complex revision 1.1.1.11
1 // The template and inlines for the -*- C++ -*- complex number classes. 2 3 // Copyright (C) 1997-2019 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 include/complex 26 * This is a Standard C++ Library header. 27 */ 28 29 // 30 // ISO C++ 14882: 26.2 Complex Numbers 31 // Note: this is not a conforming implementation. 32 // Initially implemented by Ulrich Drepper <drepper (a] cygnus.com> 33 // Improved by Gabriel Dos Reis <dosreis (a] cmla.ens-cachan.fr> 34 // 35 36 #ifndef _GLIBCXX_COMPLEX 37 #define _GLIBCXX_COMPLEX 1 38 39 #pragma GCC system_header 40 41 #include <bits/c++config.h> 42 #include <bits/cpp_type_traits.h> 43 #include <ext/type_traits.h> 44 #include <cmath> 45 #include <sstream> 46 47 // Get rid of a macro possibly defined in <complex.h> 48 #undef complex 49 50 namespace std _GLIBCXX_VISIBILITY(default) 51 { 52 _GLIBCXX_BEGIN_NAMESPACE_VERSION 53 54 /** 55 * @defgroup complex_numbers Complex Numbers 56 * @ingroup numerics 57 * 58 * Classes and functions for complex numbers. 59 * @{ 60 */ 61 62 // Forward declarations. 63 template<typename _Tp> class complex; 64 template<> class complex<float>; 65 template<> class complex<double>; 66 template<> class complex<long double>; 67 68 /// Return magnitude of @a z. 69 template<typename _Tp> _Tp abs(const complex<_Tp>&); 70 /// Return phase angle of @a z. 71 template<typename _Tp> _Tp arg(const complex<_Tp>&); 72 /// Return @a z magnitude squared. 73 template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&); 74 75 /// Return complex conjugate of @a z. 76 template<typename _Tp> 77 _GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&); 78 /// Return complex with magnitude @a rho and angle @a theta. 79 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 80 81 // Transcendentals: 82 /// Return complex cosine of @a z. 83 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 84 /// Return complex hyperbolic cosine of @a z. 85 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 86 /// Return complex base e exponential of @a z. 87 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 88 /// Return complex natural logarithm of @a z. 89 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 90 /// Return complex base 10 logarithm of @a z. 91 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 92 /// Return @a x to the @a y'th power. 93 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 94 /// Return @a x to the @a y'th power. 95 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 96 /// Return @a x to the @a y'th power. 97 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 98 const complex<_Tp>&); 99 /// Return @a x to the @a y'th power. 100 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 101 /// Return complex sine of @a z. 102 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 103 /// Return complex hyperbolic sine of @a z. 104 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 105 /// Return complex square root of @a z. 106 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 107 /// Return complex tangent of @a z. 108 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 109 /// Return complex hyperbolic tangent of @a z. 110 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 111 112 113 // 26.2.2 Primary template class complex 114 /** 115 * Template to represent complex numbers. 116 * 117 * Specializations for float, double, and long double are part of the 118 * library. Results with any other type are not guaranteed. 119 * 120 * @param Tp Type of real and imaginary values. 121 */ 122 template<typename _Tp> 123 struct complex 124 { 125 /// Value typedef. 126 typedef _Tp value_type; 127 128 /// Default constructor. First parameter is x, second parameter is y. 129 /// Unspecified parameters default to 0. 