libstdc++
|
00001 // The template and inlines for the -*- C++ -*- complex number classes. 00002 00003 // Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 00004 // 2006, 2007, 2008, 2009, 2010, 2011 00005 // Free Software Foundation, Inc. 00006 // 00007 // This file is part of the GNU ISO C++ Library. This library is free 00008 // software; you can redistribute it and/or modify it under the 00009 // terms of the GNU General Public License as published by the 00010 // Free Software Foundation; either version 3, or (at your option) 00011 // any later version. 00012 00013 // This library is distributed in the hope that it will be useful, 00014 // but WITHOUT ANY WARRANTY; without even the implied warranty of 00015 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00016 // GNU General Public License for more details. 00017 00018 // Under Section 7 of GPL version 3, you are granted additional 00019 // permissions described in the GCC Runtime Library Exception, version 00020 // 3.1, as published by the Free Software Foundation. 00021 00022 // You should have received a copy of the GNU General Public License and 00023 // a copy of the GCC Runtime Library Exception along with this program; 00024 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 00025 // <http://www.gnu.org/licenses/>. 00026 00027 /** @file include/complex 00028 * This is a Standard C++ Library header. 00029 */ 00030 00031 // 00032 // ISO C++ 14882: 26.2 Complex Numbers 00033 // Note: this is not a conforming implementation. 00034 // Initially implemented by Ulrich Drepper <drepper@cygnus.com> 00035 // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr> 00036 // 00037 00038 #ifndef _GLIBCXX_COMPLEX 00039 #define _GLIBCXX_COMPLEX 1 00040 00041 #pragma GCC system_header 00042 00043 #include <bits/c++config.h> 00044 #include <bits/cpp_type_traits.h> 00045 #include <ext/type_traits.h> 00046 #include <cmath> 00047 #include <sstream> 00048 00049 namespace std _GLIBCXX_VISIBILITY(default) 00050 { 00051 _GLIBCXX_BEGIN_NAMESPACE_VERSION 00052 00053 /** 00054 * @defgroup complex_numbers Complex Numbers 00055 * @ingroup numerics 00056 * 00057 * Classes and functions for complex numbers. 00058 * @{ 00059 */ 00060 00061 // Forward declarations. 00062 template<typename _Tp> class complex; 00063 template<> class complex<float>; 00064 template<> class complex<double>; 00065 template<> class complex<long double>; 00066 00067 /// Return magnitude of @a z. 00068 template<typename _Tp> _Tp abs(const complex<_Tp>&); 00069 /// Return phase angle of @a z. 00070 template<typename _Tp> _Tp arg(const complex<_Tp>&); 00071 /// Return @a z magnitude squared. 00072 template<typename _Tp> _Tp norm(const complex<_Tp>&); 00073 00074 /// Return complex conjugate of @a z. 00075 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); 00076 /// Return complex with magnitude @a rho and angle @a theta. 00077 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 00078 00079 // Transcendentals: 00080 /// Return complex cosine of @a z. 00081 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 00082 /// Return complex hyperbolic cosine of @a z. 00083 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 00084 /// Return complex base e exponential of @a z. 00085 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 00086 /// Return complex natural logarithm of @a z. 00087 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 00088 /// Return complex base 10 logarithm of @a z. 00089 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 00090 #ifndef __GXX_EXPERIMENTAL_CXX0X__ 00091 // DR 844. 00092 /// Return @a x to the @a y'th power. 00093 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 00094 #endif 00095 /// Return @a x to the @a y'th power. 00096 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 00097 /// Return @a x to the @a y'th power. 00098 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 00099 const complex<_Tp>&); 00100 /// Return @a x to the @a y'th power. 00101 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 00102 /// Return complex sine of @a z. 00103 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 00104 /// Return complex hyperbolic sine of @a z. 00105 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 00106 /// Return complex square root of @a z. 00107 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 00108 /// Return complex tangent of @a z. 00109 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 00110 /// Return complex hyperbolic tangent of @a z. 00111 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 00112 00113 00114 // 26.2.2 Primary template class complex 00115 /** 00116 * Template to represent complex numbers. 00117 * 00118 * Specializations for float, double, and long double are part of the 00119 * library. Results with any other type are not guaranteed. 00120 * 00121 * @param Tp Type of real and imaginary values. 00122 */ 00123 template<typename _Tp> 00124 struct complex 00125 { 00126 /// Value typedef. 00127 typedef _Tp value_type; 00128 00129 /// Default constructor. First parameter is x, second parameter is y. 00130 /// Unspecified parameters default to 0. 00131 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 00132 : _M_real(__r), _M_imag(__i) { } 00133 00134 // Lets the compiler synthesize the copy constructor 00135 // complex (const complex<_Tp>&); 00136 /// Copy constructor. 00137 template<typename _Up> 00138 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 00139 : _M_real(__z.real()), _M_imag(__z.imag()) { } 00140 00141 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 00142 // _GLIBCXX_RESOLVE_LIB_DEFECTS 00143 // DR 387. std::complex over-encapsulated. 00144 constexpr _Tp 00145 real() const { return _M_real; } 00146 00147 constexpr _Tp 00148 imag() const { return _M_imag; } 00149 #else 00150 /// Return real part of complex number. 00151 _Tp& 00152 real() { return _M_real; } 00153 00154 /// Return real part of complex number. 00155 const _Tp& 00156 real() const { return _M_real; } 00157 00158 /// Return imaginary part of complex number. 00159 _Tp& 00160 imag() { return _M_imag; } 00161 00162 /// Return imaginary part of complex number. 00163 const _Tp& 00164 imag() const { return _M_imag; } 00165 #endif 00166 00167 // _GLIBCXX_RESOLVE_LIB_DEFECTS 00168 // DR 387. std::complex over-encapsulated. 00169 void 00170 real(_Tp __val) { _M_real = __val; } 00171 00172 void 00173 imag(_Tp __val) { _M_imag = __val; } 00174 00175 /// Assign this complex number to scalar @a t. 00176 complex<_Tp>& operator=(const _Tp&); 00177 00178 /// Add @a t to this complex number. 00179 // 26.2.5/1 00180 complex<_Tp>& 00181 operator+=(const _Tp& __t) 00182 { 00183 _M_real += __t; 00184 return *this; 00185 } 00186 00187 /// Subtract @a t from this complex number. 