operator=(const complex&);
1445
1446 template<typename _Tp>
1447 complex&
1448 operator=(const complex<_Tp>& __z)
1449 {
1450 __real__ _M_value = __z.real();
1451 __imag__ _M_value = __z.imag();
1452 return *this;
1453 }
1454
1455 template<typename _Tp>
1456 complex&
1457 operator+=(const complex<_Tp>& __z)
1458 {
1459 __real__ _M_value += __z.real();
1460 __imag__ _M_value += __z.imag();
1461 return *this;
1462 }
1463
1464 template<typename _Tp>
1465 complex&
1466 operator-=(const complex<_Tp>& __z)
1467 {
1468 __real__ _M_value -= __z.real();
1469 __imag__ _M_value -= __z.imag();
1470 return *this;
1471 }
1472
1473 template<typename _Tp>
1474 complex&
1475 operator*=(const complex<_Tp>& __z)
1476 {
1477 _ComplexT __t;
1478 __real__ __t = __z.real();
1479 __imag__ __t = __z.imag();
1480 _M_value *= __t;
1481 return *this;
1482 }
1483
1484 template<typename _Tp>
1485 complex&
1486 operator/=(const complex<_Tp>& __z)
1487 {
1488 _ComplexT __t;
1489 __real__ __t = __z.real();
1490 __imag__ __t = __z.imag();
1491 _M_value /= __t;
1492 return *this;
1493 }
1494
1495 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1496
1497 private:
1498 _ComplexT _M_value;
1499 };
1500
1501 // These bits have to be at the end of this file, so that the
1502 // specializations have all been defined.
1503 inline _GLIBCXX_CONSTEXPR
1504 complex<float>::complex(const complex<double>& __z)
1505 : _M_value(__z.__rep()) { }
1506
1507 inline _GLIBCXX_CONSTEXPR
1508 complex<float>::complex(const complex<long double>& __z)
1509 : _M_value(__z.__rep()) { }
1510
1511 inline _GLIBCXX_CONSTEXPR
1512 complex<double>::complex(const complex<long double>& __z)
1513 : _M_value(__z.__rep()) { }
1514
1515 // Inhibit implicit instantiations for required instantiations,
1516 // which are defined via explicit instantiations elsewhere.
1517 // NB: This syntax is a GNU extension.
1518#if _GLIBCXX_EXTERN_TEMPLATE
1519 extern template istream& operator>>(istream&, complex<float>&);
1520 extern template ostream& operator<<(ostream&, const complex<float>&);
1521 extern template istream& operator>>(istream&, complex<double>&);
1522 extern template ostream& operator<<(ostream&, const complex<double>&);
1523 extern template istream& operator>>(istream&, complex<long double>&);
1524 extern template ostream& operator<<(ostream&, const complex<long double>&);
1525
1526#ifdef _GLIBCXX_USE_WCHAR_T
1527 extern template wistream& operator>>(wistream&, complex<float>&);
1528 extern template wostream& operator<<(wostream&, const complex<float>&);
1529 extern template wistream& operator>>(wistream&, complex<double>&);
1530 extern template wostream& operator<<(wostream&, const complex<double>&);
1531 extern template wistream& operator>>(wistream&, complex<long double>&);
1532 extern template wostream& operator<<(wostream&, const complex<long double>&);
1533#endif
1534#endif
1535
1536 // @} group complex_numbers
1537
1538_GLIBCXX_END_NAMESPACE_VERSION
1539} // namespace
1540
1541namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
1542{
1543_GLIBCXX_BEGIN_NAMESPACE_VERSION
1544
1545 // See ext/type_traits.h for the primary template.
1546 template<typename _Tp, typename _Up>
1547 struct __promote_2<std::complex<_Tp>, _Up>
1548 {
1549 public:
1550 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1551 };
1552
1553 template<typename _Tp, typename _Up>
1554 struct __promote_2<_Tp, std::complex<_Up> >
1555 {
1556 public:
1557 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1558 };
1559
1560 template<typename _Tp, typename _Up>
1561 struct __promote_2<std::complex<_Tp>, std::complex<_Up> >
1562 {
1563 public:
1564 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1565 };
1566
1567_GLIBCXX_END_NAMESPACE_VERSION
1568} // namespace
1569
1570#if __cplusplus >= 201103L
1571
1572namespace std _GLIBCXX_VISIBILITY(default)
1573{
1574_GLIBCXX_BEGIN_NAMESPACE_VERSION
1575
1576 // Forward declarations.
1577 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
1578 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
1579 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
1580
1581 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
1582 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
1583 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
1584 // DR 595.
