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/usr/include/c++/13/tr1/complex
$ cat -n /usr/include/c++/13/tr1/complex 1 // TR1 complex -*- C++ -*- 2 3 // Copyright (C) 2006-2023 Free Software Foundation, Inc. 4 // 5 // This file is part of the GNU ISO C++ Library. This library is free 6 // software; you can redistribute it and/or modify it under the 7 // terms of the GNU General Public License as published by the 8 // Free Software Foundation; either version 3, or (at your option) 9 // any later version. 10 11 // This library is distributed in the hope that it will be useful, 12 // but WITHOUT ANY WARRANTY; without even the implied warranty of 13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 // GNU General Public License for more details. 15 16 // Under Section 7 of GPL version 3, you are granted additional 17 // permissions described in the GCC Runtime Library Exception, version 18 // 3.1, as published by the Free Software Foundation. 19 20 // You should have received a copy of the GNU General Public License and 21 // a copy of the GCC Runtime Library Exception along with this program; 22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23 // <http://www.gnu.org/licenses/>. 24 25 /** @file tr1/complex 26 * This is a TR1 C++ Library header. 27 */ 28 29 #ifndef _GLIBCXX_TR1_COMPLEX 30 #define _GLIBCXX_TR1_COMPLEX 1 31 32 #pragma GCC system_header 33 34 #include <bits/requires_hosted.h> // TR1 35 36 #include <complex> 37 38 namespace std _GLIBCXX_VISIBILITY(default) 39 { 40 _GLIBCXX_BEGIN_NAMESPACE_VERSION 41 42 namespace tr1 43 { 44 /** 45 * @addtogroup complex_numbers 46 * @{ 47 */ 48 49 #if __cplusplus >= 201103L 50 using std::acos; 51 using std::asin; 52 using std::atan; 53 using std::acosh; 54 using std::asinh; 55 using std::atanh; 56 #else 57 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 58 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 59 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 60 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 61 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 62 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 63 #endif 64 65 // The std::fabs return type in C++11 mode is different (just _Tp). 66 template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&); 67 68 #if __cplusplus < 201103L 69 template<typename _Tp> 70 inline std::complex<_Tp> 71 __complex_acos(const std::complex<_Tp>& __z) 72 { 73 const std::complex<_Tp> __t = std::tr1::asin(__z); 74 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 75 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 76 } 77 78 #if _GLIBCXX_USE_C99_COMPLEX_TR1 79 inline __complex__ float 80 __complex_acos(__complex__ float __z) 81 { return __builtin_cacosf(__z); } 82 83 inline __complex__ double 84 __complex_acos(__complex__ double __z) 85 { return __builtin_cacos(__z); } 86 87 inline __complex__ long double 88 __complex_acos(const __complex__ long double& __z) 89 { return __builtin_cacosl(__z); } 90 91 template<typename _Tp> 92 inline std::complex<_Tp> 93 acos(const std::complex<_Tp>& __z) 94 { return __complex_acos(__z.__rep()); } 95 #else 96 /// acos(__z) [8.1.2]. 97 // Effects: Behaves the same as C99 function cacos, defined 98 // in subclause 7.3.5.1. 99 template<typename _Tp> 100 inline std::complex<_Tp> 101 acos(const std::complex<_Tp>& __z) 102 { return __complex_acos(__z); } 103 #endif 104 105 template<typename _Tp> 106 inline std::complex<_Tp> 107 __complex_asin(const std::complex<_Tp>& __z) 108 { 109 std::complex<_Tp> __t(-__z.imag(), __z.real()); 110 __t = std::tr1::asinh(__t); 111 return std::complex<_Tp>(__t.imag(), -__t.real()); 112 } 113 114 #if _GLIBCXX_USE_C99_COMPLEX_TR1 115 inline __complex__ float 116 __complex_asin(__complex__ float __z) 117 { return __builtin_casinf(__z); } 118 119 inline __complex__ double 120 __complex_asin(__complex__ double __z) 121 { return __builtin_casin(__z); } 122 123 inline __complex__ long double 124 __complex_asin(const __complex__ long double& __z) 125 { return __builtin_casinl(__z); } 126 127 template<typename _Tp> 128 inline std::complex<_Tp> 129 asin(const std::complex<_Tp>& __z) 130 { return __complex_asin(__z.__rep()); } 131 #else 132 /// asin(__z) [8.1.3]. 