1 // The template and inlines for the -*- C++ -*- complex number classes.
3 // Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
4 // 2006, 2007, 2008, 2009, 2010, 2011
5 // Free Software Foundation, Inc.
7 // This file is part of the GNU ISO C++ Library. This library is free
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9 // terms of the GNU General Public License as published by the
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27 /** @file include/complex
28 * This is a Standard C++ Library header.
32 // ISO C++ 14882: 26.2 Complex Numbers
33 // Note: this is not a conforming implementation.
34 // Initially implemented by Ulrich Drepper <drepper@cygnus.com>
35 // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
38 #ifndef _GLIBCXX_COMPLEX
39 #define _GLIBCXX_COMPLEX 1
41 #pragma GCC system_header
43 #include <bits/c++config.h>
44 #include <bits/cpp_type_traits.h>
45 #include <ext/type_traits.h>
49 namespace std _GLIBCXX_VISIBILITY(default)
51 _GLIBCXX_BEGIN_NAMESPACE_VERSION
54 * @defgroup complex_numbers Complex Numbers
57 * Classes and functions for complex numbers.
61 // Forward declarations.
62 template<typename _Tp> class complex;
63 template<> class complex<float>;
64 template<> class complex<double>;
65 template<> class complex<long double>;
67 /// Return magnitude of @a z.
68 template<typename _Tp> _Tp abs(const complex<_Tp>&);
69 /// Return phase angle of @a z.
70 template<typename _Tp> _Tp arg(const complex<_Tp>&);
71 /// Return @a z magnitude squared.
72 template<typename _Tp> _Tp norm(const complex<_Tp>&);
74 /// Return complex conjugate of @a z.
75 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
76 /// Return complex with magnitude @a rho and angle @a theta.
77 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
80 /// Return complex cosine of @a z.
81 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
82 /// Return complex hyperbolic cosine of @a z.
83 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
84 /// Return complex base e exponential of @a z.
85 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
86 /// Return complex natural logarithm of @a z.
87 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
88 /// Return complex base 10 logarithm of @a z.
89 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
90 #if __cplusplus < 201103L
92 /// Return @a x to the @a y'th power.
93 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
95 /// Return @a x to the @a y'th power.
96 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
97 /// Return @a x to the @a y'th power.
98 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
100 /// Return @a x to the @a y'th power.
101 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
102 /// Return complex sine of @a z.
103 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
104 /// Return complex hyperbolic sine of @a z.
105 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
106 /// Return complex square root of @a z.
107 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
108 /// Return complex tangent of @a z.
109 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
110 /// Return complex hyperbolic tangent of @a z.
111 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
114 // 26.2.2 Primary template class complex
116 * Template to represent complex numbers.
118 * Specializations for float, double, and long double are part of the
119 * library. Results with any other type are not guaranteed.
121 * @param Tp Type of real and imaginary values.
123 template<typename _Tp>
127 typedef _Tp value_type;
129 /// Default constructor. First parameter is x, second parameter is y.
130 /// Unspecified parameters default to 0.
131 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
132 : _M_real(__r), _M_imag(__i) { }
134 // Lets the compiler synthesize the copy constructor
135 // complex (const complex<_Tp>&);
136 /// Copy constructor.
137 template<typename _Up>
138 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
139 : _M_real(__z.real()), _M_imag(__z.imag()) { }
141 #if __cplusplus >= 201103L
142 // _GLIBCXX_RESOLVE_LIB_DEFECTS
143 // DR 387. std::complex over-encapsulated.
144 __attribute ((__abi_tag__ ("cxx11")))
146 real() { return _M_real; }
148 __attribute ((__abi_tag__ ("cxx11")))
150 imag() { return _M_imag; }
152 /// Return real part of complex number.
154 real() { return _M_real; }
156 /// Return real part of complex number.
158 real() const { return _M_real; }
160 /// Return imaginary part of complex number.
162 imag() { return _M_imag; }
164 /// Return imaginary part of complex number.
166 imag() const { return _M_imag; }
169 // _GLIBCXX_RESOLVE_LIB_DEFECTS
170 // DR 387. std::complex over-encapsulated.
172 real(_Tp __val) { _M_real = __val; }
175 imag(_Tp __val) { _M_imag = __val; }
177 /// Assign this complex number to scalar @a t.
178 complex<_Tp>& operator=(const _Tp&);
180 /// Add @a t to this complex number.
183 operator+=(const _Tp& __t)
189 /// Subtract @a t from this complex number.
192 operator-=(const _Tp& __t)
198 /// Multiply this complex number by @a t.
199 complex<_Tp>& operator*=(const _Tp&);
200 /// Divide this complex number by @a t.
201 complex<_Tp>& operator/=(const _Tp&);
203 // Lets the compiler synthesize the
204 // copy and assignment operator
205 // complex<_Tp>& operator= (const complex<_Tp>&);
206 /// Assign this complex number to complex @a z.
207 template<typename _Up>
208 complex<_Tp>& operator=(const complex<_Up>&);
209 /// Add @a z to this complex number.
210 template<typename _Up>
211 complex<_Tp>& operator+=(const complex<_Up>&);
212 /// Subtract @a z from this complex number.