00188 // 26.2.5/3 00189 complex<_Tp>& 00190 operator-=(const _Tp& __t) 00191 { 00192 _M_real -= __t; 00193 return *this; 00194 } 00195 00196 /// Multiply this complex number by @a t. 00197 complex<_Tp>& operator*=(const _Tp&); 00198 /// Divide this complex number by @a t. 00199 complex<_Tp>& operator/=(const _Tp&); 00200 00201 // Lets the compiler synthesize the 00202 // copy and assignment operator 00203 // complex<_Tp>& operator= (const complex<_Tp>&); 00204 /// Assign this complex number to complex @a z. 00205 template<typename _Up> 00206 complex<_Tp>& operator=(const complex<_Up>&); 00207 /// Add @a z to this complex number. 00208 template<typename _Up> 00209 complex<_Tp>& operator+=(const complex<_Up>&); 00210 /// Subtract @a z from this complex number. 00211 template<typename _Up> 00212 complex<_Tp>& operator-=(const complex<_Up>&); 00213 /// Multiply this complex number by @a z. 00214 template<typename _Up> 00215 complex<_Tp>& operator*=(const complex<_Up>&); 00216 /// Divide this complex number by @a z. 00217 template<typename _Up> 00218 complex<_Tp>& operator/=(const complex<_Up>&); 00219 00220 _GLIBCXX_USE_CONSTEXPR complex __rep() const 00221 { return *this; } 00222 00223 private: 00224 _Tp _M_real; 00225 _Tp _M_imag; 00226 }; 00227 00228 template<typename _Tp> 00229 complex<_Tp>& 00230 complex<_Tp>::operator=(const _Tp& __t) 00231 { 00232 _M_real = __t; 00233 _M_imag = _Tp(); 00234 return *this; 00235 } 00236 00237 // 26.2.5/5 00238 template<typename _Tp> 00239 complex<_Tp>& 00240 complex<_Tp>::operator*=(const _Tp& __t) 00241 { 00242 _M_real *= __t; 00243 _M_imag *= __t; 00244 return *this; 00245 } 00246 00247 // 26.2.5/7 00248 template<typename _Tp> 00249 complex<_Tp>& 00250 complex<_Tp>::operator/=(const _Tp& __t) 00251 { 00252 _M_real /= __t; 00253 _M_imag /= __t; 00254 return *this; 00255 } 00256 00257 template<typename _Tp> 00258 template<typename _Up> 00259 complex<_Tp>& 00260 complex<_Tp>::operator=(const complex<_Up>& __z) 00261 { 00262 _M_real = __z.real(); 00263 _M_imag = __z.imag(); 00264 return *this; 00265 } 00266 00267 // 26.2.5/9 00268 template<typename _Tp> 00269 template<typename _Up> 00270 complex<_Tp>& 00271 complex<_Tp>::operator+=(const complex<_Up>& __z) 00272 { 00273 _M_real += __z.real(); 00274 _M_imag += __z.imag(); 00275 return *this; 00276 } 00277 00278 // 26.2.5/11 00279 template<typename _Tp> 00280 template<typename _Up> 00281 complex<_Tp>& 00282 complex<_Tp>::operator-=(const complex<_Up>& __z) 00283 { 00284 _M_real -= __z.real(); 00285 _M_imag -= __z.imag(); 00286 return *this; 00287 } 00288 00289 // 26.2.5/13 00290 // XXX: This is a grammar school implementation. 00291 template<typename _Tp> 00292 template<typename _Up> 00293 complex<_Tp>& 00294 complex<_Tp>::operator*=(const complex<_Up>& __z) 00295 { 00296 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 00297 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 00298 _M_real = __r; 00299 return *this; 00300 } 00301 00302 // 26.2.5/15 00303 // XXX: This is a grammar school implementation. 00304 template<typename _Tp> 00305 template<typename _Up> 00306 complex<_Tp>& 00307 complex<_Tp>::operator/=(const complex<_Up>& __z) 00308 { 00309 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 00310 const _Tp __n = std::norm(__z); 00311 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 00312 _M_real = __r / __n; 00313 return *this; 00314 } 00315 00316 // Operators: 00317 //@{ 00318 /// Return new complex value @a x plus @a y. 00319 template<typename _Tp> 00320 inline complex<_Tp> 00321 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 00322 { 00323 complex<_Tp> __r = __x; 00324 __r += __y; 00325 return __r; 00326 } 00327 00328 template<typename _Tp> 00329 inline complex<_Tp> 00330 operator+(const complex<_Tp>& __x, const _Tp& __y) 00331 { 00332 complex<_Tp> __r = __x; 00333 __r += __y; 00334 return __r; 00335 } 00336 00337 template<typename _Tp> 00338 inline complex<_Tp> 00339 operator+(const _Tp& __x, const complex<_Tp>& __y) 00340 { 00341 complex<_Tp> __r = __y; 00342 __r += __x; 00343 return __r; 00344 } 00345 //@} 00346 00347 //@{ 00348 /// Return new complex value @a x minus @a y. 00349 template<typename _Tp> 00350 inline complex<_Tp> 00351 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 00352 { 00353 complex<_Tp> __r = __x; 00354 __r -= __y; 00355 return __r; 00356 } 00357 00358 template<typename _Tp> 00359 inline complex<_Tp> 00360 operator-(const complex<_Tp>& __x, const _Tp& __y) 00361 { 00362 complex<_Tp> __r = __x; 00363 __r -= __y; 00364 return __r; 00365 } 00366 00367 template<typename _Tp> 00368 inline complex<_Tp> 00369 operator-(const _Tp& __x, const complex<_Tp>& __y) 00370 { 00371 complex<_Tp> __r(__x, -__y.imag()); 00372 __r -= __y.real(); 00373 return __r; 00374 } 00375 //@} 00376 00377 //@{ 00378 /// Return new complex value @a x times @a y. 00379 template<typename _Tp> 00380 inline complex<_Tp> 00381 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 00382 { 00383 complex<_Tp> __r = __x; 00384 __r *= __y; 00385 return __r; 00386 } 00387 00388 template<typename _Tp> 00389 inline complex<_Tp> 00390 operator*(const complex<_Tp>& __x, const _Tp& __y) 00391 { 00392 complex<_Tp> __r = __x; 00393 __r *= __y; 00394 return __r; 00395 } 00396 00397 template<typename _Tp> 00398 inline complex<_Tp> 00399 operator*(const _Tp& __x, const complex<_Tp>& __y) 00400 { 00401 complex<_Tp> __r = __y; 00402 __r *= __x; 00403 return __r; 00404 } 00405 //@} 00406 00407 //@{ 00408 /// Return new complex value @a x divided by @a y. 00409 template<typename _Tp> 00410 inline complex<_Tp> 00411 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 00412 { 00413 complex<_Tp> __r = __x; 00414 __r /= __y; 00415 return __r; 00416 } 00417 00418 template<typename _Tp> 00419 inline complex<_Tp> 00420 operator/(const complex<_Tp>& __x, const _Tp& __y) 00421 { 00422 complex<_Tp> __r = __x; 00423 __r /= __y; 00424 return __r; 00425 } 00426 00427 template<typename _Tp> 00428 inline complex<_Tp> 00429 operator/(const _Tp& __x, const complex<_Tp>& __y) 00430 { 00431 complex<_Tp> __r = __x; 00432 __r /= __y; 00433 return __r; 00434 } 00435 //@} 00436 00437 /// Return @a x. 00438 template<typename _Tp> 00439 inline complex<_Tp> 00440 operator+(const complex<_Tp>& __x) 00441 { return __x; } 00442 00443 /// Return complex negation of @a x. 00444 template<typename _Tp> 00445 inline complex<_Tp> 00446 operator-(const complex<_Tp>& __x) 00447 { return complex<_Tp>(-__x.real(), -__x.imag()); } 00448 00449 //@{ 00450 /// Return true if @a x is equal to @a y. 00451 template<typename _Tp> 00452 inline _GLIBCXX_CONSTEXPR bool 00453 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 00454 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 00455 00456 template<typename _Tp> 00457 inline _GLIBCXX_CONSTEXPR bool 00458 operator==(const complex<_Tp>& __x, const _Tp& __y) 00459 { return __x.real() == __y && __x.imag() == _Tp(); } 00460 00461 template<typename _Tp> 00462 inline _GLIBCXX_CONSTEXPR bool 00463 operator==(const _Tp& __x, const complex<_Tp>& __y) 00464 { return __x == __y.real() && _Tp() == __y.imag(); } 00465 //@} 00466 00467 //@{ 00468 /// Return false if @a x is equal to @a y. 00469 template<typename _Tp> 00470 inline _GLIBCXX_CONSTEXPR bool 00471 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 00472 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 00473 00474 template<typename _Tp> 00475 inline _GLIBCXX_CONSTEXPR bool 00476 operator!