133 // Effects: Behaves the same as C99 function casin, defined 134 // in subclause 7.3.5.2. 135 template<typename _Tp> 136 inline std::complex<_Tp> 137 asin(const std::complex<_Tp>& __z) 138 { return __complex_asin(__z); } 139 #endif 140 141 template<typename _Tp> 142 std::complex<_Tp> 143 __complex_atan(const std::complex<_Tp>& __z) 144 { 145 const _Tp __r2 = __z.real() * __z.real(); 146 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 147 148 _Tp __num = __z.imag() + _Tp(1.0); 149 _Tp __den = __z.imag() - _Tp(1.0); 150 151 __num = __r2 + __num * __num; 152 __den = __r2 + __den * __den; 153 154 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 155 _Tp(0.25) * log(__num / __den)); 156 } 157 158 #if _GLIBCXX_USE_C99_COMPLEX_TR1 159 inline __complex__ float 160 __complex_atan(__complex__ float __z) 161 { return __builtin_catanf(__z); } 162 163 inline __complex__ double 164 __complex_atan(__complex__ double __z) 165 { return __builtin_catan(__z); } 166 167 inline __complex__ long double 168 __complex_atan(const __complex__ long double& __z) 169 { return __builtin_catanl(__z); } 170 171 template<typename _Tp> 172 inline std::complex<_Tp> 173 atan(const std::complex<_Tp>& __z) 174 { return __complex_atan(__z.__rep()); } 175 #else 176 /// atan(__z) [8.1.4]. 177 // Effects: Behaves the same as C99 function catan, defined 178 // in subclause 7.3.5.3. 179 template<typename _Tp> 180 inline std::complex<_Tp> 181 atan(const std::complex<_Tp>& __z) 182 { return __complex_atan(__z); } 183 #endif 184 185 template<typename _Tp> 186 std::complex<_Tp> 187 __complex_acosh(const std::complex<_Tp>& __z) 188 { 189 // Kahan's formula. 190 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 191 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 192 } 193 194 #if _GLIBCXX_USE_C99_COMPLEX_TR1 195 inline __complex__ float 196 __complex_acosh(__complex__ float __z) 197 { return __builtin_cacoshf(__z); } 198 199 inline __complex__ double 200 __complex_acosh(__complex__ double __z) 201 { return __builtin_cacosh(__z); } 202 203 inline __complex__ long double 204 __complex_acosh(const __complex__ long double& __z) 205 { return __builtin_cacoshl(__z); } 206 207 template<typename _Tp> 208 inline std::complex<_Tp> 209 acosh(const std::complex<_Tp>& __z) 210 { return __complex_acosh(__z.__rep()); } 211 #else 212 /// acosh(__z) [8.1.5]. 213 // Effects: Behaves the same as C99 function cacosh, defined 214 // in subclause 7.3.6.1. 215 template<typename _Tp> 216 inline std::complex<_Tp> 217 acosh(const std::complex<_Tp>& __z) 218 { return __complex_acosh(__z); } 219 #endif 220 221 template<typename _Tp> 222 std::complex<_Tp> 223 __complex_asinh(const std::complex<_Tp>& __z) 224 { 225 std::complex<_Tp> __t((__z.real() - __z.imag()) 226 * (__z.real() + __z.imag()) + _Tp(1.0), 227 _Tp(2.0) * __z.real() * __z.imag()); 228 __t = std::sqrt(__t); 229 230 return std::log(__t + __z); 231 } 232 233 #if _GLIBCXX_USE_C99_COMPLEX_TR1 234 inline __complex__ float 235 __complex_asinh(__complex__ float __z) 236 { return __builtin_casinhf(__z); } 237 238 inline __complex__ double 239 __complex_asinh(__complex__ double __z) 240 { return __builtin_casinh(__z); } 241 242 inline __complex__ long double 243 __complex_asinh(const __complex__ long double& __z) 244 { return __builtin_casinhl(__z); } 245 246 template<typename _Tp> 247 inline std::complex<_Tp> 248 asinh(const std::complex<_Tp>& __z) 249 { return __complex_asinh(__z.__rep()); } 250 #else 251 /// asinh(__z) [8.1.6]. 252 // Effects: Behaves the same as C99 function casin, defined 253 // in subclause 7.3.6.2. 254 template<typename _Tp> 255 inline std::complex<_Tp> 256 asinh(const std::complex<_Tp>& __z) 257 { return __complex_asinh(__z); } 258 #endif 259 260 template<typename _Tp> 261 std::complex<_Tp> 262 __complex_atanh(const std::complex<_Tp>& __z) 263 { 264 const _Tp __i2 = __z.imag() * __z.imag(); 265 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 266 267 _Tp __num = _Tp(1.0) + __z.real(); 268 _Tp __den = _Tp(1.0) - __z.real(); 269 270 __num = __i2 + __num * __num; 271 __den = __i2 + __den * __den; 272 273 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 274 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 275 } 276 277 #if _GLIBCXX_USE_C99_COMPLEX_TR1 278 inline __complex__ float 279 __complex_atanh(__complex__ float __z) 280 { return __builtin_catanhf(__z); } 281 282 inline __complex__ double 283 __complex_atanh(__complex__ double __z) 284 { return __builtin_catanh(__z); } 285 286 inline __complex__ long double 287 __complex_atanh(const __complex__ long double& __z) 288 { return __builtin_catanhl(__z); } 289 290 template<typename _Tp> 291 inline std::complex<_Tp> 292 atanh(const std::complex<_Tp>& __z) 293 { return __complex_atanh(__z.