213 template<typename _Up>
214 complex<_Tp>& operator-=(const complex<_Up>&);
215 /// Multiply this complex number by @a z.
216 template<typename _Up>
217 complex<_Tp>& operator*=(const complex<_Up>&);
218 /// Divide this complex number by @a z.
219 template<typename _Up>
220 complex<_Tp>& operator/=(const complex<_Up>&);
222 _GLIBCXX_USE_CONSTEXPR complex __rep() const
230 template<typename _Tp>
232 complex<_Tp>::operator=(const _Tp& __t)
240 template<typename _Tp>
242 complex<_Tp>::operator*=(const _Tp& __t)
250 template<typename _Tp>
252 complex<_Tp>::operator/=(const _Tp& __t)
259 template<typename _Tp>
260 template<typename _Up>
262 complex<_Tp>::operator=(const complex<_Up>& __z)
264 _M_real = __z.real();
265 _M_imag = __z.imag();
270 template<typename _Tp>
271 template<typename _Up>
273 complex<_Tp>::operator+=(const complex<_Up>& __z)
275 _M_real += __z.real();
276 _M_imag += __z.imag();
281 template<typename _Tp>
282 template<typename _Up>
284 complex<_Tp>::operator-=(const complex<_Up>& __z)
286 _M_real -= __z.real();
287 _M_imag -= __z.imag();
292 // XXX: This is a grammar school implementation.
293 template<typename _Tp>
294 template<typename _Up>
296 complex<_Tp>::operator*=(const complex<_Up>& __z)
298 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
299 _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
305 // XXX: This is a grammar school implementation.
306 template<typename _Tp>
307 template<typename _Up>
309 complex<_Tp>::operator/=(const complex<_Up>& __z)
311 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
312 const _Tp __n = std::norm(__z);
313 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
320 /// Return new complex value @a x plus @a y.
321 template<typename _Tp>
323 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
325 complex<_Tp> __r = __x;
330 template<typename _Tp>
332 operator+(const complex<_Tp>& __x, const _Tp& __y)
334 complex<_Tp> __r = __x;
339 template<typename _Tp>
341 operator+(const _Tp& __x, const complex<_Tp>& __y)
343 complex<_Tp> __r = __y;
350 /// Return new complex value @a x minus @a y.
351 template<typename _Tp>
353 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
355 complex<_Tp> __r = __x;
360 template<typename _Tp>
362 operator-(const complex<_Tp>& __x, const _Tp& __y)
364 complex<_Tp> __r = __x;
369 template<typename _Tp>
371 operator-(const _Tp& __x, const complex<_Tp>& __y)
373 complex<_Tp> __r(__x, -__y.imag());
380 /// Return new complex value @a x times @a y.
381 template<typename _Tp>
383 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
385 complex<_Tp> __r = __x;
390 template<typename _Tp>
392 operator*(const complex<_Tp>& __x, const _Tp& __y)
394 complex<_Tp> __r = __x;
399 template<typename _Tp>
401 operator*(const _Tp& __x, const complex<_Tp>& __y)
403 complex<_Tp> __r = __y;
410 /// Return new complex value @a x divided by @a y.
411 template<typename _Tp>
413 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
415 complex<_Tp> __r = __x;
420 template<typename _Tp>
422 operator/(const complex<_Tp>& __x, const _Tp& __y)
424 complex<_Tp> __r = __x;
429 template<typename _Tp>
431 operator/(const _Tp& __x, const complex<_Tp>& __y)
433 complex<_Tp> __r = __x;
440 template<typename _Tp>
442 operator+(const complex<_Tp>& __x)
445 /// Return complex negation of @a x.
446 template<typename _Tp>
448 operator-(const complex<_Tp>& __x)
449 { return complex<_Tp>(-__x.real(), -__x.imag()); }
452 /// Return true if @a x is equal to @a y.
453 template<typename _Tp>
454 inline _GLIBCXX_CONSTEXPR bool
455 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
456 { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
458 template<typename _Tp>
459 inline _GLIBCXX_CONSTEXPR bool
460 operator==(const complex<_Tp>& __x, const _Tp& __y)
461 { return __x.real() == __y && __x.imag() == _Tp(); }
463 template<typename _Tp>
464 inline _GLIBCXX_CONSTEXPR bool
465 operator==(const _Tp& __x, const complex<_Tp>& __y)
466 { return __x == __y.real() && _Tp() == __y.imag(); }
470 /// Return false if @a x is equal to @a y.
471 template<typename _Tp>
472 inline _GLIBCXX_CONSTEXPR bool
473 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
474 { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
476 template<typename _Tp>
477 inline _GLIBCXX_CONSTEXPR bool
478 operator!=(const complex<_Tp>& __x, const _Tp& __y)
479 { return __x.real() != __y || __x.imag() != _Tp(); }
481 template<typename _Tp>
482 inline _GLIBCXX_CONSTEXPR bool
483 operator!=(const _Tp& __x, const complex<_Tp>& __y)
484 { return __x != __y.real() || _Tp() != __y.imag(); }
487 /// Extraction operator for complex values.