=(const complex<_Tp>& __x, const _Tp& __y) 00477 { return __x.real() != __y || __x.imag() != _Tp(); } 00478 00479 template<typename _Tp> 00480 inline _GLIBCXX_CONSTEXPR bool 00481 operator!=(const _Tp& __x, const complex<_Tp>& __y) 00482 { return __x != __y.real() || _Tp() != __y.imag(); } 00483 //@} 00484 00485 /// Extraction operator for complex values. 00486 template<typename _Tp, typename _CharT, class _Traits> 00487 basic_istream<_CharT, _Traits>& 00488 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 00489 { 00490 _Tp __re_x, __im_x; 00491 _CharT __ch; 00492 __is >> __ch; 00493 if (__ch == '(') 00494 { 00495 __is >> __re_x >> __ch; 00496 if (__ch == ',') 00497 { 00498 __is >> __im_x >> __ch; 00499 if (__ch == ')') 00500 __x = complex<_Tp>(__re_x, __im_x); 00501 else 00502 __is.setstate(ios_base::failbit); 00503 } 00504 else if (__ch == ')') 00505 __x = __re_x; 00506 else 00507 __is.setstate(ios_base::failbit); 00508 } 00509 else 00510 { 00511 __is.putback(__ch); 00512 __is >> __re_x; 00513 __x = __re_x; 00514 } 00515 return __is; 00516 } 00517 00518 /// Insertion operator for complex values. 00519 template<typename _Tp, typename _CharT, class _Traits> 00520 basic_ostream<_CharT, _Traits>& 00521 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 00522 { 00523 basic_ostringstream<_CharT, _Traits> __s; 00524 __s.flags(__os.flags()); 00525 __s.imbue(__os.getloc()); 00526 __s.precision(__os.precision()); 00527 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 00528 return __os << __s.str(); 00529 } 00530 00531 // Values 00532 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 00533 template<typename _Tp> 00534 inline constexpr _Tp 00535 real(const complex<_Tp>& __z) 00536 { return __z.real(); } 00537 00538 template<typename _Tp> 00539 inline constexpr _Tp 00540 imag(const complex<_Tp>& __z) 00541 { return __z.imag(); } 00542 #else 00543 template<typename _Tp> 00544 inline _Tp& 00545 real(complex<_Tp>& __z) 00546 { return __z.real(); } 00547 00548 template<typename _Tp> 00549 inline const _Tp& 00550 real(const complex<_Tp>& __z) 00551 { return __z.real(); } 00552 00553 template<typename _Tp> 00554 inline _Tp& 00555 imag(complex<_Tp>& __z) 00556 { return __z.imag(); } 00557 00558 template<typename _Tp> 00559 inline const _Tp& 00560 imag(const complex<_Tp>& __z) 00561 { return __z.imag(); } 00562 #endif 00563 00564 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 00565 template<typename _Tp> 00566 inline _Tp 00567 __complex_abs(const complex<_Tp>& __z) 00568 { 00569 _Tp __x = __z.real(); 00570 _Tp __y = __z.imag(); 00571 const _Tp __s = std::max(abs(__x), abs(__y)); 00572 if (__s == _Tp()) // well ... 00573 return __s; 00574 __x /= __s; 00575 __y /= __s; 00576 return __s * sqrt(__x * __x + __y * __y); 00577 } 00578 00579 #if _GLIBCXX_USE_C99_COMPLEX 00580 inline float 00581 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 00582 00583 inline double 00584 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 00585 00586 inline long double 00587 __complex_abs(const __complex__ long double& __z) 00588 { return __builtin_cabsl(__z); } 00589 00590 template<typename _Tp> 00591 inline _Tp 00592 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 00593 #else 00594 template<typename _Tp> 00595 inline _Tp 00596 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 00597 #endif 00598 00599 00600 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 00601 template<typename _Tp> 00602 inline _Tp 00603 __complex_arg(const complex<_Tp>& __z) 00604 { return atan2(__z.imag(), __z.real()); } 00605 00606 #if _GLIBCXX_USE_C99_COMPLEX 00607 inline float 00608 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 00609 00610 inline double 00611 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 00612 00613 inline long double 00614 __complex_arg(const __complex__ long double& __z) 00615 { return __builtin_cargl(__z); } 00616 00617 template<typename _Tp> 00618 inline _Tp 00619 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 00620 #else 00621 template<typename _Tp> 00622 inline _Tp 00623 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 00624 #endif 00625 00626 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 00627 // As defined, norm() is -not- a norm is the common mathematical 00628 // sens used in numerics. The helper class _Norm_helper<> tries to 00629 // distinguish between builtin floating point and the rest, so as 00630 // to deliver an answer as close as possible to the real value. 00631 template<bool> 00632 struct _Norm_helper 00633 { 00634 template<typename _Tp> 00635 static inline _Tp _S_do_it(const complex<_Tp>& __z) 00636 { 00637 const _Tp __x = __z.real(); 00638 const _Tp __y = __z.imag(); 00639 return __x * __x + __y * __y; 00640 } 00641 }; 00642 00643 template<> 00644 struct _Norm_helper<true> 00645 { 00646 template<typename _Tp> 00647 static inline _Tp _S_do_it(const complex<_Tp>& __z) 00648 { 00649 _Tp __res = std::abs(__z); 00650 return __res * __res; 00651 } 00652 }; 00653 00654 template<typename _Tp> 00655 inline _Tp 00656 norm(const complex<_Tp>& __z) 00657 { 00658 return _Norm_helper<__is_floating<_Tp>::__value 00659 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 00660 } 00661 00662 template<typename _Tp> 00663 inline complex<_Tp> 00664 polar(const _Tp& __rho, const _Tp& __theta) 00665 { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } 00666 00667 template<typename _Tp> 00668 inline complex<_Tp> 00669 conj(const complex<_Tp>& __z) 00670 { return complex<_Tp>(__z.real(), -__z.imag()); } 00671 00672 // Transcendentals 00673 00674 // 26.2.8/1 cos(__z): Returns the cosine of __z. 00675 template<typename _Tp> 00676 inline complex<_Tp> 00677 __complex_cos(const complex<_Tp>& __z) 00678 { 00679 const _Tp __x = __z.real(); 00680 const _Tp __y = __z.imag(); 00681 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 00682 } 00683 00684 #if _GLIBCXX_USE_C99_COMPLEX 00685 inline __complex__ float 00686 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 00687 00688 inline __complex__ double 00689 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 00690 00691 inline __complex__ long double 00692 __complex_cos(const __complex__ long double& __z) 00693 { return __builtin_ccosl(__z); } 00694 00695 template<typename _Tp> 00696 inline complex<_Tp> 00697 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 00698 #else 00699 template<typename _Tp> 00700 inline complex<_Tp> 00701 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 00702 #endif 00703 00704 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 00705 template<typename _Tp> 00706 inline complex<_Tp> 00707 __complex_cosh(const complex<_Tp>& __z) 00708 { 00709 const _Tp __x = __z.real(); 00710 const _Tp __y = __z.imag(); 00711 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 00712 } 00713 00714 #if _GLIBCXX_USE_C99_COMPLEX 00715 inline __complex__ float 00716 