1585 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
1586
1587 template<typename _Tp>
1588 inline std::complex<_Tp>
1589 __complex_acos(const std::complex<_Tp>& __z)
1590 {
1591 const std::complex<_Tp> __t = std::asin(__z);
1592 const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
1593 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
1594 }
1595
1596#if _GLIBCXX_USE_C99_COMPLEX_TR1
1597 inline __complex__ float
1598 __complex_acos(__complex__ float __z)
1599 { return __builtin_cacosf(__z); }
1600
1601 inline __complex__ double
1602 __complex_acos(__complex__ double __z)
1603 { return __builtin_cacos(__z); }
1604
1605 inline __complex__ long double
1606 __complex_acos(const __complex__ long double& __z)
1607 { return __builtin_cacosl(__z); }
1608
1609 template<typename _Tp>
1610 inline std::complex<_Tp>
1611 acos(const std::complex<_Tp>& __z)
1612 { return __complex_acos(__z.__rep()); }
1613#else
1614 /// acos(__z) [8.1.2].
1615 // Effects: Behaves the same as C99 function cacos, defined
1616 // in subclause 7.3.5.1.
1617 template<typename _Tp>
1618 inline std::complex<_Tp>
1619 acos(const std::complex<_Tp>& __z)
1620 { return __complex_acos(__z); }
1621#endif
1622
1623 template<typename _Tp>
1624 inline std::complex<_Tp>
1625 __complex_asin(const std::complex<_Tp>& __z)
1626 {
1627 std::complex<_Tp> __t(-__z.imag(), __z.real());
1628 __t = std::asinh(__t);
1629 return std::complex<_Tp>(__t.imag(), -__t.real());
1630 }
1631
1632#if _GLIBCXX_USE_C99_COMPLEX_TR1
1633 inline __complex__ float
1634 __complex_asin(__complex__ float __z)
1635 { return __builtin_casinf(__z); }
1636
1637 inline __complex__ double
1638 __complex_asin(__complex__ double __z)
1639 { return __builtin_casin(__z); }
1640
1641 inline __complex__ long double
1642 __complex_asin(const __complex__ long double& __z)
1643 { return __builtin_casinl(__z); }
1644
1645 template<typename _Tp>
1646 inline std::complex<_Tp>
1647 asin(const std::complex<_Tp>& __z)
1648 { return __complex_asin(__z.__rep()); }
1649#else
1650 /// asin(__z) [8.1.3].
1651 // Effects: Behaves the same as C99 function casin, defined
1652 // in subclause 7.3.5.2.
1653 template<typename _Tp>
1654 inline std::complex<_Tp>
1655 asin(const std::complex<_Tp>& __z)
1656 { return __complex_asin(__z); }
1657#endif
1658
1659 template<typename _Tp>
1660 std::complex<_Tp>
1661 __complex_atan(const std::complex<_Tp>& __z)
1662 {
1663 const _Tp __r2 = __z.real() * __z.real();
1664 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
1665
1666 _Tp __num = __z.imag() + _Tp(1.0);
1667 _Tp __den = __z.imag() - _Tp(1.0);
1668
1669 __num = __r2 + __num * __num;
1670 __den = __r2 + __den * __den;
1671
1672 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
1673 _Tp(0.25) * log(__num / __den));
1674 }
1675
1676#if _GLIBCXX_USE_C99_COMPLEX_TR1
1677 inline __complex__ float
1678 __complex_atan(__complex__ float __z)
1679 { return __builtin_catanf(__z); }
1680
1681 inline __complex__ double
1682 __complex_atan(__complex__ double __z)
1683 { return __builtin_catan(__z); }
1684
1685 inline __complex__ long double
1686 __complex_atan(const __complex__ long double& __z)
1687 { return __builtin_catanl(__z); }
1688
1689 template<typename _Tp>
1690 inline std::complex<_Tp>
1691 atan(const std::complex<_Tp>& __z)
1692 { return __complex_atan(__z.__rep()); }
1693#else
1694 /// atan(__z) [8.1.4].
1695 // Effects: Behaves the same as C99 function catan, defined
1696 // in subclause 7.3.5.3.
1697 template<typename _Tp>
1698 inline std::complex<_Tp>
1699 atan(const std::complex<_Tp>& __z)
1700 { return __complex_atan(__z); }
1701#endif
1702
1703 template<typename _Tp>
1704 std::complex<_Tp>
1705 __complex_acosh(const std::complex<_Tp>& __z)
1706 {
1707 // Kahan's formula.