488 template<typename _Tp, typename _CharT, class _Traits>
489 basic_istream<_CharT, _Traits>&
490 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
497 __is >> __re_x >> __ch;
500 __is >> __im_x >> __ch;
502 __x = complex<_Tp>(__re_x, __im_x);
504 __is.setstate(ios_base::failbit);
506 else if (__ch == ')')
509 __is.setstate(ios_base::failbit);
520 /// Insertion operator for complex values.
521 template<typename _Tp, typename _CharT, class _Traits>
522 basic_ostream<_CharT, _Traits>&
523 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
525 basic_ostringstream<_CharT, _Traits> __s;
526 __s.flags(__os.flags());
527 __s.imbue(__os.getloc());
528 __s.precision(__os.precision());
529 __s << '(' << __x.real() << ',' << __x.imag() << ')';
530 return __os << __s.str();
534 #if __cplusplus >= 201103L
535 template<typename _Tp>
537 real(const complex<_Tp>& __z)
538 { return __z.real(); }
540 template<typename _Tp>
542 imag(const complex<_Tp>& __z)
543 { return __z.imag(); }
545 template<typename _Tp>
547 real(complex<_Tp>& __z)
548 { return __z.real(); }
550 template<typename _Tp>
552 real(const complex<_Tp>& __z)
553 { return __z.real(); }
555 template<typename _Tp>
557 imag(complex<_Tp>& __z)
558 { return __z.imag(); }
560 template<typename _Tp>
562 imag(const complex<_Tp>& __z)
563 { return __z.imag(); }
566 // 26.2.7/3 abs(__z): Returns the magnitude of __z.
567 template<typename _Tp>
569 __complex_abs(const complex<_Tp>& __z)
571 _Tp __x = __z.real();
572 _Tp __y = __z.imag();
573 const _Tp __s = std::max(abs(__x), abs(__y));
574 if (__s == _Tp()) // well ...
578 return __s * sqrt(__x * __x + __y * __y);
581 #if _GLIBCXX_USE_C99_COMPLEX
583 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
586 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
589 __complex_abs(const __complex__ long double& __z)
590 { return __builtin_cabsl(__z); }
592 template<typename _Tp>
594 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
596 template<typename _Tp>
598 abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
602 // 26.2.7/4: arg(__z): Returns the phase angle of __z.
603 template<typename _Tp>
605 __complex_arg(const complex<_Tp>& __z)
606 { return atan2(__z.imag(), __z.real()); }
608 #if _GLIBCXX_USE_C99_COMPLEX
610 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
613 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
616 __complex_arg(const __complex__ long double& __z)
617 { return __builtin_cargl(__z); }
619 template<typename _Tp>
621 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
623 template<typename _Tp>
625 arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
628 // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
629 // As defined, norm() is -not- a norm is the common mathematical
630 // sens used in numerics. The helper class _Norm_helper<> tries to
631 // distinguish between builtin floating point and the rest, so as
632 // to deliver an answer as close as possible to the real value.
636 template<typename _Tp>
637 static inline _Tp _S_do_it(const complex<_Tp>& __z)
639 const _Tp __x = __z.real();
640 const _Tp __y = __z.imag();
641 return __x * __x + __y * __y;
646 struct _Norm_helper<true>
648 template<typename _Tp>
649 static inline _Tp _S_do_it(const complex<_Tp>& __z)
651 _Tp __res = std::abs(__z);
652 return __res * __res;
656 template<typename _Tp>
658 norm(const complex<_Tp>& __z)
660 return _Norm_helper<__is_floating<_Tp>::__value
661 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
664 template<typename _Tp>
666 polar(const _Tp& __rho, const _Tp& __theta)
667 { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
669 template<typename _Tp>
671 conj(const complex<_Tp>& __z)
672 { return complex<_Tp>(__z.real(), -__z.imag()); }
676 // 26.2.8/1 cos(__z): Returns the cosine of __z.
677 template<typename _Tp>
679 __complex_cos(const complex<_Tp>& __z)
681 const _Tp __x = __z.real();
682 const _Tp __y = __z.imag();
683 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
686 #if _GLIBCXX_USE_C99_COMPLEX
687 inline __complex__ float
688 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
690 inline __complex__ double
691 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
693 inline __complex__ long double
694 __complex_cos(const __complex__ long double& __z)
695 { return __builtin_ccosl(__z); }
697 template<typename _Tp>
699 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
701 template<typename _Tp>
703 cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
706 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
707 template<typename _Tp>
709 __complex_cosh(const complex<_Tp>& __z)
711 const _Tp __x = __z.real();
712 const _Tp __y = __z.imag();
713 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
716 #if _GLIBCXX_USE_C99_COMPLEX
717 inline __complex__ float
718 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
720 inline __complex__ double
721 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
723 inline __complex__ long double
724 __complex_cosh(const __complex__ long double& __z)
725 { return __builtin_ccoshl(__z); }
727 template<typename _Tp>
729 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
731 template<typename _Tp>
733 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
736 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
737 template<typename _Tp>
739 __complex_exp(const complex<_Tp>& __z)
740 { return std::polar(exp(__z.real()), __z.imag()); }
742 #if _GLIBCXX_USE_C99_COMPLEX
743 inline __complex__ float
744 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
746 inline __complex__ double
747 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
749 inline __complex__ long double
750 __complex_exp(const __complex__ long double& __z)
751 { return __builtin_cexpl(__z); }
753 template<typename _Tp>
755 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
757 template<typename _Tp>
759 exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
762 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
763 // The branch cut is along the negative axis.
