38 #ifndef _GLIBCXX_COMPLEX
39 #define _GLIBCXX_COMPLEX 1
41 #pragma GCC system_header
49 namespace std _GLIBCXX_VISIBILITY(default)
51 _GLIBCXX_BEGIN_NAMESPACE_VERSION
63 template<>
class complex<float>;
64 template<>
class complex<double>;
65 template<>
class complex<long double>;
90 #ifndef __GXX_EXPERIMENTAL_CXX0X__
123 template<
typename _Tp>
131 _GLIBCXX_CONSTEXPR
complex(
const _Tp& __r = _Tp(),
const _Tp& __i = _Tp())
132 : _M_real(__r), _M_imag(__i) { }
137 template<
typename _Up>
139 : _M_real(__z.real()), _M_imag(__z.imag()) { }
141 #ifdef __GXX_EXPERIMENTAL_CXX0X__
145 real()
const {
return _M_real; }
148 imag()
const {
return _M_imag; }
152 real() {
return _M_real; }
156 real()
const {
return _M_real; }
160 imag() {
return _M_imag; }
164 imag()
const {
return _M_imag; }
170 real(_Tp __val) { _M_real = __val; }
173 imag(_Tp __val) { _M_imag = __val; }
205 template<
typename _Up>
208 template<
typename _Up>
211 template<
typename _Up>
214 template<
typename _Up>
217 template<
typename _Up>
220 _GLIBCXX_USE_CONSTEXPR
complex __rep()
const
228 template<
typename _Tp>
238 template<
typename _Tp>
248 template<
typename _Tp>
257 template<
typename _Tp>
258 template<
typename _Up>
262 _M_real = __z.real();
263 _M_imag = __z.imag();
268 template<
typename _Tp>
269 template<
typename _Up>
273 _M_real += __z.real();
274 _M_imag += __z.imag();
279 template<
typename _Tp>
280 template<
typename _Up>
284 _M_real -= __z.real();
285 _M_imag -= __z.imag();
291 template<
typename _Tp>
292 template<
typename _Up>
296 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
297 _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
304 template<
typename _Tp>
305 template<
typename _Up>
309 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
311 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
319 template<
typename _Tp>
328 template<
typename _Tp>
337 template<
typename _Tp>
349 template<
typename _Tp>
358 template<
typename _Tp>
367 template<
typename _Tp>
379 template<
typename _Tp>
388 template<
typename _Tp>
397 template<
typename _Tp>
409 template<
typename _Tp>
418 template<
typename _Tp>
427 template<
typename _Tp>
438 template<
typename _Tp>
444 template<
typename _Tp>
451 template<
typename _Tp>
452 inline _GLIBCXX_CONSTEXPR
bool
454 {
return __x.real() == __y.real() && __x.imag() == __y.imag(); }
456 template<
typename _Tp>
457 inline _GLIBCXX_CONSTEXPR
bool
459 {
return __x.real() == __y && __x.imag() == _Tp(); }
461 template<
typename _Tp>
462 inline _GLIBCXX_CONSTEXPR
bool
464 {
return __x == __y.real() && _Tp() == __y.imag(); }
469 template<
typename _Tp>
470 inline _GLIBCXX_CONSTEXPR
bool
472 {
return __x.real() != __y.real() || __x.imag() != __y.imag(); }
474 template<
typename _Tp>
475 inline _GLIBCXX_CONSTEXPR
bool
477 {
return __x.real() != __y || __x.imag() != _Tp(); }
479 template<
typename _Tp>
480 inline _GLIBCXX_CONSTEXPR
bool
482 {
return __x != __y.real() || _Tp() != __y.imag(); }
486 template<
typename _Tp,
typename _CharT,
class _Traits>
487 basic_istream<_CharT, _Traits>&
495 __is >> __re_x >> __ch;
498 __is >> __im_x >> __ch;
504 else if (__ch ==
')')
519 template<
typename _Tp,
typename _CharT,
class _Traits>
520 basic_ostream<_CharT, _Traits>&
521 operator<<(basic_ostream<_CharT, _Traits>& __os,
const complex<_Tp>& __x)
524 __s.
flags(__os.flags());
525 __s.