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 00717 00718 inline __complex__ double 00719 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 00720 00721 inline __complex__ long double 00722 __complex_cosh(const __complex__ long double& __z) 00723 { return __builtin_ccoshl(__z); } 00724 00725 template<typename _Tp> 00726 inline complex<_Tp> 00727 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 00728 #else 00729 template<typename _Tp> 00730 inline complex<_Tp> 00731 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 00732 #endif 00733 00734 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 00735 template<typename _Tp> 00736 inline complex<_Tp> 00737 __complex_exp(const complex<_Tp>& __z) 00738 { return std::polar(exp(__z.real()), __z.imag()); } 00739 00740 #if _GLIBCXX_USE_C99_COMPLEX 00741 inline __complex__ float 00742 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 00743 00744 inline __complex__ double 00745 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 00746 00747 inline __complex__ long double 00748 __complex_exp(const __complex__ long double& __z) 00749 { return __builtin_cexpl(__z); } 00750 00751 template<typename _Tp> 00752 inline complex<_Tp> 00753 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 00754 #else 00755 template<typename _Tp> 00756 inline complex<_Tp> 00757 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 00758 #endif 00759 00760 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 00761 // The branch cut is along the negative axis. 00762 template<typename _Tp> 00763 inline complex<_Tp> 00764 __complex_log(const complex<_Tp>& __z) 00765 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 00766 00767 #if _GLIBCXX_USE_C99_COMPLEX 00768 inline __complex__ float 00769 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 00770 00771 inline __complex__ double 00772 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 00773 00774 inline __complex__ long double 00775 __complex_log(const __complex__ long double& __z) 00776 { return __builtin_clogl(__z); } 00777 00778 template<typename _Tp> 00779 inline complex<_Tp> 00780 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 00781 #else 00782 template<typename _Tp> 00783 inline complex<_Tp> 00784 log(const complex<_Tp>& __z) { return __complex_log(__z); } 00785 #endif 00786 00787 template<typename _Tp> 00788 inline complex<_Tp> 00789 log10(const complex<_Tp>& __z) 00790 { return std::log(__z) / log(_Tp(10.0)); } 00791 00792 // 26.2.8/10 sin(__z): Returns the sine of __z. 00793 template<typename _Tp> 00794 inline complex<_Tp> 00795 __complex_sin(const complex<_Tp>& __z) 00796 { 00797 const _Tp __x = __z.real(); 00798 const _Tp __y = __z.imag(); 00799 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 00800 } 00801 00802 #if _GLIBCXX_USE_C99_COMPLEX 00803 inline __complex__ float 00804 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 00805 00806 inline __complex__ double 00807 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 00808 00809 inline __complex__ long double 00810 __complex_sin(const __complex__ long double& __z) 00811 { return __builtin_csinl(__z); } 00812 00813 template<typename _Tp> 00814 inline complex<_Tp> 00815 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 00816 #else 00817 template<typename _Tp> 00818 inline complex<_Tp> 00819 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 00820 #endif 00821 00822 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 00823 template<typename _Tp> 00824 inline complex<_Tp> 00825 __complex_sinh(const complex<_Tp>& __z) 00826 { 00827 const _Tp __x = __z.real(); 00828 const _Tp __y = __z.imag(); 00829 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 00830 } 00831 00832 #if _GLIBCXX_USE_C99_COMPLEX 00833 inline __complex__ float 00834 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 00835 00836 inline __complex__ double 00837 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 00838 00839 inline __complex__ long double 00840 __complex_sinh(const __complex__ long double& __z) 00841 { return __builtin_csinhl(__z); } 00842 00843 template<typename _Tp> 00844 inline complex<_Tp> 00845 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 00846 #else 00847 template<typename _Tp> 00848 inline complex<_Tp> 00849 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 00850 #endif 00851 00852 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 00853 // The branch cut is on the negative axis. 00854 template<typename _Tp> 00855 complex<_Tp> 00856 __complex_sqrt(const complex<_Tp>& __z) 00857 { 00858 _Tp __x = __z.real(); 00859 _Tp __y = __z.imag(); 00860 00861 if (__x == _Tp()) 00862 { 00863 _Tp __t = sqrt(abs(__y) / 2); 00864 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 00865 } 00866 else 00867 { 00868 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 00869 _Tp __u = __t / 2; 00870 return __x > _Tp() 00871 ? complex<_Tp>(__u, __y / __t) 00872 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 00873 } 00874 } 00875 00876 #if _GLIBCXX_USE_C99_COMPLEX 00877 inline __complex__ float 00878 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 00879 00880 inline __complex__ double 00881 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 00882 00883 inline __complex__ long double 00884 __complex_sqrt(const __complex__ long double& __z) 00885 { return __builtin_csqrtl(__z); } 00886 00887 template<typename _Tp> 00888 inline complex<_Tp> 00889 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 00890 #else 00891 template<typename _Tp> 00892 inline complex<_Tp> 00893 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 00894 #endif 00895 00896 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 00897 00898 template<typename _Tp> 00899 inline complex<_Tp> 00900 __complex_tan(const complex<_Tp>& __z) 00901 { return std::sin(__z) / std::cos(__z); } 00902 00903 #if _GLIBCXX_USE_C99_COMPLEX 00904 inline __complex__ float 00905 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 00906 00907 inline __complex__ double 00908 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 00909 00910 inline __complex__ long double 00911 __complex_tan(const __complex__ long double& __z) 00912 { return __builtin_ctanl(__z); } 00913 00914 template<typename _Tp> 00915 inline complex<_Tp> 00916 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 00917 #else 00918 template<typename _Tp> 00919 inline complex<_Tp> 00920 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 00921 #endif 00922 00923 00924 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 00925 00926 template<typename _Tp> 00927 inline complex<_Tp> 00928 __complex_tanh(const complex<_Tp>& __z) 00929 { return std::sinh(__z) / std::cosh(__z); } 00930 00931 #if _GLIBCXX_USE_C99_COMPLEX 00932 inline __complex__ float 00933 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 00934 00935 inline __complex__ double 00936 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 00937 00938 inline __complex__ long double 00939 __complex_tanh(const __complex__ long double& __z) 00940 { return __builtin_ctanhl(__z); } 00941 00942 template<typename _Tp> 00943 inline complex<_Tp> 00944 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 00945 #else 00946 template<typename _Tp> 00947 inline complex<_Tp> 00948 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 00949 #endif 00950 00951 00952 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 00953 // raised to the __y-th power. The branch 00954 // cut is on the negative axis. 00955 #ifndef __GXX_EXPERIMENTAL_CXX0X__ 00956 template<typename _Tp> 00957 complex<_Tp> 00958 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 00959 { 00960 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 00961 00962 while (__n >>= 1) 00963 { 00964 __x *= __x; 00965 if (__n % 2) 00966 __y *= __x; 00967 } 00968 00969 return __y; 00970 } 00971 00972 // _GLIBCXX_RESOLVE_LIB_DEFECTS 00973 // DR 844. complex pow return type is ambiguous. 