764 template<typename _Tp>
766 __complex_log(const complex<_Tp>& __z)
767 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
769 #if _GLIBCXX_USE_C99_COMPLEX
770 inline __complex__ float
771 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
773 inline __complex__ double
774 __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
776 inline __complex__ long double
777 __complex_log(const __complex__ long double& __z)
778 { return __builtin_clogl(__z); }
780 template<typename _Tp>
782 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
784 template<typename _Tp>
786 log(const complex<_Tp>& __z) { return __complex_log(__z); }
789 template<typename _Tp>
791 log10(const complex<_Tp>& __z)
792 { return std::log(__z) / log(_Tp(10.0)); }
794 // 26.2.8/10 sin(__z): Returns the sine of __z.
795 template<typename _Tp>
797 __complex_sin(const complex<_Tp>& __z)
799 const _Tp __x = __z.real();
800 const _Tp __y = __z.imag();
801 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
804 #if _GLIBCXX_USE_C99_COMPLEX
805 inline __complex__ float
806 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
808 inline __complex__ double
809 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
811 inline __complex__ long double
812 __complex_sin(const __complex__ long double& __z)
813 { return __builtin_csinl(__z); }
815 template<typename _Tp>
817 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
819 template<typename _Tp>
821 sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
824 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
825 template<typename _Tp>
827 __complex_sinh(const complex<_Tp>& __z)
829 const _Tp __x = __z.real();
830 const _Tp __y = __z.imag();
831 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
834 #if _GLIBCXX_USE_C99_COMPLEX
835 inline __complex__ float
836 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
838 inline __complex__ double
839 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
841 inline __complex__ long double
842 __complex_sinh(const __complex__ long double& __z)
843 { return __builtin_csinhl(__z); }
845 template<typename _Tp>
847 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
849 template<typename _Tp>
851 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
854 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
855 // The branch cut is on the negative axis.
856 template<typename _Tp>
858 __complex_sqrt(const complex<_Tp>& __z)
860 _Tp __x = __z.real();
861 _Tp __y = __z.imag();
865 _Tp __t = sqrt(abs(__y) / 2);
866 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
870 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
873 ? complex<_Tp>(__u, __y / __t)
874 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
878 #if _GLIBCXX_USE_C99_COMPLEX
879 inline __complex__ float
880 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
882 inline __complex__ double
883 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
885 inline __complex__ long double
886 __complex_sqrt(const __complex__ long double& __z)
887 { return __builtin_csqrtl(__z); }
889 template<typename _Tp>
891 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
893 template<typename _Tp>
895 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
898 // 26.2.8/14 tan(__z): Return the complex tangent of __z.
900 template<typename _Tp>
902 __complex_tan(const complex<_Tp>& __z)
903 { return std::sin(__z) / std::cos(__z); }
905 #if _GLIBCXX_USE_C99_COMPLEX
906 inline __complex__ float
907 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
909 inline __complex__ double
910 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
912 inline __complex__ long double
913 __complex_tan(const __complex__ long double& __z)
914 { return __builtin_ctanl(__z); }
916 template<typename _Tp>
918 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
920 template<typename _Tp>
922 tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
926 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
928 template<typename _Tp>
930 __complex_tanh(const complex<_Tp>& __z)
931 { return std::sinh(__z) / std::cosh(__z); }
933 #if _GLIBCXX_USE_C99_COMPLEX
934 inline __complex__ float
935 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
937 inline __complex__ double
938 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
940 inline __complex__ long double
941 __complex_tanh(const __complex__ long double& __z)
942 { return __builtin_ctanhl(__z); }
944 template<typename _Tp>
946 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
948 template<typename _Tp>
950 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
954 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
955 // raised to the __y-th power. The branch
956 // cut is on the negative axis.
957 #if __cplusplus < 201103L
958 template<typename _Tp>
960 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
962 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
974 // _GLIBCXX_RESOLVE_LIB_DEFECTS
975 // DR 844. complex pow return type is ambiguous.
976 template<typename _Tp>
978 pow(const complex<_Tp>& __z, int __n)
981 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -__n)
982 : std::__complex_pow_unsigned(__z, __n);
986 template<typename _Tp>
988 pow(const complex<_Tp>& __x, const _Tp& __y)
990 #ifndef _GLIBCXX_USE_C99_COMPLEX
994 if (__x.imag() == _Tp() && __x.real() > _Tp())
995 return pow(__x.real(), __y);
997 complex<_Tp> __t = std::log(__x);
998 return std::polar(exp(__y * __t.real()), __y * __t.imag());
1001 template<typename _Tp>
1003 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1004 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
1006 #if _GLIBCXX_USE_C99_COMPLEX
1007 inline __complex__ float
1008 __complex_pow(__complex__ float __x, __complex__ float __y)
1009 { return __builtin_cpowf(__x, __y); }
1011 inline __complex__ double
1012 __complex_pow(__complex__ double __x, __complex__ double __y)
1013 { return __builtin_cpow(__x, __y); }
1015 inline __complex__ long double
1016 __complex_pow(const __complex__ long double& __x,
1017 const __complex__ long double& __y)
1018 { return __builtin_cpowl(__x, __y); }
1020 template<typename _Tp>
1022 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1023 { return __complex_pow(__x.__rep(), __y.__rep()); }
1025 template<typename _Tp>
1027 pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1028 { return __complex_pow(__x, __y); }
1031 template<typename _Tp>
1033 pow(const _Tp& __x, const complex<_Tp>& __y)
1035 return __x > _Tp() ? std::polar(pow(__x, __y.real()),
1036 __y.imag() * log(__x))
1037 : std::pow(complex<_Tp>(__x), __y);
1040 /// 26.2.3 complex specializations
1041 /// complex<float> specialization
1043 struct complex<float>
1045 typedef float value_type;
1046 typedef __complex__ float _ComplexT;
1048 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1050 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
1051 #if __cplusplus >= 201103L
1052 : _M_value{ __r, __i } { }
1055 __real__ _M_value = __r;
1056 __imag__ _M_value = __i;
1060 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
1061 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1063 #if __cplusplus >= 201103L
1064 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1065 // DR 387. std::complex over-encapsulated.