__rep()); } 294 #else 295 /// atanh(__z) [8.1.7]. 296 // Effects: Behaves the same as C99 function catanh, defined 297 // in subclause 7.3.6.3. 298 template<typename _Tp> 299 inline std::complex<_Tp> 300 atanh(const std::complex<_Tp>& __z) 301 { return __complex_atanh(__z); } 302 #endif 303 304 #endif // C++11 305 306 template<typename _Tp> 307 inline std::complex<_Tp> 308 /// fabs(__z) [8.1.8]. 309 // Effects: Behaves the same as C99 function cabs, defined 310 // in subclause 7.3.8.1. 311 fabs(const std::complex<_Tp>& __z) 312 { return std::abs(__z); } 313 314 /// Additional overloads [8.1.9]. 315 #if __cplusplus < 201103L 316 317 template<typename _Tp> 318 inline typename __gnu_cxx::__promote<_Tp>::__type 319 arg(_Tp __x) 320 { 321 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 322 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 323 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 324 : __type(); 325 #else 326 return std::arg(std::complex<__type>(__x)); 327 #endif 328 } 329 330 template<typename _Tp> 331 inline typename __gnu_cxx::__promote<_Tp>::__type 332 imag(_Tp) 333 { return _Tp(); } 334 335 template<typename _Tp> 336 inline typename __gnu_cxx::__promote<_Tp>::__type 337 norm(_Tp __x) 338 { 339 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 340 return __type(__x) * __type(__x); 341 } 342 343 template<typename _Tp> 344 inline typename __gnu_cxx::__promote<_Tp>::__type 345 real(_Tp __x) 346 { return __x; } 347 348 #endif 349 350 template<typename _Tp, typename _Up> 351 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 352 pow(const std::complex<_Tp>& __x, const _Up& __y) 353 { 354 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 355 return std::pow(std::complex<__type>(__x), __type(__y)); 356 } 357 358 template<typename _Tp, typename _Up> 359 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 360 pow(const _Tp& __x, const std::complex<_Up>& __y) 361 { 362 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 363 return std::pow(__type(__x), std::complex<__type>(__y)); 364 } 365 366 template<typename _Tp, typename _Up> 367 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 368 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 369 { 370 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 371 return std::pow(std::complex<__type>(__x), 372 std::complex<__type>(__y)); 373 } 374 375 using std::arg; 376 377 template<typename _Tp> 378 inline std::complex<_Tp> 379 conj(const std::complex<_Tp>& __z) 380 { return std::conj(__z); } 381 382 template<typename _Tp> 383 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 384 conj(_Tp __x) 385 { return __x; } 386 387 using std::imag; 388 using std::norm; 389 using std::polar; 390 391 template<typename _Tp, typename _Up> 392 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 393 polar(const _Tp& __rho, const _Up& __theta) 394 { 395 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 396 return std::polar(__type(__rho), __type(__theta)); 397 } 398 399 using std::real; 400 401 template<typename _Tp> 402 inline std::complex<_Tp> 403 pow(const std::complex<_Tp>& __x, const _Tp& __y) 404 { return std::pow(__x, __y); } 405 406 template<typename _Tp> 407 inline std::complex<_Tp> 408 pow(const _Tp& __x, const std::complex<_Tp>& __y) 409 { return std::pow(__x, __y); } 410 411 template<typename _Tp> 412 inline std::complex<_Tp> 413 pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y) 414 { return std::pow(__x, __y); } 415 416 /// @} group complex_numbers 417 } 418 419 _GLIBCXX_END_NAMESPACE_VERSION 420 } 421 422 #endif // _GLIBCXX_TR1_COMPLEX
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