00974 template<typename _Tp> 00975 inline complex<_Tp> 00976 pow(const complex<_Tp>& __z, int __n) 00977 { 00978 return __n < 0 00979 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -__n) 00980 : std::__complex_pow_unsigned(__z, __n); 00981 } 00982 #endif 00983 00984 template<typename _Tp> 00985 complex<_Tp> 00986 pow(const complex<_Tp>& __x, const _Tp& __y) 00987 { 00988 #ifndef _GLIBCXX_USE_C99_COMPLEX 00989 if (__x == _Tp()) 00990 return _Tp(); 00991 #endif 00992 if (__x.imag() == _Tp() && __x.real() > _Tp()) 00993 return pow(__x.real(), __y); 00994 00995 complex<_Tp> __t = std::log(__x); 00996 return std::polar(exp(__y * __t.real()), __y * __t.imag()); 00997 } 00998 00999 template<typename _Tp> 01000 inline complex<_Tp> 01001 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 01002 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 01003 01004 #if _GLIBCXX_USE_C99_COMPLEX 01005 inline __complex__ float 01006 __complex_pow(__complex__ float __x, __complex__ float __y) 01007 { return __builtin_cpowf(__x, __y); } 01008 01009 inline __complex__ double 01010 __complex_pow(__complex__ double __x, __complex__ double __y) 01011 { return __builtin_cpow(__x, __y); } 01012 01013 inline __complex__ long double 01014 __complex_pow(const __complex__ long double& __x, 01015 const __complex__ long double& __y) 01016 { return __builtin_cpowl(__x, __y); } 01017 01018 template<typename _Tp> 01019 inline complex<_Tp> 01020 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 01021 { return __complex_pow(__x.__rep(), __y.__rep()); } 01022 #else 01023 template<typename _Tp> 01024 inline complex<_Tp> 01025 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 01026 { return __complex_pow(__x, __y); } 01027 #endif 01028 01029 template<typename _Tp> 01030 inline complex<_Tp> 01031 pow(const _Tp& __x, const complex<_Tp>& __y) 01032 { 01033 return __x > _Tp() ? std::polar(pow(__x, __y.real()), 01034 __y.imag() * log(__x)) 01035 : std::pow(complex<_Tp>(__x), __y); 01036 } 01037 01038 // 26.2.3 complex specializations 01039 // complex<float> specialization 01040 template<> 01041 struct complex<float> 01042 { 01043 typedef float value_type; 01044 typedef __complex__ float _ComplexT; 01045 01046 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 01047 01048 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 01049 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 01050 // The list-initialization extension to __complex__ types is 01051 // not available in GCC 4.6. Thus libstdc++/48760 cannot be 01052 // fixed in C++0x mode, unfortunately. 01053 : _M_value(__r + __i * 1.0fi) { } 01054 #else 01055 { 01056 __real__ _M_value = __r; 01057 __imag__ _M_value = __i; 01058 } 01059 #endif 01060 01061 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 01062 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 01063 01064 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 01065 // _GLIBCXX_RESOLVE_LIB_DEFECTS 01066 // DR 387. std::complex over-encapsulated. 01067 constexpr float 01068 real() const { return __real__ _M_value; } 01069 01070 constexpr float 01071 imag() const { return __imag__ _M_value; } 01072 #else 01073 float& 01074 real() { return __real__ _M_value; } 01075 01076 const float& 01077 real() const { return __real__ _M_value; } 01078 01079 float& 01080 imag() { return __imag__ _M_value; } 01081 01082 const float& 01083 imag() const { return __imag__ _M_value; } 01084 #endif 01085 01086 // _GLIBCXX_RESOLVE_LIB_DEFECTS 01087 // DR 387. std::complex over-encapsulated. 01088 void 01089 real(float __val) { __real__ _M_value = __val; } 01090 01091 void 01092 imag(float __val) { __imag__ _M_value = __val; } 01093 01094 complex& 01095 operator=(float __f) 01096 { 01097 _M_value = __f; 01098 return *this; 01099 } 01100 01101 complex& 01102 operator+=(float __f) 01103 { 01104 _M_value += __f; 01105 return *this; 01106 } 01107 01108 complex& 01109 operator-=(float __f) 01110 { 01111 _M_value -= __f; 01112 return *this; 01113 } 01114 01115 complex& 01116 operator*=(float __f) 01117 { 01118 _M_value *= __f; 01119 return *this; 01120 } 01121 01122 complex& 01123 operator/=(float __f) 01124 { 01125 _M_value /= __f; 01126 return *this; 01127 } 01128 01129 // Let the compiler synthesize the copy and assignment 01130 // operator. It always does a pretty good job. 01131 // complex& operator=(const complex&); 01132 01133 template<typename _Tp> 01134 complex& 01135 operator=(const complex<_Tp>& __z) 01136 { 01137 __real__ _M_value = __z.real(); 01138 __imag__ _M_value = __z.imag(); 01139 return *this; 01140 } 01141 01142 template<typename _Tp> 01143 complex& 01144 operator+=(const complex<_Tp>& __z) 01145 { 01146 __real__ _M_value += __z.real(); 01147 __imag__ _M_value += __z.imag(); 01148 return *this; 01149 } 01150 01151 template<class _Tp> 01152 complex& 01153 operator-=(const complex<_Tp>& __z) 01154 { 01155 __real__ _M_value -= __z.real(); 01156 __imag__ _M_value -= __z.imag(); 01157 return *this; 01158 } 01159 01160 template<class _Tp> 01161 complex& 01162 operator*=(const complex<_Tp>& __z) 01163 { 01164 _ComplexT __t; 01165 __real__ __t = __z.real(); 01166 __imag__ __t = __z.imag(); 01167 _M_value *= __t; 01168 return *this; 01169 } 01170 01171 template<class _Tp> 01172 complex& 01173 operator/=(const complex<_Tp>& __z) 01174 { 01175 _ComplexT __t; 01176 __real__ __t = __z.real(); 01177 __imag__ __t = __z.imag(); 01178 _M_value /= __t; 01179 return *this; 01180 } 01181 01182 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 01183 01184 private: 01185 _ComplexT _M_value; 01186 }; 01187 01188 // 26.2.3 complex specializations 01189 // complex<double> specialization 01190 template<> 01191 struct complex<double> 01192 { 01193 typedef double value_type; 01194 typedef __complex__ double _ComplexT; 01195 01196 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 01197 01198 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 01199 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 01200 // The list-initialization extension to __complex__ types is 01201 // not available in GCC 4.6. Thus libstdc++/48760 cannot be 01202 // fixed in C++0x mode, unfortunately. 