imbue(__os.getloc());
527 __s <<
'(' << __x.real() <<
',' << __x.imag() <<
')';
528 return __os << __s.
str();
532 #ifdef __GXX_EXPERIMENTAL_CXX0X__
533 template<
typename _Tp>
535 real(
const complex<_Tp>& __z)
536 {
return __z.real(); }
538 template<
typename _Tp>
540 imag(
const complex<_Tp>& __z)
541 {
return __z.imag(); }
543 template<
typename _Tp>
545 real(complex<_Tp>& __z)
546 {
return __z.real(); }
548 template<
typename _Tp>
550 real(
const complex<_Tp>& __z)
551 {
return __z.real(); }
553 template<
typename _Tp>
555 imag(complex<_Tp>& __z)
556 {
return __z.imag(); }
558 template<
typename _Tp>
560 imag(
const complex<_Tp>& __z)
561 {
return __z.imag(); }
565 template<
typename _Tp>
567 __complex_abs(
const complex<_Tp>& __z)
569 _Tp __x = __z.real();
570 _Tp __y = __z.imag();
576 return __s *
sqrt(__x * __x + __y * __y);
579 #if _GLIBCXX_USE_C99_COMPLEX
581 __complex_abs(__complex__
float __z) {
return __builtin_cabsf(__z); }
584 __complex_abs(__complex__
double __z) {
return __builtin_cabs(__z); }
587 __complex_abs(
const __complex__
long double& __z)
588 {
return __builtin_cabsl(__z); }
590 template<
typename _Tp>
592 abs(
const complex<_Tp>& __z) {
return __complex_abs(__z.__rep()); }
594 template<
typename _Tp>
601 template<
typename _Tp>
603 __complex_arg(
const complex<_Tp>& __z)
604 {
return atan2(__z.imag(), __z.real()); }
606 #if _GLIBCXX_USE_C99_COMPLEX
608 __complex_arg(__complex__
float __z) {
return __builtin_cargf(__z); }
611 __complex_arg(__complex__
double __z) {
return __builtin_carg(__z); }
614 __complex_arg(
const __complex__
long double& __z)
615 {
return __builtin_cargl(__z); }
617 template<
typename _Tp>
619 arg(
const complex<_Tp>& __z) {
return __complex_arg(__z.__rep()); }
621 template<
typename _Tp>
634 template<
typename _Tp>
635 static inline _Tp _S_do_it(
const complex<_Tp>& __z)
637 const _Tp __x = __z.real();
638 const _Tp __y = __z.imag();
639 return __x * __x + __y * __y;
644 struct _Norm_helper<true>
646 template<
typename _Tp>
647 static inline _Tp _S_do_it(
const complex<_Tp>& __z)
650 return __res * __res;
654 template<
typename _Tp>
658 return _Norm_helper<__is_floating<_Tp>::__value
659 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
662 template<
typename _Tp>
664 polar(
const _Tp& __rho,
const _Tp& __theta)
667 template<
typename _Tp>
675 template<
typename _Tp>
677 __complex_cos(
const complex<_Tp>& __z)
679 const _Tp __x = __z.real();
680 const _Tp __y = __z.imag();
684 #if _GLIBCXX_USE_C99_COMPLEX
685 inline __complex__
float
686 __complex_cos(__complex__
float __z) {
return __builtin_ccosf(__z); }
688 inline __complex__
double
689 __complex_cos(__complex__
double __z) {
return __builtin_ccos(__z); }
691 inline __complex__
long double
692 __complex_cos(
const __complex__
long double& __z)
693 {
return __builtin_ccosl(__z); }
695 template<
typename _Tp>
697 cos(
const complex<_Tp>& __z) {
return __complex_cos(__z.__rep()); }
699 template<
typename _Tp>
705 template<
typename _Tp>
707 __complex_cosh(
const complex<_Tp>& __z)
709 const _Tp __x = __z.real();
710 const _Tp __y = __z.imag();
714 #if _GLIBCXX_USE_C99_COMPLEX
715 inline __complex__
float
716 __complex_cosh(__complex__
float __z) {
return __builtin_ccoshf(__z); }
718 inline __complex__
double
719 __complex_cosh(__complex__
double __z) {
return __builtin_ccosh(__z); }
721 inline __complex__
long double
722 __complex_cosh(
const __complex__
long double& __z)
723 {
return __builtin_ccoshl(__z); }
725 template<
typename _Tp>
727 cosh(
const complex<_Tp>& __z) {
return __complex_cosh(__z.__rep()); }
729 template<
