libstdc++
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00001 // TR1 complex -*- C++ -*- 00002 00003 // Copyright (C) 2006-2013 Free Software Foundation, Inc. 00004 // 00005 // This file is part of the GNU ISO C++ Library. This library is free 00006 // software; you can redistribute it and/or modify it under the 00007 // terms of the GNU General Public License as published by the 00008 // Free Software Foundation; either version 3, or (at your option) 00009 // any later version. 00010 00011 // This library is distributed in the hope that it will be useful, 00012 // but WITHOUT ANY WARRANTY; without even the implied warranty of 00013 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 00014 // GNU General Public License for more details. 00015 00016 // Under Section 7 of GPL version 3, you are granted additional 00017 // permissions described in the GCC Runtime Library Exception, version 00018 // 3.1, as published by the Free Software Foundation. 00019 00020 // You should have received a copy of the GNU General Public License and 00021 // a copy of the GCC Runtime Library Exception along with this program; 00022 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 00023 // <http://www.gnu.org/licenses/>. 00024 00025 /** @file tr1/complex 00026 * This is a TR1 C++ Library header. 00027 */ 00028 00029 #ifndef _GLIBCXX_TR1_COMPLEX 00030 #define _GLIBCXX_TR1_COMPLEX 1 00031 00032 #pragma GCC system_header 00033 00034 #include <complex> 00035 00036 namespace std _GLIBCXX_VISIBILITY(default) 00037 { 00038 namespace tr1 00039 { 00040 _GLIBCXX_BEGIN_NAMESPACE_VERSION 00041 00042 /** 00043 * @addtogroup complex_numbers 00044 * @{ 00045 */ 00046 00047 #if __cplusplus >= 201103L 00048 using std::acos; 00049 using std::asin; 00050 using std::atan; 00051 #else 00052 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 00053 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 00054 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 00055 #endif 00056 00057 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 00058 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 00059 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 00060 00061 // The std::fabs return type in C++0x mode is different (just _Tp). 00062 template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&); 00063 00064 #if __cplusplus < 201103L 00065 template<typename _Tp> 00066 inline std::complex<_Tp> 00067 __complex_acos(const std::complex<_Tp>& __z) 00068 { 00069 const std::complex<_Tp> __t = std::tr1::asin(__z); 00070 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 00071 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 00072 } 00073 00074 #if _GLIBCXX_USE_C99_COMPLEX_TR1 00075 inline __complex__ float 00076 __complex_acos(__complex__ float __z) 00077 { return __builtin_cacosf(__z); } 00078 00079 inline __complex__ double 00080 __complex_acos(__complex__ double __z) 00081 { return __builtin_cacos(__z); } 00082 00083 inline __complex__ long double 00084 __complex_acos(const __complex__ long double& __z) 00085 { return __builtin_cacosl(__z); } 00086 00087 template<typename _Tp> 00088 inline std::complex<_Tp> 00089 acos(const std::complex<_Tp>& __z) 00090 { return __complex_acos(__z.__rep()); } 00091 #else 00092 /// acos(__z) [8.1.2]. 00093 // Effects: Behaves the same as C99 function cacos, defined 00094 // in subclause 7.3.5.1. 00095 template<typename _Tp> 00096 inline std::complex<_Tp> 00097 acos(const std::complex<_Tp>& __z) 00098 { return __complex_acos(__z); } 00099 #endif 00100 00101 template<typename _Tp> 00102 inline std::complex<_Tp> 00103 __complex_asin(const std::complex<_Tp>& __z) 00104 { 00105 std::complex<_Tp> __t(-__z.imag(), __z.real()); 00106 __t = std::tr1::asinh(__t); 00107 return std::complex<_Tp>(__t.imag(), -__t.real()); 00108 } 00109 00110 #if _GLIBCXX_USE_C99_COMPLEX_TR1 00111 inline __complex__ float 00112 __complex_asin(__complex__ float __z) 00113 { return __builtin_casinf(__z); } 00114 00115 inline __complex__ double 00116 __complex_asin(__complex__ double __z) 00117 { return __builtin_casin(__z); } 00118 00119 inline __complex__ long double 00120 __complex_asin(const __complex__ long double& __z) 00121 { return __builtin_casinl(__z); } 00122 00123 template<typename _Tp> 00124 inline std::complex<_Tp> 00125 asin(const std::complex<_Tp>& __z) 00126 { return __complex_asin(__z.__rep()); } 00127 #else 00128 /// asin(__z) [8.1.3]. 