01203 : _M_value(__r + __i * 1.0i) { } 01204 #else 01205 { 01206 __real__ _M_value = __r; 01207 __imag__ _M_value = __i; 01208 } 01209 #endif 01210 01211 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 01212 : _M_value(__z.__rep()) { } 01213 01214 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 01215 01216 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 01217 // _GLIBCXX_RESOLVE_LIB_DEFECTS 01218 // DR 387. std::complex over-encapsulated. 01219 constexpr double 01220 real() const { return __real__ _M_value; } 01221 01222 constexpr double 01223 imag() const { return __imag__ _M_value; } 01224 #else 01225 double& 01226 real() { return __real__ _M_value; } 01227 01228 const double& 01229 real() const { return __real__ _M_value; } 01230 01231 double& 01232 imag() { return __imag__ _M_value; } 01233 01234 const double& 01235 imag() const { return __imag__ _M_value; } 01236 #endif 01237 01238 // _GLIBCXX_RESOLVE_LIB_DEFECTS 01239 // DR 387. std::complex over-encapsulated. 01240 void 01241 real(double __val) { __real__ _M_value = __val; } 01242 01243 void 01244 imag(double __val) { __imag__ _M_value = __val; } 01245 01246 complex& 01247 operator=(double __d) 01248 { 01249 _M_value = __d; 01250 return *this; 01251 } 01252 01253 complex& 01254 operator+=(double __d) 01255 { 01256 _M_value += __d; 01257 return *this; 01258 } 01259 01260 complex& 01261 operator-=(double __d) 01262 { 01263 _M_value -= __d; 01264 return *this; 01265 } 01266 01267 complex& 01268 operator*=(double __d) 01269 { 01270 _M_value *= __d; 01271 return *this; 01272 } 01273 01274 complex& 01275 operator/=(double __d) 01276 { 01277 _M_value /= __d; 01278 return *this; 01279 } 01280 01281 // The compiler will synthesize this, efficiently. 01282 // complex& operator=(const complex&); 01283 01284 template<typename _Tp> 01285 complex& 01286 operator=(const complex<_Tp>& __z) 01287 { 01288 __real__ _M_value = __z.real(); 01289 __imag__ _M_value = __z.imag(); 01290 return *this; 01291 } 01292 01293 template<typename _Tp> 01294 complex& 01295 operator+=(const complex<_Tp>& __z) 01296 { 01297 __real__ _M_value += __z.real(); 01298 __imag__ _M_value += __z.imag(); 01299 return *this; 01300 } 01301 01302 template<typename _Tp> 01303 complex& 01304 operator-=(const complex<_Tp>& __z) 01305 { 01306 __real__ _M_value -= __z.real(); 01307 __imag__ _M_value -= __z.imag(); 01308 return *this; 01309 } 01310 01311 template<typename _Tp> 01312 complex& 01313 operator*=(const complex<_Tp>& __z) 01314 { 01315 _ComplexT __t; 01316 __real__ __t = __z.real(); 01317 __imag__ __t = __z.imag(); 01318 _M_value *= __t; 01319 return *this; 01320 } 01321 01322 template<typename _Tp> 01323 complex& 01324 operator/=(const complex<_Tp>& __z) 01325 { 01326 _ComplexT __t; 01327 __real__ __t = __z.real(); 01328 __imag__ __t = __z.imag(); 01329 _M_value /= __t; 01330 return *this; 01331 } 01332 01333 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 01334 01335 private: 01336 _ComplexT _M_value; 01337 }; 01338 01339 // 26.2.3 complex specializations 01340 // complex<long double> specialization 01341 template<> 01342 struct complex<long double> 01343 { 01344 typedef long double value_type; 01345 typedef __complex__ long double _ComplexT; 01346 01347 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 01348 01349 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 01350 long double __i = 0.0L) 01351 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 01352 // The list-initialization extension to __complex__ types is 01353 // not available in GCC 4.6. Thus libstdc++/48760 cannot be 01354 // fixed in C++0x mode, unfortunately. 01355 : _M_value(__r + __i * 1.0Li) { } 01356 #else 01357 { 01358 __real__ _M_value = __r; 01359 __imag__ _M_value = __i; 01360 } 01361 #endif 01362 01363 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 01364 : _M_value(__z.__rep()) { } 01365 01366 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 01367 : _M_value(__z.__rep()) { } 01368 01369 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 01370 // _GLIBCXX_RESOLVE_LIB_DEFECTS 01371 // DR 387. std::complex over-encapsulated. 01372 constexpr long double 01373 real() const { return __real__ _M_value; } 01374 01375 constexpr long double 01376 imag() const { return __imag__ _M_value; } 01377 #else 01378 long double& 01379 real() { return __real__ _M_value; } 01380 01381 const long double& 01382 real() const { return __real__ _M_value; } 01383 01384 long double& 01385 imag() { return __imag__ _M_value; } 01386 01387 const long double& 01388 imag() const { return __imag__ _M_value; } 01389 #endif 01390 01391 // _GLIBCXX_RESOLVE_LIB_DEFECTS 01392 // DR 387. std::complex over-encapsulated. 01393 void 01394 real(long double __val) { __real__ _M_value = __val; } 01395 01396 void 01397 imag(long double __val) { __imag__ _M_value = __val; } 01398 01399 complex& 01400 operator=(long double __r) 01401 { 01402 _M_value = __r; 01403 return *this; 01404 } 01405 01406 complex& 01407 operator+=(long double __r) 01408 { 01409 _M_value += __r; 01410 return *this; 01411 } 01412 01413 complex& 01414 operator-=(long double __r) 01415 { 01416 _M_value -= __r; 01417 return *this; 01418 } 01419 01420 complex& 01421 operator*=(long double __r) 01422 { 01423 _M_value *= __r; 01424 return *this; 01425 } 01426 01427 complex& 01428 operator/=(long double __r) 01429 { 01430 _M_value /= __r; 01431 return *this; 01432 } 01433 01434 // The compiler knows how to do this efficiently 01435 // complex& operator=(const complex&); 01436 01437 template<typename _Tp> 01438 complex& 01439 operator=(const complex<_Tp>& __z) 01440 { 01441 __real__ _M_value = __z.real(); 01442 __imag__ _M_value = __z.imag(); 01443 return *this; 01444 } 01445 01446 template<typename _Tp> 01447 complex& 01448 operator+=(const complex<_Tp>& __z) 01449 { 01450 __real__ _M_value += __z.real(); 01451 __imag__ _M_value += __z.imag(); 01452 return *this; 01453 } 01454 01455 template<typename _Tp> 01456 complex& 01457 operator-=(const complex<_Tp>& __z) 01458 { 01459 __real__ _M_value -= __z.real(); 01460 __imag__ _M_value -= __z.imag(); 01461 return *this; 01462 } 01463 01464 template<typename _Tp> 01465 complex& 01466 operator*=(const complex<_Tp>& __z) 01467 { 01468 _ComplexT __t; 01469 __real__ __t = __z.real(); 01470 __imag__ __t = __z.imag(); 01471 _M_value *= __t; 01472 return *this; 01473 } 01474 01475 template<typename _Tp> 01476 complex& 01477 operator/=(const complex<_Tp>& __z) 01478 { 01479 _ComplexT __t; 01480 __real__ __t = __z.real(); 01481 __imag__ __t = __z.imag(); 01482 _M_value /= __t; 01483 return *this; 01484 } 01485 01486 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 01487 01488 private: 01489 _ComplexT _M_value; 01490 }; 01491 01492 // These bits have to be at the end of this file, so that the 01493 // specializations have all been defined. 01494 inline _GLIBCXX_CONSTEXPR 01495 complex<float>::complex(const complex<double>& __z) 01496 : _M_value(__z.__rep()) { } 01497 01498 inline _GLIBCXX_CONSTEXPR 01499 complex<float>::complex(const complex<long double>& __z) 01500 : _M_value(__z.