typename _Tp>
735 template<
typename _Tp>
737 __complex_exp(
const complex<_Tp>& __z)
740 #if _GLIBCXX_USE_C99_COMPLEX
741 inline __complex__
float
742 __complex_exp(__complex__
float __z) {
return __builtin_cexpf(__z); }
744 inline __complex__
double
745 __complex_exp(__complex__
double __z) {
return __builtin_cexp(__z); }
747 inline __complex__
long double
748 __complex_exp(
const __complex__
long double& __z)
749 {
return __builtin_cexpl(__z); }
751 template<
typename _Tp>
753 exp(
const complex<_Tp>& __z) {
return __complex_exp(__z.__rep()); }
755 template<
typename _Tp>
762 template<
typename _Tp>
764 __complex_log(
const complex<_Tp>& __z)
767 #if _GLIBCXX_USE_C99_COMPLEX
768 inline __complex__
float
769 __complex_log(__complex__
float __z) {
return __builtin_clogf(__z); }
771 inline __complex__
double
772 __complex_log(__complex__
double __z) {
return __builtin_clog(__z); }
774 inline __complex__
long double
775 __complex_log(
const __complex__
long double& __z)
776 {
return __builtin_clogl(__z); }
778 template<
typename _Tp>
780 log(
const complex<_Tp>& __z) {
return __complex_log(__z.__rep()); }
782 template<
typename _Tp>
787 template<
typename _Tp>
793 template<
typename _Tp>
795 __complex_sin(
const complex<_Tp>& __z)
797 const _Tp __x = __z.real();
798 const _Tp __y = __z.imag();
802 #if _GLIBCXX_USE_C99_COMPLEX
803 inline __complex__
float
804 __complex_sin(__complex__
float __z) {
return __builtin_csinf(__z); }
806 inline __complex__
double
807 __complex_sin(__complex__
double __z) {
return __builtin_csin(__z); }
809 inline __complex__
long double
810 __complex_sin(
const __complex__
long double& __z)
811 {
return __builtin_csinl(__z); }
813 template<
typename _Tp>
815 sin(
const complex<_Tp>& __z) {
return __complex_sin(__z.__rep()); }
817 template<
typename _Tp>
823 template<
typename _Tp>
825 __complex_sinh(
const complex<_Tp>& __z)
827 const _Tp __x = __z.real();
828 const _Tp __y = __z.imag();
832 #if _GLIBCXX_USE_C99_COMPLEX
833 inline __complex__
float
834 __complex_sinh(__complex__
float __z) {
return __builtin_csinhf(__z); }
836 inline __complex__
double
837 __complex_sinh(__complex__
double __z) {
return __builtin_csinh(__z); }
839 inline __complex__
long double
840 __complex_sinh(
const __complex__
long double& __z)
841 {
return __builtin_csinhl(__z); }
843 template<
typename _Tp>
845 sinh(
const complex<_Tp>& __z) {
return __complex_sinh(__z.__rep()); }
847 template<
typename _Tp>
854 template<
typename _Tp>
856 __complex_sqrt(
const complex<_Tp>& __z)
858 _Tp __x = __z.real();
859 _Tp __y = __z.imag();
864 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
871 ? complex<_Tp>(__u, __y / __t)
872 : complex<_Tp>(
abs(__y) / __t, __y < _Tp() ? -__u : __u);
876 #if _GLIBCXX_USE_C99_COMPLEX
877 inline __complex__
float
878 __complex_sqrt(__complex__
float __z) {
return __builtin_csqrtf(__z); }
880 inline __complex__
double
881 __complex_sqrt(__complex__
double __z) {
return __builtin_csqrt(__z); }
883 inline __complex__
long double
884 __complex_sqrt(
const __complex__
long double& __z)
885 {
return __builtin_csqrtl(__z); }
887 template<
typename _Tp>
889 sqrt(
const complex<_Tp>& __z) {
return __complex_sqrt(__z.__rep()); }
891 template<
typename _Tp>
898 template<
typename _Tp>
900 __complex_tan(
const complex<_Tp>& __z)
903 #if _GLIBCXX_USE_C99_COMPLEX
904 inline __complex__
float
905 __complex_tan(__complex__
float __z) {
return __builtin_ctanf(__z); }
907 inline __complex__
double
908 __complex_tan(__complex__
double __z) {
return __builtin_ctan(__z); }
910 inline __complex__
long double