1066 __attribute ((__abi_tag__ ("cxx11")))
1068 real() { return __real__ _M_value; }
1070 __attribute ((__abi_tag__ ("cxx11")))
1072 imag() { return __imag__ _M_value; }
1075 real() { return __real__ _M_value; }
1078 real() const { return __real__ _M_value; }
1081 imag() { return __imag__ _M_value; }
1084 imag() const { return __imag__ _M_value; }
1087 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1088 // DR 387. std::complex over-encapsulated.
1090 real(float __val) { __real__ _M_value = __val; }
1093 imag(float __val) { __imag__ _M_value = __val; }
1096 operator=(float __f)
1103 operator+=(float __f)
1110 operator-=(float __f)
1117 operator*=(float __f)
1124 operator/=(float __f)
1130 // Let the compiler synthesize the copy and assignment
1131 // operator. It always does a pretty good job.
1132 // complex& operator=(const complex&);
1134 template<typename _Tp>
1136 operator=(const complex<_Tp>& __z)
1138 __real__ _M_value = __z.real();
1139 __imag__ _M_value = __z.imag();
1143 template<typename _Tp>
1145 operator+=(const complex<_Tp>& __z)
1147 __real__ _M_value += __z.real();
1148 __imag__ _M_value += __z.imag();
1154 operator-=(const complex<_Tp>& __z)
1156 __real__ _M_value -= __z.real();
1157 __imag__ _M_value -= __z.imag();
1163 operator*=(const complex<_Tp>& __z)
1166 __real__ __t = __z.real();
1167 __imag__ __t = __z.imag();
1174 operator/=(const complex<_Tp>& __z)
1177 __real__ __t = __z.real();
1178 __imag__ __t = __z.imag();
1183 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1189 /// 26.2.3 complex specializations
1190 /// complex<double> specialization
1192 struct complex<double>
1194 typedef double value_type;
1195 typedef __complex__ double _ComplexT;
1197 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1199 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
1200 #if __cplusplus >= 201103L
1201 : _M_value{ __r, __i } { }
1204 __real__ _M_value = __r;
1205 __imag__ _M_value = __i;
1209 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1210 : _M_value(__z.__rep()) { }
1212 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1214 #if __cplusplus >= 201103L
1215 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1216 // DR 387. std::complex over-encapsulated.
1217 __attribute ((__abi_tag__ ("cxx11")))
1219 real() { return __real__ _M_value; }
1221 __attribute ((__abi_tag__ ("cxx11")))
1223 imag() { return __imag__ _M_value; }
1226 real() { return __real__ _M_value; }
1229 real() const { return __real__ _M_value; }
1232 imag() { return __imag__ _M_value; }
1235 imag() const { return __imag__ _M_value; }
1238 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1239 // DR 387. std::complex over-encapsulated.
1241 real(double __val) { __real__ _M_value = __val; }
1244 imag(double __val) { __imag__ _M_value = __val; }
1247 operator=(double __d)
1254 operator+=(double __d)
1261 operator-=(double __d)
1268 operator*=(double __d)
1275 operator/=(double __d)
1281 // The compiler will synthesize this, efficiently.
1282 // complex& operator=(const complex&);
1284 template<typename _Tp>
1286 operator=(const complex<_Tp>& __z)
1288 __real__ _M_value = __z.real();
1289 __imag__ _M_value = __z.imag();
1293 template<typename _Tp>
1295 operator+=(const complex<_Tp>& __z)
1297 __real__ _M_value += __z.real();
1298 __imag__ _M_value += __z.imag();
1302 template<typename _Tp>
1304 operator-=(const complex<_Tp>& __z)
1306 __real__ _M_value -= __z.real();
1307 __imag__ _M_value -= __z.imag();
1311 template<typename _Tp>
1313 operator*=(const complex<_Tp>& __z)
1316 __real__ __t = __z.real();
1317 __imag__ __t = __z.imag();
1322 template<typename _Tp>
1324 operator/=(const complex<_Tp>& __z)
1327 __real__ __t = __z.real();
1328 __imag__ __t = __z.imag();
1333 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1339 /// 26.2.3 complex specializations
1340 /// complex<long double> specialization
1342 struct complex<long double>
1344 typedef long double value_type;
1345 typedef __complex__ long double _ComplexT;
1347 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1349 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
1350 long double __i = 0.0L)
1351 #if __cplusplus >= 201103L
1352 : _M_value{ __r, __i } { }
1355 __real__ _M_value = __r;
1356 __imag__ _M_value = __i;
1360 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1361 : _M_value(__z.__rep()) { }
1363 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
1364 : _M_value(__z.__rep()) { }
1366 #if __cplusplus >= 201103L
1367 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1368 // DR 387. std::complex over-encapsulated.