__rep()) { } 01501 01502 inline _GLIBCXX_CONSTEXPR 01503 complex<double>::complex(const complex<long double>& __z) 01504 : _M_value(__z.__rep()) { } 01505 01506 // Inhibit implicit instantiations for required instantiations, 01507 // which are defined via explicit instantiations elsewhere. 01508 // NB: This syntax is a GNU extension. 01509 #if _GLIBCXX_EXTERN_TEMPLATE 01510 extern template istream& operator>>(istream&, complex<float>&); 01511 extern template ostream& operator<<(ostream&, const complex<float>&); 01512 extern template istream& operator>>(istream&, complex<double>&); 01513 extern template ostream& operator<<(ostream&, const complex<double>&); 01514 extern template istream& operator>>(istream&, complex<long double>&); 01515 extern template ostream& operator<<(ostream&, const complex<long double>&); 01516 01517 #ifdef _GLIBCXX_USE_WCHAR_T 01518 extern template wistream& operator>>(wistream&, complex<float>&); 01519 extern template wostream& operator<<(wostream&, const complex<float>&); 01520 extern template wistream& operator>>(wistream&, complex<double>&); 01521 extern template wostream& operator<<(wostream&, const complex<double>&); 01522 extern template wistream& operator>>(wistream&, complex<long double>&); 01523 extern template wostream& operator<<(wostream&, const complex<long double>&); 01524 #endif 01525 #endif 01526 01527 // @} group complex_numbers 01528 01529 _GLIBCXX_END_NAMESPACE_VERSION 01530 } // namespace 01531 01532 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 01533 { 01534 _GLIBCXX_BEGIN_NAMESPACE_VERSION 01535 01536 // See ext/type_traits.h for the primary template. 01537 template<typename _Tp, typename _Up> 01538 struct __promote_2<std::complex<_Tp>, _Up> 01539 { 01540 public: 01541 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 01542 }; 01543 01544 template<typename _Tp, typename _Up> 01545 struct __promote_2<_Tp, std::complex<_Up> > 01546 { 01547 public: 01548 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 01549 }; 01550 01551 template<typename _Tp, typename _Up> 01552 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 01553 { 01554 public: 01555 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 01556 }; 01557 01558 _GLIBCXX_END_NAMESPACE_VERSION 01559 } // namespace 01560 01561 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 01562 01563 namespace std _GLIBCXX_VISIBILITY(default) 01564 { 01565 _GLIBCXX_BEGIN_NAMESPACE_VERSION 01566 01567 // Forward declarations. 01568 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 01569 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 01570 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 01571 01572 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 01573 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 01574 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 01575 // DR 595. 01576 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 01577 01578 template<typename _Tp> 01579 inline std::complex<_Tp> 01580 __complex_acos(const std::complex<_Tp>& __z) 01581 { 01582 const std::complex<_Tp> __t = std::asin(__z); 01583 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 01584 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 01585 } 01586 01587 #if _GLIBCXX_USE_C99_COMPLEX_TR1 01588 inline __complex__ float 01589 __complex_acos(__complex__ float __z) 01590 { return __builtin_cacosf(__z); } 01591 01592 inline __complex__ double 01593 __complex_acos(__complex__ double __z) 01594 { return __builtin_cacos(__z); } 01595 01596 inline __complex__ long double 01597 __complex_acos(const __complex__ long double& __z) 01598 { return __builtin_cacosl(__z); } 01599 01600 template<typename _Tp> 01601 inline std::complex<_Tp> 01602 acos(const std::complex<_Tp>& __z) 01603 { return __complex_acos(__z.__rep()); } 01604 #else 01605 /// acos(__z) [8.1.2]. 01606 // Effects: Behaves the same as C99 function cacos, defined 01607 // in subclause 7.3.5.1. 01608 template<typename _Tp> 01609 inline std::complex<_Tp> 01610 acos(const std::complex<_Tp>& __z) 01611 { return __complex_acos(__z); } 01612 #endif 01613 01614 template<typename _Tp> 01615 inline std::complex<_Tp> 01616 __complex_asin(const std::complex<_Tp>& __z) 01617 { 01618 std::complex<_Tp> __t(-__z.imag(), __z.real()); 01619 __t = std::asinh(__t); 01620 return std::complex<_Tp>(__t.imag(), -__t.real()); 01621 } 01622 01623 #if _GLIBCXX_USE_C99_COMPLEX_TR1 01624 inline __complex__ float 01625 __complex_asin(__complex__ float __z) 01626 { return __builtin_casinf(__z); } 01627 01628 inline __complex__ double 01629 __complex_asin(__complex__ double __z) 01630 { return __builtin_casin(__z); } 01631 01632 inline __complex__ long double 01633 __complex_asin(const __complex__ long double& __z) 01634 { return __builtin_casinl(__z); } 01635 01636 template<typename _Tp> 01637 inline std::complex<_Tp> 01638 asin(const std::complex<_Tp>& __z) 01639 { return __complex_asin(__z.__rep()); } 01640 #else 01641 /// asin(__z) [8.1.3]. 01642 // Effects: Behaves the same as C99 function casin, defined 01643 // in subclause 7.3.5.2. 01644 template<typename _Tp> 01645 inline std::complex<_Tp> 01646 asin(const std::complex<_Tp>& __z) 01647 { return __complex_asin(__z); } 01648 #endif 01649 01650 template<typename _Tp> 01651 std::complex<_Tp> 01652 __complex_atan(const std::complex<_Tp>& __z) 01653 { 01654 const _Tp __r2 = __z.real() * __z.real(); 01655 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 01656 01657 _Tp __num = __z.imag() + _Tp(1.0); 01658 _Tp __den = __z.imag() - _Tp(1.0); 01659 01660 __num = __r2 + __num * __num; 01661 __den = __r2 + __den * __den; 01662 01663 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 01664 _Tp(0.25) * log(__num / __den)); 01665 } 01666 01667 #if _GLIBCXX_USE_C99_COMPLEX_TR1 01668 inline __complex__ float 01669 __complex_atan(__complex__ float __z) 01670 { return __builtin_catanf(__z); } 01671 01672 inline __complex__ double 01673 __complex_atan(__complex__ double __z) 01674 { return __builtin_catan(__z); } 01675 01676 inline __complex__ long double 01677 __complex_atan(const __complex__ long double& __z) 01678 { return __builtin_catanl(__z); } 01679 01680 template<typename _Tp> 01681 inline std::complex<_Tp> 01682 atan(const std::complex<_Tp>& __z) 01683 { return __complex_atan(__z.__rep()); } 01684 #else 01685 /// atan(__z) [8.1.4]. 01686 // Effects: Behaves the same as C99 function catan, defined 01687 // in subclause 7.3.5.3. 01688 template<typename _Tp> 01689 inline std::complex<_Tp> 01690 atan(const std::complex<_Tp>& __z) 01691 { return __complex_atan(__z); } 01692 #endif 01693 01694 template<typename _Tp> 01695 std::complex<_Tp> 01696 __complex_acosh(const std::complex<_Tp>& __z) 01697 { 01698 // Kahan's formula. 