911 __complex_tan(
const __complex__
long double& __z)
912 {
return __builtin_ctanl(__z); }
914 template<
typename _Tp>
916 tan(
const complex<_Tp>& __z) {
return __complex_tan(__z.__rep()); }
918 template<
typename _Tp>
926 template<
typename _Tp>
928 __complex_tanh(
const complex<_Tp>& __z)
931 #if _GLIBCXX_USE_C99_COMPLEX
932 inline __complex__
float
933 __complex_tanh(__complex__
float __z) {
return __builtin_ctanhf(__z); }
935 inline __complex__
double
936 __complex_tanh(__complex__
double __z) {
return __builtin_ctanh(__z); }
938 inline __complex__
long double
939 __complex_tanh(
const __complex__
long double& __z)
940 {
return __builtin_ctanhl(__z); }
942 template<
typename _Tp>
944 tanh(
const complex<_Tp>& __z) {
return __complex_tanh(__z.__rep()); }
946 template<
typename _Tp>
955 #ifndef __GXX_EXPERIMENTAL_CXX0X__
956 template<
typename _Tp>
958 __complex_pow_unsigned(complex<_Tp> __x,
unsigned __n)
960 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
974 template<
typename _Tp>
976 pow(
const complex<_Tp>& __z,
int __n)
979 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -__n)
980 : std::__complex_pow_unsigned(__z, __n);
984 template<
typename _Tp>
988 #ifndef _GLIBCXX_USE_C99_COMPLEX
992 if (__x.imag() == _Tp() && __x.real() > _Tp())
993 return pow(__x.real(), __y);
999 template<
typename _Tp>
1001 __complex_pow(
const complex<_Tp>& __x,
const complex<_Tp>& __y)
1002 {
return __x == _Tp() ? _Tp() : std::
exp(__y * std::
log(__x)); }
1004 #if _GLIBCXX_USE_C99_COMPLEX
1005 inline __complex__
float
1006 __complex_pow(__complex__
float __x, __complex__
float __y)
1007 {
return __builtin_cpowf(__x, __y); }
1009 inline __complex__
double
1010 __complex_pow(__complex__
double __x, __complex__
double __y)
1011 {
return __builtin_cpow(__x, __y); }
1013 inline __complex__
long double
1014 __complex_pow(
const __complex__
long double& __x,
1015 const __complex__
long double& __y)
1016 {
return __builtin_cpowl(__x, __y); }
1018 template<
typename _Tp>
1020 pow(
const complex<_Tp>& __x,
const complex<_Tp>& __y)
1021 {
return __complex_pow(__x.__rep(), __y.__rep()); }
1023 template<
typename _Tp>
1026 {
return __complex_pow(__x, __y); }
1029 template<
typename _Tp>
1034 __y.imag() *
log(__x))
1041 struct complex<float>
1044 typedef __complex__
float _ComplexT;
1046 _GLIBCXX_CONSTEXPR
complex(_ComplexT __z) : _M_value(__z) { }
1048 _GLIBCXX_CONSTEXPR
complex(
float __r = 0.0f,
float __i = 0.0f)
1049 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1053 : _M_value(__r + __i * 1.0fi) { }
1056 __real__ _M_value = __r;
1057 __imag__ _M_value = __i;
1061 explicit _GLIBCXX_CONSTEXPR
complex(
const complex<double>&);
1062 explicit _GLIBCXX_CONSTEXPR
complex(
const complex<long double>&);
1064 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1068 real()
const {
return __real__ _M_value; }
1071 imag()
const {
return __imag__ _M_value; }
1074 real() {
return __real__ _M_value; }
1077 real()
const {
return __real__ _M_value; }
1080 imag() {
return __imag__ _M_value; }
1083 imag()
const {
return __imag__ _M_value; }
1089 real(
float __val) { __real__ _M_value = __val; }
1092 imag(
float __val) { __imag__ _M_value = __val; }
1133 template<
typename _Tp>
1137 __real__ _M_value = __z.real();
1138 __imag__ _M_value = __z.imag();
1142 template<
typename _Tp>
1146 __real__ _M_value += __z.real();
1147 __imag__ _M_value += __z.imag();
1155 __real__ _M_value -= __z.real();
1156 __imag__ _M_value -= __z.imag();
1165 __real__ __t = __z.real();
1166 __imag__ __t = __z.imag();
1176 __real__ __t = __z.real();
1177 __imag__ __t = __z.imag();