1369 __attribute ((__abi_tag__ ("cxx11")))
1370 constexpr long double
1371 real() { return __real__ _M_value; }
1373 __attribute ((__abi_tag__ ("cxx11")))
1374 constexpr long double
1375 imag() { return __imag__ _M_value; }
1378 real() { return __real__ _M_value; }
1381 real() const { return __real__ _M_value; }
1384 imag() { return __imag__ _M_value; }
1387 imag() const { return __imag__ _M_value; }
1390 // _GLIBCXX_RESOLVE_LIB_DEFECTS
1391 // DR 387. std::complex over-encapsulated.
1393 real(long double __val) { __real__ _M_value = __val; }
1396 imag(long double __val) { __imag__ _M_value = __val; }
1399 operator=(long double __r)
1406 operator+=(long double __r)
1413 operator-=(long double __r)
1420 operator*=(long double __r)
1427 operator/=(long double __r)
1433 // The compiler knows how to do this efficiently
1434 // complex& operator=(const complex&);
1436 template<typename _Tp>
1438 operator=(const complex<_Tp>& __z)
1440 __real__ _M_value = __z.real();
1441 __imag__ _M_value = __z.imag();
1445 template<typename _Tp>
1447 operator+=(const complex<_Tp>& __z)
1449 __real__ _M_value += __z.real();
1450 __imag__ _M_value += __z.imag();
1454 template<typename _Tp>
1456 operator-=(const complex<_Tp>& __z)
1458 __real__ _M_value -= __z.real();
1459 __imag__ _M_value -= __z.imag();
1463 template<typename _Tp>
1465 operator*=(const complex<_Tp>& __z)
1468 __real__ __t = __z.real();
1469 __imag__ __t = __z.imag();
1474 template<typename _Tp>
1476 operator/=(const complex<_Tp>& __z)
1479 __real__ __t = __z.real();
1480 __imag__ __t = __z.imag();
1485 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1491 // These bits have to be at the end of this file, so that the
1492 // specializations have all been defined.
1493 inline _GLIBCXX_CONSTEXPR
1494 complex<float>::complex(const complex<double>& __z)
1495 : _M_value(__z.__rep()) { }
1497 inline _GLIBCXX_CONSTEXPR
1498 complex<float>::complex(const complex<long double>& __z)
1499 : _M_value(__z.__rep()) { }
1501 inline _GLIBCXX_CONSTEXPR
1502 complex<double>::complex(const complex<long double>& __z)
1503 : _M_value(__z.__rep()) { }
1505 // Inhibit implicit instantiations for required instantiations,
1506 // which are defined via explicit instantiations elsewhere.
1507 // NB: This syntax is a GNU extension.
1508 #if _GLIBCXX_EXTERN_TEMPLATE
1509 extern template istream& operator>>(istream&, complex<float>&);
1510 extern template ostream& operator<<(ostream&, const complex<float>&);
1511 extern template istream& operator>>(istream&, complex<double>&);
1512 extern template ostream& operator<<(ostream&, const complex<double>&);
1513 extern template istream& operator>>(istream&, complex<long double>&);
1514 extern template ostream& operator<<(ostream&, const complex<long double>&);
1516 #ifdef _GLIBCXX_USE_WCHAR_T
1517 extern template wistream& operator>>(wistream&, complex<float>&);
1518 extern template wostream& operator<<(wostream&, const complex<float>&);
1519 extern template wistream& operator>>(wistream&, complex<double>&);
1520 extern template wostream& operator<<(wostream&, const complex<double>&);
1521 extern template wistream& operator>>(wistream&, complex<long double>&);
1522 extern template wostream& operator<<(wostream&, const complex<long double>&);
1526 // @} group complex_numbers
1528 _GLIBCXX_END_NAMESPACE_VERSION
1531 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
1533 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1535 // See ext/type_traits.h for the primary template.
1536 template<typename _Tp, typename _Up>
1537 struct __promote_2<std::complex<_Tp>, _Up>
1540 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1543 template<typename _Tp, typename _Up>
1544 struct __promote_2<_Tp, std::complex<_Up> >
1547 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1550 template<typename _Tp, typename _Up>
1551 struct __promote_2<std::complex<_Tp>, std::complex<_Up> >
1554 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1557 _GLIBCXX_END_NAMESPACE_VERSION
1560 #if __cplusplus >= 201103L
1562 namespace std _GLIBCXX_VISIBILITY(default)
1564 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1566 // Forward declarations.