00129 // Effects: Behaves the same as C99 function casin, defined 00130 // in subclause 7.3.5.2. 00131 template<typename _Tp> 00132 inline std::complex<_Tp> 00133 asin(const std::complex<_Tp>& __z) 00134 { return __complex_asin(__z); } 00135 #endif 00136 00137 template<typename _Tp> 00138 std::complex<_Tp> 00139 __complex_atan(const std::complex<_Tp>& __z) 00140 { 00141 const _Tp __r2 = __z.real() * __z.real(); 00142 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 00143 00144 _Tp __num = __z.imag() + _Tp(1.0); 00145 _Tp __den = __z.imag() - _Tp(1.0); 00146 00147 __num = __r2 + __num * __num; 00148 __den = __r2 + __den * __den; 00149 00150 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 00151 _Tp(0.25) * log(__num / __den)); 00152 } 00153 00154 #if _GLIBCXX_USE_C99_COMPLEX_TR1 00155 inline __complex__ float 00156 __complex_atan(__complex__ float __z) 00157 { return __builtin_catanf(__z); } 00158 00159 inline __complex__ double 00160 __complex_atan(__complex__ double __z) 00161 { return __builtin_catan(__z); } 00162 00163 inline __complex__ long double 00164 __complex_atan(const __complex__ long double& __z) 00165 { return __builtin_catanl(__z); } 00166 00167 template<typename _Tp> 00168 inline std::complex<_Tp> 00169 atan(const std::complex<_Tp>& __z) 00170 { return __complex_atan(__z.__rep()); } 00171 #else 00172 /// atan(__z) [8.1.4]. 00173 // Effects: Behaves the same as C99 function catan, defined 00174 // in subclause 7.3.5.3. 00175 template<typename _Tp> 00176 inline std::complex<_Tp> 00177 atan(const std::complex<_Tp>& __z) 00178 { return __complex_atan(__z); } 00179 #endif 00180 00181 #endif // C++11 00182 00183 template<typename _Tp> 00184 std::complex<_Tp> 00185 __complex_acosh(const std::complex<_Tp>& __z) 00186 { 00187 // Kahan's formula. 00188 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 00189 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 00190 } 00191 00192 #if _GLIBCXX_USE_C99_COMPLEX_TR1 00193 inline __complex__ float 00194 __complex_acosh(__complex__ float __z) 00195 { return __builtin_cacoshf(__z); } 00196 00197 inline __complex__ double 00198 __complex_acosh(__complex__ double __z) 00199 { return __builtin_cacosh(__z); } 00200 00201 inline __complex__ long double 00202 __complex_acosh(const __complex__ long double& __z) 00203 { return __builtin_cacoshl(__z); } 00204 00205 template<typename _Tp> 00206 inline std::complex<_Tp> 00207 acosh(const std::complex<_Tp>& __z) 00208 { return __complex_acosh(__z.__rep()); } 00209 #else 00210 /// acosh(__z) [8.1.5]. 00211 // Effects: Behaves the same as C99 function cacosh, defined 00212 // in subclause 7.3.6.1. 00213 template<typename _Tp> 00214 inline std::complex<_Tp> 00215 acosh(const std::complex<_Tp>& __z) 00216 { return __complex_acosh(__z); } 00217 #endif 00218 00219 template<typename _Tp> 00220 std::complex<_Tp> 00221 __complex_asinh(const std::complex<_Tp>& __z) 00222 { 00223 std::complex<_Tp> __t((__z.real() - __z.imag()) 00224 * (__z.real() + __z.imag()) + _Tp(1.0), 00225 _Tp(2.0) * __z.real() * __z.imag()); 00226 __t = std::sqrt(__t); 00227 00228 return std::log(__t + __z); 00229 } 00230 00231 #if _GLIBCXX_USE_C99_COMPLEX_TR1 00232 inline __complex__ float 00233 __complex_asinh(__complex__ float __z) 00234 { return __builtin_casinhf(__z); } 00235 00236 inline __complex__ double 00237 __complex_asinh(__complex__ double __z) 00238 { return __builtin_casinh(__z); } 00239 00240 inline __complex__ long double 00241 __complex_asinh(const __complex__ long double& __z) 00242 { return __builtin_casinhl(__z); } 00243 00244 template<typename _Tp> 00245 inline std::complex<_Tp> 00246 asinh(const std::complex<_Tp>& __z) 00247 { return __complex_asinh(__z.__rep()); } 00248 #else 00249 /// asinh(__z) [8.1.6]. 00250 // Effects: Behaves the same as C99 function casin, defined 00251 // in subclause 7.3.6.2. 