01699 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 01700 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 01701 } 01702 01703 #if _GLIBCXX_USE_C99_COMPLEX_TR1 01704 inline __complex__ float 01705 __complex_acosh(__complex__ float __z) 01706 { return __builtin_cacoshf(__z); } 01707 01708 inline __complex__ double 01709 __complex_acosh(__complex__ double __z) 01710 { return __builtin_cacosh(__z); } 01711 01712 inline __complex__ long double 01713 __complex_acosh(const __complex__ long double& __z) 01714 { return __builtin_cacoshl(__z); } 01715 01716 template<typename _Tp> 01717 inline std::complex<_Tp> 01718 acosh(const std::complex<_Tp>& __z) 01719 { return __complex_acosh(__z.__rep()); } 01720 #else 01721 /// acosh(__z) [8.1.5]. 01722 // Effects: Behaves the same as C99 function cacosh, defined 01723 // in subclause 7.3.6.1. 01724 template<typename _Tp> 01725 inline std::complex<_Tp> 01726 acosh(const std::complex<_Tp>& __z) 01727 { return __complex_acosh(__z); } 01728 #endif 01729 01730 template<typename _Tp> 01731 std::complex<_Tp> 01732 __complex_asinh(const std::complex<_Tp>& __z) 01733 { 01734 std::complex<_Tp> __t((__z.real() - __z.imag()) 01735 * (__z.real() + __z.imag()) + _Tp(1.0), 01736 _Tp(2.0) * __z.real() * __z.imag()); 01737 __t = std::sqrt(__t); 01738 01739 return std::log(__t + __z); 01740 } 01741 01742 #if _GLIBCXX_USE_C99_COMPLEX_TR1 01743 inline __complex__ float 01744 __complex_asinh(__complex__ float __z) 01745 { return __builtin_casinhf(__z); } 01746 01747 inline __complex__ double 01748 __complex_asinh(__complex__ double __z) 01749 { return __builtin_casinh(__z); } 01750 01751 inline __complex__ long double 01752 __complex_asinh(const __complex__ long double& __z) 01753 { return __builtin_casinhl(__z); } 01754 01755 template<typename _Tp> 01756 inline std::complex<_Tp> 01757 asinh(const std::complex<_Tp>& __z) 01758 { return __complex_asinh(__z.__rep()); } 01759 #else 01760 /// asinh(__z) [8.1.6]. 01761 // Effects: Behaves the same as C99 function casin, defined 01762 // in subclause 7.3.6.2. 01763 template<typename _Tp> 01764 inline std::complex<_Tp> 01765 asinh(const std::complex<_Tp>& __z) 01766 { return __complex_asinh(__z); } 01767 #endif 01768 01769 template<typename _Tp> 01770 std::complex<_Tp> 01771 __complex_atanh(const std::complex<_Tp>& __z) 01772 { 01773 const _Tp __i2 = __z.imag() * __z.imag(); 01774 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 01775 01776 _Tp __num = _Tp(1.0) + __z.real(); 01777 _Tp __den = _Tp(1.0) - __z.real(); 01778 01779 __num = __i2 + __num * __num; 01780 __den = __i2 + __den * __den; 01781 01782 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 01783 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 01784 } 01785 01786 #if _GLIBCXX_USE_C99_COMPLEX_TR1 01787 inline __complex__ float 01788 __complex_atanh(__complex__ float __z) 01789 { return __builtin_catanhf(__z); } 01790 01791 inline __complex__ double 01792 __complex_atanh(__complex__ double __z) 01793 { return __builtin_catanh(__z); } 01794 01795 inline __complex__ long double 01796 __complex_atanh(const __complex__ long double& __z) 01797 { return __builtin_catanhl(__z); } 01798 01799 template<typename _Tp> 01800 inline std::complex<_Tp> 01801 atanh(const std::complex<_Tp>& __z) 01802 { return __complex_atanh(__z.__rep()); } 01803 #else 01804 /// atanh(__z) [8.1.7]. 01805 // Effects: Behaves the same as C99 function catanh, defined 01806 // in subclause 7.3.6.3. 01807 template<typename _Tp> 01808 inline std::complex<_Tp> 01809 atanh(const std::complex<_Tp>& __z) 01810 { return __complex_atanh(__z); } 01811 #endif 01812 01813 template<typename _Tp> 01814 inline _Tp 01815 /// fabs(__z) [8.1.8]. 01816 // Effects: Behaves the same as C99 function cabs, defined 01817 // in subclause 7.3.8.1. 01818 fabs(const std::complex<_Tp>& __z) 01819 { return std::abs(__z); } 01820 01821 /// Additional overloads [8.1.9]. 01822 template<typename _Tp> 01823 inline typename __gnu_cxx::__promote<_Tp>::__type 01824 arg(_Tp __x) 01825 { 01826 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 01827 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 01828 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 01829 : __type(); 01830 #else 01831 return std::arg(std::complex<__type>(__x)); 01832 #endif 01833 } 01834 01835 template<typename _Tp> 01836 inline typename __gnu_cxx::__promote<_Tp>::__type 01837 imag(_Tp) 01838 { return _Tp(); } 01839 01840 template<typename _Tp> 01841 inline typename __gnu_cxx::__promote<_Tp>::__type 01842 norm(_Tp __x) 01843 { 01844 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 01845 return __type(__x) * __type(__x); 01846 } 01847 01848 template<typename _Tp> 01849 inline typename __gnu_cxx::__promote<_Tp>::__type 01850 real(_Tp __x) 01851 { return __x; } 01852 01853 template<typename _Tp, typename _Up> 01854 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 01855 pow(const std::complex<_Tp>& __x, const _Up& __y) 01856 { 01857 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 01858 return std::pow(std::complex<__type>(__x), __type(__y)); 01859 } 01860 01861 template<typename _Tp, typename _Up> 01862 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 01863 pow(const _Tp& __x, const std::complex<_Up>& __y) 01864 { 01865 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 01866 return std::pow(__type(__x), std::complex<__type>(__y)); 01867 } 01868 01869 template<typename _Tp, typename _Up> 01870 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 01871 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 01872 { 01873 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 01874 return std::pow(std::complex<__type>(__x), 01875 std::complex<__type>(__y)); 01876 } 01877 01878 // Forward declarations. 01879 // DR 781. 01880 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); 01881 01882 template<typename _Tp> 01883 std::complex<_Tp> 01884 __complex_proj(const std::complex<_Tp>& __z) 01885 { 01886 const _Tp __den = (__z.real() * __z.real() 01887 + __z.imag() * __z.imag() + _Tp(1.0)); 01888 01889 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, 01890 (_Tp(2.0) * __z.imag()) / __den); 01891 } 01892 01893 #if _GLIBCXX_USE_C99_COMPLEX 01894 inline __complex__ float 01895 __complex_proj(__complex__ float __z) 01896 { return __builtin_cprojf(__z); } 01897 01898 inline __complex__ double 01899 __complex_proj(__complex__ double __z) 01900 { return __builtin_cproj(__z); } 01901 01902 inline __complex__ long double 01903 __complex_proj(const __complex__ long double& __z) 01904 { return __builtin_cprojl(__z); } 01905 01906 template<typename _Tp> 01907 inline std::complex<_Tp> 01908 proj(const std::complex<_Tp>& __z) 01909 { return __complex_proj(__z.__rep()); } 01910 #else 01911 template<typename _Tp> 01912 inline std::complex<_Tp> 01913 proj(const std::complex<_Tp>& __z) 01914 { return __complex_proj(__z); } 01915 #endif 01916 01917 // DR 1137. 01918 template<typename _Tp> 01919 inline typename __gnu_cxx::__promote<_Tp>::__type 01920 proj(_Tp __x) 01921 { return __x; } 01922 01923 template<typename _Tp> 01924 inline typename __gnu_cxx::__promote<_Tp>::__type 01925 conj(_Tp __x) 01926 { return __x; } 01927 01928 _GLIBCXX_END_NAMESPACE_VERSION 01929 } // namespace 01930 01931 #endif // __GXX_EXPERIMENTAL_CXX0X__ 01932 01933 #endif /* _GLIBCXX_COMPLEX */