1567 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
1568 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
1569 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
1571 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
1572 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
1573 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
1575 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
1577 template<typename _Tp>
1578 inline std::complex<_Tp>
1579 __complex_acos(const std::complex<_Tp>& __z)
1581 const std::complex<_Tp> __t = std::asin(__z);
1582 const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
1583 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
1586 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1587 inline __complex__ float
1588 __complex_acos(__complex__ float __z)
1589 { return __builtin_cacosf(__z); }
1591 inline __complex__ double
1592 __complex_acos(__complex__ double __z)
1593 { return __builtin_cacos(__z); }
1595 inline __complex__ long double
1596 __complex_acos(const __complex__ long double& __z)
1597 { return __builtin_cacosl(__z); }
1599 template<typename _Tp>
1600 inline std::complex<_Tp>
1601 acos(const std::complex<_Tp>& __z)
1602 { return __complex_acos(__z.__rep()); }
1604 /// acos(__z) [8.1.2].
1605 // Effects: Behaves the same as C99 function cacos, defined
1606 // in subclause 7.3.5.1.
1607 template<typename _Tp>
1608 inline std::complex<_Tp>
1609 acos(const std::complex<_Tp>& __z)
1610 { return __complex_acos(__z); }
1613 template<typename _Tp>
1614 inline std::complex<_Tp>
1615 __complex_asin(const std::complex<_Tp>& __z)
1617 std::complex<_Tp> __t(-__z.imag(), __z.real());
1618 __t = std::asinh(__t);
1619 return std::complex<_Tp>(__t.imag(), -__t.real());
1622 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1623 inline __complex__ float
1624 __complex_asin(__complex__ float __z)
1625 { return __builtin_casinf(__z); }
1627 inline __complex__ double
1628 __complex_asin(__complex__ double __z)
1629 { return __builtin_casin(__z); }
1631 inline __complex__ long double
1632 __complex_asin(const __complex__ long double& __z)
1633 { return __builtin_casinl(__z); }
1635 template<typename _Tp>
1636 inline std::complex<_Tp>
1637 asin(const std::complex<_Tp>& __z)
1638 { return __complex_asin(__z.__rep()); }
1640 /// asin(__z) [8.1.3].
1641 // Effects: Behaves the same as C99 function casin, defined
1642 // in subclause 7.3.5.2.
1643 template<typename _Tp>
1644 inline std::complex<_Tp>
1645 asin(const std::complex<_Tp>& __z)
1646 { return __complex_asin(__z); }
1649 template<typename _Tp>
1651 __complex_atan(const std::complex<_Tp>& __z)
1653 const _Tp __r2 = __z.real() * __z.real();
1654 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
1656 _Tp __num = __z.imag() + _Tp(1.0);
1657 _Tp __den = __z.imag() - _Tp(1.0);
1659 __num = __r2 + __num * __num;
1660 __den = __r2 + __den * __den;
1662 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
1663 _Tp(0.25) * log(__num / __den));
1666 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1667 inline __complex__ float
1668 __complex_atan(__complex__ float __z)
1669 { return __builtin_catanf(__z); }
1671 inline __complex__ double
1672 __complex_atan(__complex__ double __z)
1673 { return __builtin_catan(__z); }
1675 inline __complex__ long double
1676 __complex_atan(const __complex__ long double& __z)
1677 { return __builtin_catanl(__z); }
1679 template<typename _Tp>
1680 inline std::complex<_Tp>
1681 atan(const std::complex<_Tp>& __z)
1682 { return __complex_atan(__z.__rep()); }
1684 /// atan(__z) [8.1.4].
1685 // Effects: Behaves the same as C99 function catan, defined
1686 // in subclause 7.3.5.3.
1687 template<typename _Tp>
1688 inline std::complex<_Tp>
1689 atan(const std::complex<_Tp>& __z)
1690 { return __complex_atan(__z); }
1693 template<typename _Tp>
1695 __complex_acosh(const std::complex<_Tp>& __z)
1698 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
1699 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
1702 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1703 inline __complex__ float
1704 __complex_acosh(__complex__ float __z)
1705 { return __builtin_cacoshf(__z); }
1707 inline __complex__ double
1708 __complex_acosh(__complex__ double __z)
1709 { return __builtin_cacosh(__z); }
1711 inline __complex__ long double
1712 __complex_acosh(const __complex__ long double& __z)
1713 { return __builtin_cacoshl(__z); }
1715 template<typename _Tp>
1716 inline std::complex<_Tp>
1717 acosh(const std::complex<_Tp>& __z)
1718 { return __complex_acosh(__z.__rep()); }
1720 /// acosh(__z) [8.1.5].
1721 // Effects: Behaves the same as C99 function cacosh, defined
1722 // in subclause 7.3.6.1.
1723 template<typename _Tp>
1724 inline std::complex<_Tp>
1725 acosh(const std::complex<_Tp>& __z)
1726 { return __complex_acosh(__z); }
1729 template<typename _Tp>
1731 __complex_asinh(const std::complex<_Tp>& __z)
1733 std::complex<_Tp> __t((__z.real() - __z.imag())
1734 * (__z.real() + __z.imag()) + _Tp(1.0),
1735 _Tp(2.0) * __z.real() * __z.imag());
1736 __t = std::sqrt(__t);
1738 return std::log(__t + __z);
1741 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1742 inline __complex__ float
1743 __complex_asinh(__complex__ float __z)
1744 { return __builtin_casinhf(__z); }
1746 inline __complex__ double
1747 __complex_asinh(__complex__ double __z)
1748 { return __builtin_casinh(__z); }
1750 inline __complex__ long double
1751 __complex_asinh(const __complex__ long double& __z)
1752 { return __builtin_casinhl(__z); }
1754 template<typename _Tp>
1755 inline std::complex<_Tp>
1756 asinh(const std::complex<_Tp>& __z)
1757 { return __complex_asinh(__z.__rep()); }
1759 /// asinh(__z) [8.1.6].