1182 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep()
const {
return _M_value; }
1191 struct complex<double>
1194 typedef __complex__
double _ComplexT;
1196 _GLIBCXX_CONSTEXPR
complex(_ComplexT __z) : _M_value(__z) { }
1198 _GLIBCXX_CONSTEXPR
complex(
double __r = 0.0,
double __i = 0.0)
1199 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1203 : _M_value(__r + __i * 1.0i) { }
1206 __real__ _M_value = __r;
1207 __imag__ _M_value = __i;
1211 _GLIBCXX_CONSTEXPR
complex(
const complex<float>& __z)
1212 : _M_value(__z.__rep()) { }
1214 explicit _GLIBCXX_CONSTEXPR
complex(
const complex<long double>&);
1216 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1220 real()
const {
return __real__ _M_value; }
1223 imag()
const {
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; }
1241 real(
double __val) { __real__ _M_value = __val; }
1244 imag(
double __val) { __imag__ _M_value = __val; }
1284 template<
typename _Tp>
1288 __real__ _M_value = __z.real();
1289 __imag__ _M_value = __z.imag();
1293 template<
typename _Tp>
1297 __real__ _M_value += __z.real();
1298 __imag__ _M_value += __z.imag();
1302 template<
typename _Tp>
1306 __real__ _M_value -= __z.real();
1307 __imag__ _M_value -= __z.imag();
1311 template<
typename _Tp>
1316 __real__ __t = __z.real();
1317 __imag__ __t = __z.imag();
1322 template<
typename _Tp>
1327 __real__ __t = __z.real();
1328 __imag__ __t = __z.imag();
1333 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep()
const {
return _M_value; }
1342 struct complex<long double>
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 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1355 : _M_value(__r + __i * 1.0Li) { }
1358 __real__ _M_value = __r;
1359 __imag__ _M_value = __i;
1363 _GLIBCXX_CONSTEXPR
complex(
const complex<float>& __z)
1364 : _M_value(__z.__rep()) { }
1366 _GLIBCXX_CONSTEXPR
complex(
const complex<double>& __z)
1367 : _M_value(__z.__rep()) { }
1369 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1372 constexpr
long double
1373 real()
const {
return __real__ _M_value; }
1375 constexpr
long double
1376 imag()
const {
return __imag__ _M_value; }
1379 real() {
return __real__ _M_value; }
1382 real()
const {
return __real__ _M_value; }
1385 imag() {
return __imag__ _M_value; }
1388 imag()
const {
return __imag__ _M_value; }
1394 real(
long double __val) { __real__ _M_value = __val; }
1397 imag(
long double __val) { __imag__ _M_value = __val; }
1437 template<
typename _Tp>
1441 __real__ _M_value = __z.real();
1442 __imag__ _M_value = __z.imag();
1446 template<
typename _Tp>
1450 __real__ _M_value += __z.real();
1451 __imag__ _M_value += __z.imag();
1455 template<
typename _Tp>
1459 __real__ _M_value -= __z.real();
1460 __imag__ _M_value -= __z.imag();
1464 template<
typename _Tp>
1469 __real__ __t = __z.real();
1470 __imag__ __t = __z.imag();
1475 template<
typename _Tp>
1480 __real__ __t = __z.real();
1481 __imag__ __t = __z.imag();
1486 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep()
const {
return _M_value; }
1494 inline _GLIBCXX_CONSTEXPR
1496 : _M_value(__z.__rep()) { }
1498 inline _GLIBCXX_CONSTEXPR
1499 complex<float>::complex(
const complex<long double>& __z)
1500 : _M_value(__z.__rep()) { }
1502 inline _GLIBCXX_CONSTEXPR
1503 complex<double>::complex(
const complex<long double>& __z)
1504 : _M_value(__z.__rep()) { }
1509 #if _GLIBCXX_EXTERN_TEMPLATE
1511 extern template ostream& operator<<(ostream&, const complex<float>&);
1513 extern template ostream& operator<<(ostream&, const complex<double>&);
1515 extern template ostream& operator<<(ostream&, const complex<long double>&);