1708 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
1709 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
1710 }
1711
1712#if _GLIBCXX_USE_C99_COMPLEX_TR1
1713 inline __complex__ float
1714 __complex_acosh(__complex__ float __z)
1715 { return __builtin_cacoshf(__z); }
1716
1717 inline __complex__ double
1718 __complex_acosh(__complex__ double __z)
1719 { return __builtin_cacosh(__z); }
1720
1721 inline __complex__ long double
1722 __complex_acosh(const __complex__ long double& __z)
1723 { return __builtin_cacoshl(__z); }
1724
1725 template<typename _Tp>
1726 inline std::complex<_Tp>
1727 acosh(const std::complex<_Tp>& __z)
1728 { return __complex_acosh(__z.__rep()); }
1729#else
1730 /// acosh(__z) [8.1.5].
1731 // Effects: Behaves the same as C99 function cacosh, defined
1732 // in subclause 7.3.6.1.
1733 template<typename _Tp>
1734 inline std::complex<_Tp>
1735 acosh(const std::complex<_Tp>& __z)
1736 { return __complex_acosh(__z); }
1737#endif
1738
1739 template<typename _Tp>
1740 std::complex<_Tp>
1741 __complex_asinh(const std::complex<_Tp>& __z)
1742 {
1743 std::complex<_Tp> __t((__z.real() - __z.imag())
1744 * (__z.real() + __z.imag()) + _Tp(1.0),
1745 _Tp(2.0) * __z.real() * __z.imag());
1746 __t = std::sqrt(__t);
1747
1748 return std::log(__t + __z);
1749 }
1750
1751#if _GLIBCXX_USE_C99_COMPLEX_TR1
1752 inline __complex__ float
1753 __complex_asinh(__complex__ float __z)
1754 { return __builtin_casinhf(__z); }
1755
1756 inline __complex__ double
1757 __complex_asinh(__complex__ double __z)
1758 { return __builtin_casinh(__z); }
1759
1760 inline __complex__ long double
1761 __complex_asinh(const __complex__ long double& __z)
1762 { return __builtin_casinhl(__z); }
1763
1764 template<typename _Tp>
1765 inline std::complex<_Tp>
1766 asinh(const std::complex<_Tp>& __z)
1767 { return __complex_asinh(__z.__rep()); }
1768#else
1769 /// asinh(__z) [8.1.6].
1770 // Effects: Behaves the same as C99 function casin, defined
1771 // in subclause 7.3.6.2.
1772 template<typename _Tp>
1773 inline std::complex<_Tp>
1774 asinh(const std::complex<_Tp>& __z)
1775 { return __complex_asinh(__z); }
1776#endif
1777
1778 template<typename _Tp>
1779 std::complex<_Tp>
1780 __complex_atanh(const std::complex<_Tp>& __z)
1781 {
1782 const _Tp __i2 = __z.imag() * __z.imag();
1783 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
1784
1785 _Tp __num = _Tp(1.0) + __z.real();
1786 _Tp __den = _Tp(1.0) - __z.real();
1787
1788 __num = __i2 + __num * __num;
1789 __den = __i2 + __den * __den;
1790
1791 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
1792 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
1793 }
1794
1795#if _GLIBCXX_USE_C99_COMPLEX_TR1
1796 inline __complex__ float
1797 __complex_atanh(__complex__ float __z)
1798 { return __builtin_catanhf(__z); }
1799
1800 inline __complex__ double
1801 __complex_atanh(__complex__ double __z)
1802 { return __builtin_catanh(__z); }
1803
1804 inline __complex__ long double
1805 __complex_atanh(const __complex__ long double& __z)
1806 { return __builtin_catanhl(__z); }
1807
1808 template<typename _Tp>
1809 inline std::complex<_Tp>
1810 atanh(const std::complex<_Tp>& __z)
1811 { return __complex_atanh(__z.__rep()); }
1812#else
1813 /// atanh(__z) [8.1.7].
1814 // Effects: Behaves the same as C99 function catanh, defined
1815 // in subclause 7.3.6.3.
1816 template<typename _Tp>
1817 inline std::complex<_Tp>
1818 atanh(const std::complex<_Tp>& __z)
1819 { return __complex_atanh(__z); }
1820#endif
1821
1822 template<typename _Tp>
1823 inline _Tp
1824 /// fabs(__z) [8.1.8].
1825 // Effects: Behaves the same as C99 function cabs, defined
1826 // in subclause 7.3.8.1.
1827 fabs(const std::complex<_Tp>& __z)
1828 { return std::abs(__z); }
1829
1830 /// Additional overloads [8.1.9].