1760 // Effects: Behaves the same as C99 function casin, defined
1761 // in subclause 7.3.6.2.
1762 template<typename _Tp>
1763 inline std::complex<_Tp>
1764 asinh(const std::complex<_Tp>& __z)
1765 { return __complex_asinh(__z); }
1768 template<typename _Tp>
1770 __complex_atanh(const std::complex<_Tp>& __z)
1772 const _Tp __i2 = __z.imag() * __z.imag();
1773 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
1775 _Tp __num = _Tp(1.0) + __z.real();
1776 _Tp __den = _Tp(1.0) - __z.real();
1778 __num = __i2 + __num * __num;
1779 __den = __i2 + __den * __den;
1781 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
1782 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
1785 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1786 inline __complex__ float
1787 __complex_atanh(__complex__ float __z)
1788 { return __builtin_catanhf(__z); }
1790 inline __complex__ double
1791 __complex_atanh(__complex__ double __z)
1792 { return __builtin_catanh(__z); }
1794 inline __complex__ long double
1795 __complex_atanh(const __complex__ long double& __z)
1796 { return __builtin_catanhl(__z); }
1798 template<typename _Tp>
1799 inline std::complex<_Tp>
1800 atanh(const std::complex<_Tp>& __z)
1801 { return __complex_atanh(__z.__rep()); }
1803 /// atanh(__z) [8.1.7].
1804 // Effects: Behaves the same as C99 function catanh, defined
1805 // in subclause 7.3.6.3.
1806 template<typename _Tp>
1807 inline std::complex<_Tp>
1808 atanh(const std::complex<_Tp>& __z)
1809 { return __complex_atanh(__z); }
1812 template<typename _Tp>
1814 /// fabs(__z) [8.1.8].
1815 // Effects: Behaves the same as C99 function cabs, defined
1816 // in subclause 7.3.8.1.
1817 fabs(const std::complex<_Tp>& __z)
1818 { return std::abs(__z); }
1820 /// Additional overloads [8.1.9].
1821 template<typename _Tp>
1822 inline typename __gnu_cxx::__promote<_Tp>::__type
1825 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1826 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
1827 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
1830 return std::arg(std::complex<__type>(__x));
1834 template<typename _Tp>
1835 inline typename __gnu_cxx::__promote<_Tp>::__type
1839 template<typename _Tp>
1840 inline typename __gnu_cxx::__promote<_Tp>::__type
1843 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1844 return __type(__x) * __type(__x);
1847 template<typename _Tp>
1848 inline typename __gnu_cxx::__promote<_Tp>::__type
1852 template<typename _Tp, typename _Up>
1853 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1854 pow(const std::complex<_Tp>& __x, const _Up& __y)
1856 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1857 return std::pow(std::complex<__type>(__x), __type(__y));
1860 template<typename _Tp, typename _Up>
1861 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1862 pow(const _Tp& __x, const std::complex<_Up>& __y)
1864 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1865 return std::pow(__type(__x), std::complex<__type>(__y));
1868 template<typename _Tp, typename _Up>
1869 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1870 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
1872 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1873 return std::pow(std::complex<__type>(__x),
1874 std::complex<__type>(__y));
1877 // Forward declarations.
1879 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
1881 template<typename _Tp>
1883 __complex_proj(const std::complex<_Tp>& __z)
1885 const _Tp __den = (__z.real() * __z.real()
1886 + __z.imag() * __z.imag() + _Tp(1.0));
1888 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
1889 (_Tp(2.0) * __z.imag()) / __den);
1892 #if _GLIBCXX_USE_C99_COMPLEX
1893 inline __complex__ float
1894 __complex_proj(__complex__ float __z)
1895 { return __builtin_cprojf(__z); }
1897 inline __complex__ double
1898 __complex_proj(__complex__ double __z)
1899 { return __builtin_cproj(__z); }
1901 inline __complex__ long double
1902 __complex_proj(const __complex__ long double& __z)
1903 { return __builtin_cprojl(__z); }
1905 template<typename _Tp>
1906 inline std::complex<_Tp>
1907 proj(const std::complex<_Tp>& __z)
1908 { return __complex_proj(__z.__rep()); }
1910 template<typename _Tp>
1911 inline std::complex<_Tp>
1912 proj(const std::complex<_Tp>& __z)
1913 { return __complex_proj(__z); }
1917 template<typename _Tp>
1918 inline typename __gnu_cxx::__promote<_Tp>::__type
1922 template<typename _Tp>
1923 inline typename __gnu_cxx::__promote<_Tp>::__type
1927 _GLIBCXX_END_NAMESPACE_VERSION
1932 #endif /* _GLIBCXX_COMPLEX */