1517 #ifdef _GLIBCXX_USE_WCHAR_T
1519 extern template wostream& operator<<(wostream&, const complex<float>&);
1521 extern template wostream& operator<<(wostream&, const complex<double>&);
1523 extern template wostream& operator<<(wostream&, const complex<long double>&);
1529 _GLIBCXX_END_NAMESPACE_VERSION
1532 namespace __gnu_cxx _GLIBCXX_VISIBILITY(
default)
1534 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1537 template<
typename _Tp,
typename _Up>
1538 struct __promote_2<std::complex<_Tp>, _Up>
1544 template<
typename _Tp,
typename _Up>
1545 struct __promote_2<_Tp, std::complex<_Up> >
1551 template<
typename _Tp,
typename _Up>
1552 struct __promote_2<std::complex<_Tp>,
std::complex<_Up> >
1558 _GLIBCXX_END_NAMESPACE_VERSION
1561 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1563 namespace std _GLIBCXX_VISIBILITY(default)
1565 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1578 template<
typename _Tp>
1583 const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
1587 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1588 inline __complex__
float
1589 __complex_acos(__complex__
float __z)
1590 {
return __builtin_cacosf(__z); }
1592 inline __complex__
double
1593 __complex_acos(__complex__
double __z)
1594 {
return __builtin_cacos(__z); }
1596 inline __complex__
long double
1597 __complex_acos(
const __complex__
long double& __z)
1598 {
return __builtin_cacosl(__z); }
1600 template<
typename _Tp>
1603 {
return __complex_acos(__z.__rep()); }
1608 template<
typename _Tp>
1611 {
return __complex_acos(__z); }
1614 template<
typename _Tp>
1623 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1624 inline __complex__
float
1625 __complex_asin(__complex__
float __z)
1626 {
return __builtin_casinf(__z); }
1628 inline __complex__
double
1629 __complex_asin(__complex__
double __z)
1630 {
return __builtin_casin(__z); }
1632 inline __complex__
long double
1633 __complex_asin(
const __complex__
long double& __z)
1634 {
return __builtin_casinl(__z); }
1636 template<
typename _Tp>
1639 {
return __complex_asin(__z.__rep()); }
1644 template<
typename _Tp>
1647 {
return __complex_asin(__z); }
1650 template<
typename _Tp>
1654 const _Tp __r2 = __z.real() * __z.real();
1655 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
1657 _Tp __num = __z.imag() + _Tp(1.0);
1658 _Tp __den = __z.imag() - _Tp(1.0);
1660 __num = __r2 + __num * __num;
1661 __den = __r2 + __den * __den;
1664 _Tp(0.25) *
log(__num / __den));
1667 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1668 inline __complex__
float
1669 __complex_atan(__complex__
float __z)
1670 {
return __builtin_catanf(__z); }
1672 inline __complex__
double
1673 __complex_atan(__complex__
double __z)
1674 {
return __builtin_catan(__z); }
1676 inline __complex__
long double
1677 __complex_atan(
const __complex__
long double& __z)
1678 {
return __builtin_catanl(__z); }
1680 template<
typename _Tp>
1683 {
return __complex_atan(__z.__rep()); }
1688 template<
typename _Tp>
1691 {
return __complex_atan(__z); }
1694 template<
typename _Tp>
1700 +
std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
1703 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1704 inline __complex__
float
1705 __complex_acosh(__complex__
float __z)
1706 {
return __builtin_cacoshf(__z); }
1708 inline __complex__
double
1709 __complex_acosh(__complex__
double __z)
1710 {
return __builtin_cacosh(__z); }
1712 inline __complex__
long double
1713 __complex_acosh(
const __complex__
long double& __z)
1714 {
return __builtin_cacoshl(__z); }
1716 template<