1831 template<typename _Tp>
1832 inline typename __gnu_cxx::__promote<_Tp>::__type
1833 arg(_Tp __x)
1834 {
1835 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1836#if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
1837 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
1838 : __type();
1839#else
1840 return std::arg(std::complex<__type>(__x));
1841#endif
1842 }
1843
1844 template<typename _Tp>
1845 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
1846 imag(_Tp)
1847 { return _Tp(); }
1848
1849 template<typename _Tp>
1850 inline typename __gnu_cxx::__promote<_Tp>::__type
1851 norm(_Tp __x)
1852 {
1853 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1854 return __type(__x) * __type(__x);
1855 }
1856
1857 template<typename _Tp>
1858 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
1859 real(_Tp __x)
1860 { return __x; }
1861
1862 template<typename _Tp, typename _Up>
1863 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1864 pow(const std::complex<_Tp>& __x, const _Up& __y)
1865 {
1866 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1867 return std::pow(std::complex<__type>(__x), __type(__y));
1868 }
1869
1870 template<typename _Tp, typename _Up>
1871 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1872 pow(const _Tp& __x, const std::complex<_Up>& __y)
1873 {
1874 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1875 return std::pow(__type(__x), std::complex<__type>(__y));
1876 }
1877
1878 template<typename _Tp, typename _Up>
1879 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1880 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
1881 {
1882 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1883 return std::pow(std::complex<__type>(__x),
1884 std::complex<__type>(__y));
1885 }
1886
1887 // Forward declarations.
1888 // DR 781.
1889 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
1890
1891 template<typename _Tp>
1892 std::complex<_Tp>
1893 __complex_proj(const std::complex<_Tp>& __z)
1894 {
1895 const _Tp __den = (__z.real() * __z.real()
1896 + __z.imag() * __z.imag() + _Tp(1.0));
1897
1898 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
1899 (_Tp(2.0) * __z.imag()) / __den);
1900 }
1901
1902#if _GLIBCXX_USE_C99_COMPLEX
1903 inline __complex__ float
1904 __complex_proj(__complex__ float __z)
1905 { return __builtin_cprojf(__z); }
1906
1907 inline __complex__ double
1908 __complex_proj(__complex__ double __z)
1909 { return __builtin_cproj(__z); }
1910
1911 inline __complex__ long double
1912 __complex_proj(const __complex__ long double& __z)
1913 { return __builtin_cprojl(__z); }
1914
1915 template<typename _Tp>
1916 inline std::complex<_Tp>
1917 proj(const std::complex<_Tp>& __z)
1918 { return __complex_proj(__z.__rep()); }
1919#else
1920 template<typename _Tp>
1921 inline std::complex<_Tp>
1922 proj(const std::complex<_Tp>& __z)
1923 { return __complex_proj(__z); }
1924#endif
1925
1926 template<typename _Tp>
1927 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
1928 proj(_Tp __x)
1929 {
1930 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1931 return std::proj(std::complex<__type>(__x));
1932 }
1933
1934 template<typename _Tp>
1935 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
1936 conj(_Tp __x)
1937 {
1938 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1939 return std::complex<__type>(__x, -__type());
1940 }
1941
1942_GLIBCXX_END_NAMESPACE_VERSION
1943
1944#if __cplusplus > 201103L
1945
1946inline namespace literals {
1947inline namespace complex_literals {
1948_GLIBCXX_BEGIN_NAMESPACE_VERSION
1949
1950#define __cpp_lib_complex_udls 201309
1951
1952 constexpr std::complex<float>
1953 operator""if(long double __num)
1954 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
1955
1956 constexpr std::complex<float>
1957 operator""if(unsigned long long __num)
1958 { return std::complex<float>{0.0F, static_cast<float>(__num)}; }
1959
1960 constexpr std::complex<double>
1961 operator""i(long double __num)
1962 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
1963
1964 constexpr std::complex<double>
1965 operator""i(unsigned long long __num)
1966 { return std::complex<double>{0.0, static_cast<double>(__num)}; }
1967
1968 constexpr std::complex<long double>
1969 operator""il(long double __num)
1970 { return std::complex<long double>{0.0L, __num}; }
1971
1972 constexpr std::complex<long double>
1973 operator""il(unsigned long long __num)
1974 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; }
1975
1976_GLIBCXX_END_NAMESPACE_VERSION
1977} // inline namespace complex_literals
1978} // inline namespace literals
1979
1980#endif // C++14
1981
1982} // namespace
1983
1984#endif // C++11
1985
1986#endif /* _GLIBCXX_COMPLEX */
1987