00252 template<typename _Tp> 00253 inline std::complex<_Tp> 00254 asinh(const std::complex<_Tp>& __z) 00255 { return __complex_asinh(__z); } 00256 #endif 00257 00258 template<typename _Tp> 00259 std::complex<_Tp> 00260 __complex_atanh(const std::complex<_Tp>& __z) 00261 { 00262 const _Tp __i2 = __z.imag() * __z.imag(); 00263 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 00264 00265 _Tp __num = _Tp(1.0) + __z.real(); 00266 _Tp __den = _Tp(1.0) - __z.real(); 00267 00268 __num = __i2 + __num * __num; 00269 __den = __i2 + __den * __den; 00270 00271 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 00272 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 00273 } 00274 00275 #if _GLIBCXX_USE_C99_COMPLEX_TR1 00276 inline __complex__ float 00277 __complex_atanh(__complex__ float __z) 00278 { return __builtin_catanhf(__z); } 00279 00280 inline __complex__ double 00281 __complex_atanh(__complex__ double __z) 00282 { return __builtin_catanh(__z); } 00283 00284 inline __complex__ long double 00285 __complex_atanh(const __complex__ long double& __z) 00286 { return __builtin_catanhl(__z); } 00287 00288 template<typename _Tp> 00289 inline std::complex<_Tp> 00290 atanh(const std::complex<_Tp>& __z) 00291 { return __complex_atanh(__z.__rep()); } 00292 #else 00293 /// atanh(__z) [8.1.7]. 00294 // Effects: Behaves the same as C99 function catanh, defined 00295 // in subclause 7.3.6.3. 00296 template<typename _Tp> 00297 inline std::complex<_Tp> 00298 atanh(const std::complex<_Tp>& __z) 00299 { return __complex_atanh(__z); } 00300 #endif 00301 00302 template<typename _Tp> 00303 inline std::complex<_Tp> 00304 /// fabs(__z) [8.1.8]. 00305 // Effects: Behaves the same as C99 function cabs, defined 00306 // in subclause 7.3.8.1. 00307 fabs(const std::complex<_Tp>& __z) 00308 { return std::abs(__z); } 00309 00310 /// Additional overloads [8.1.9]. 00311 #if __cplusplus < 201103L 00312 00313 template<typename _Tp> 00314 inline typename __gnu_cxx::__promote<_Tp>::__type 00315 arg(_Tp __x) 00316 { 00317 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 00318 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 00319 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 00320 : __type(); 00321 #else 00322 return std::arg(std::complex<__type>(__x)); 00323 #endif 00324 } 00325 00326 template<typename _Tp> 00327 inline typename __gnu_cxx::__promote<_Tp>::__type 00328 imag(_Tp) 00329 { return _Tp(); } 00330 00331 template<typename _Tp> 00332 inline typename __gnu_cxx::__promote<_Tp>::__type 00333 norm(_Tp __x) 00334 { 00335 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 00336 return __type(__x) * __type(__x); 00337 } 00338 00339 template<typename _Tp> 00340 inline typename __gnu_cxx::__promote<_Tp>::__type 00341 real(_Tp __x) 00342 { return __x; } 00343 00344 #endif 00345 00346 template<typename _Tp, typename _Up> 00347 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 00348 pow(const std::complex<_Tp>& __x, const _Up& __y) 00349 { 00350 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 00351 return std::pow(std::complex<__type>(__x), __type(__y)); 00352 } 00353 00354 template<typename _Tp, typename _Up> 00355 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 00356 pow(const _Tp& __x, const std::complex<_Up>& __y) 00357 { 00358 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 00359 return std::pow(__type(__x), std::complex<__type>(__y)); 00360 } 00361 00362 template<typename _Tp, typename _Up> 00363 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 00364 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 00365 { 00366 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 00367 return std::pow(std::complex<__type>(__x), 00368 std::complex<__type>(__y)); 00369 } 00370 00371 using std::arg; 00372 00373 template<typename _Tp> 00374 inline std::complex<_Tp> 00375 conj(const std::complex<_Tp>& __z) 00376 { return std::conj(__z); } 00377 00378 template<typename _Tp> 00379 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 00380 conj(_Tp __x) 00381 { return __x; } 00382 00383 using std::imag; 00384 using std::norm; 00385 using std::polar; 00386 00387 template<typename _Tp, typename _Up> 00388 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 00389 polar(const _Tp& __rho, const _Up& __theta) 00390 { 00391 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 00392 return std::polar(__type(__rho), __type(__theta)); 00393 } 00394 00395 using std::real; 00396 00397 template<typename _Tp> 00398 inline std::complex<_Tp> 00399 pow(const std::complex<_Tp>& __x, const _Tp& __y) 00400 { return std::pow(__x, __y); } 00401 00402 template<typename _Tp> 00403 inline std::complex<_Tp> 00404 pow(const _Tp& __x, const std::complex<_Tp>& __y) 00405 { return std::pow(__x, __y); } 00406 00407 template<typename _Tp> 00408 inline std::complex<_Tp> 00409 pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y) 00410 { return std::pow(__x, __y); } 00411 00412 // @} group complex_numbers 00413 00414 _GLIBCXX_END_NAMESPACE_VERSION 00415 } 00416 } 00417 00418 #endif // _GLIBCXX_TR1_COMPLEX