typename _Tp>
1719 {
return __complex_acosh(__z.__rep()); }
1724 template<
typename _Tp>
1727 {
return __complex_acosh(__z); }
1730 template<
typename _Tp>
1735 * (__z.real() + __z.imag()) + _Tp(1.0),
1736 _Tp(2.0) * __z.real() * __z.imag());
1742 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1743 inline __complex__
float
1744 __complex_asinh(__complex__
float __z)
1745 {
return __builtin_casinhf(__z); }
1747 inline __complex__
double
1748 __complex_asinh(__complex__
double __z)
1749 {
return __builtin_casinh(__z); }
1751 inline __complex__
long double
1752 __complex_asinh(
const __complex__
long double& __z)
1753 {
return __builtin_casinhl(__z); }
1755 template<
typename _Tp>
1758 {
return __complex_asinh(__z.__rep()); }
1763 template<
typename _Tp>
1766 {
return __complex_asinh(__z); }
1769 template<
typename _Tp>
1773 const _Tp __i2 = __z.imag() * __z.imag();
1774 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
1776 _Tp __num = _Tp(1.0) + __z.real();
1777 _Tp __den = _Tp(1.0) - __z.real();
1779 __num = __i2 + __num * __num;
1780 __den = __i2 + __den * __den;
1783 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
1786 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1787 inline __complex__
float
1788 __complex_atanh(__complex__
float __z)
1789 {
return __builtin_catanhf(__z); }
1791 inline __complex__
double
1792 __complex_atanh(__complex__
double __z)
1793 {
return __builtin_catanh(__z); }
1795 inline __complex__
long double
1796 __complex_atanh(
const __complex__
long double& __z)
1797 {
return __builtin_catanhl(__z); }
1799 template<
typename _Tp>
1802 {
return __complex_atanh(__z.__rep()); }
1807 template<
typename _Tp>
1810 {
return __complex_atanh(__z); }
1813 template<
typename _Tp>
1822 template<
typename _Tp>
1823 inline typename __gnu_cxx::__promote<_Tp>::__type
1826 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1827 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
1828 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
1835 template<
typename _Tp>
1836 inline typename __gnu_cxx::__promote<_Tp>::__type
1840 template<
typename _Tp>
1841 inline typename __gnu_cxx::__promote<_Tp>::__type
1844 typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1845 return __type(__x) * __type(__x);
1848 template<
typename _Tp>
1849 inline typename __gnu_cxx::__promote<_Tp>::__type
1853 template<
typename _Tp,
typename _Up>
1857 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1861 template<
typename _Tp,
typename _Up>
1865 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1869 template<
typename _Tp,
typename _Up>
1873 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1882 template<
typename _Tp>
1886 const _Tp __den = (__z.real() * __z.real()
1887 + __z.imag() * __z.imag() + _Tp(1.0));
1890 (_Tp(2.0) * __z.imag()) / __den);
1893 #if _GLIBCXX_USE_C99_COMPLEX
1894 inline __complex__
float
1895 __complex_proj(__complex__
float __z)
1896 {
return __builtin_cprojf(__z); }
1898 inline __complex__
double
1899 __complex_proj(__complex__
double __z)
1900 {
return __builtin_cproj(__z); }
1902 inline __complex__
long double
1903 __complex_proj(
const __complex__
long double& __z)
1904 {
return __builtin_cprojl(__z); }
1906 template<
typename _Tp>
1909 {
return __complex_proj(__z.__rep()); }
1911 template<
typename _Tp>
1914 {
return __complex_proj(__z); }
1918 template<
typename _Tp>
1919 inline typename __gnu_cxx::__promote<_Tp>::__type
1923 template<
typename _Tp>
1924 inline typename __gnu_cxx::__promote<_Tp>::__type
1928 _GLIBCXX_END_NAMESPACE_VERSION
1931 #endif // __GXX_EXPERIMENTAL_CXX0X__