130 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 131 : _M_real(__r), _M_imag(__i) { } 132 133 // Let the compiler synthesize the copy constructor 134 #if __cplusplus >= 201103L 135 constexpr complex(const complex&) = default; 136 #endif 137 138 /// Converting constructor. 139 template<typename _Up> 140 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 141 : _M_real(__z.real()), _M_imag(__z.imag()) { } 142 143 #if __cplusplus >= 201103L 144 // _GLIBCXX_RESOLVE_LIB_DEFECTS 145 // DR 387. std::complex over-encapsulated. 146 _GLIBCXX_ABI_TAG_CXX11 147 constexpr _Tp 148 real() const { return _M_real; } 149 150 _GLIBCXX_ABI_TAG_CXX11 151 constexpr _Tp 152 imag() const { return _M_imag; } 153 #else 154 /// Return real part of complex number. 155 _Tp& 156 real() { return _M_real; } 157 158 /// Return real part of complex number. 159 const _Tp& 160 real() const { return _M_real; } 161 162 /// Return imaginary part of complex number. 163 _Tp& 164 imag() { return _M_imag; } 165 166 /// Return imaginary part of complex number. 167 const _Tp& 168 imag() const { return _M_imag; } 169 #endif 170 171 // _GLIBCXX_RESOLVE_LIB_DEFECTS 172 // DR 387. std::complex over-encapsulated. 173 _GLIBCXX20_CONSTEXPR void 174 real(_Tp __val) { _M_real = __val; } 175 176 _GLIBCXX20_CONSTEXPR void 177 imag(_Tp __val) { _M_imag = __val; } 178 179 /// Assign a scalar to this complex number. 180 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&); 181 182 /// Add a scalar to this complex number. 183 // 26.2.5/1 184 _GLIBCXX20_CONSTEXPR complex<_Tp>& 185 operator+=(const _Tp& __t) 186 { 187 _M_real += __t; 188 return *this; 189 } 190 191 /// Subtract a scalar from this complex number. 192 // 26.2.5/3 193 _GLIBCXX20_CONSTEXPR complex<_Tp>& 194 operator-=(const _Tp& __t) 195 { 196 _M_real -= __t; 197 return *this; 198 } 199 200 /// Multiply this complex number by a scalar. 201 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&); 202 /// Divide this complex number by a scalar. 203 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&); 204 205 // Let the compiler synthesize the copy assignment operator 206 #if __cplusplus >= 201103L 207 _GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default; 208 #endif 209 210 /// Assign another complex number to this one. 211 template<typename _Up> 212 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&); 213 /// Add another complex number to this one. 214 template<typename _Up> 215 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&); 216 /// Subtract another complex number from this one. 217 template<typename _Up> 218 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&); 219 /// Multiply this complex number by another. 220 template<typename _Up> 221 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&); 222 /// Divide this complex number by another. 223 template<typename _Up> 224 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&); 225 226 _GLIBCXX_CONSTEXPR complex __rep() const 227 { return *this; } 228 229 private: 230 _Tp _M_real; 231 _Tp _M_imag; 232 }; 233 234 template<typename _Tp> 235 _GLIBCXX20_CONSTEXPR complex<_Tp>& 236 complex<_Tp>::operator=(const _Tp& __t) 237 { 238 _M_real = __t; 239 _M_imag = _Tp(); 240 return *this; 241 } 242 243 // 26.2.5/5 244 template<typename _Tp> 245 _GLIBCXX20_CONSTEXPR complex<_Tp>& 246 complex<_Tp>::operator*=(const _Tp& __t) 247 { 248 _M_real *= __t; 249 _M_imag *= __t; 250 return *this; 251 } 252 253 // 26.2.5/7 254 template<typename _Tp> 255 _GLIBCXX20_CONSTEXPR complex<_Tp>& 256 complex<_Tp>::operator/=(const _Tp& __t) 257 { 258 _M_real /= __t; 259 _M_imag /= __t; 260 return *this; 261 } 262 263 template<typename _Tp> 264 template<typename _Up> 265 _GLIBCXX20_CONSTEXPR complex<_Tp>& 266 complex<_Tp>::operator=(const complex<_Up>& __z) 267 { 268 _M_real = __z.real(); 269 _M_imag = __z.imag(); 270 return *this; 271 } 272 273 // 26.2.5/9 274 template<typename _Tp> 275 template<typename _Up> 276 _GLIBCXX20_CONSTEXPR complex<_Tp>& 277 complex<_Tp>::operator+=(const complex<_Up>& __z) 278 { 279 _M_real += __z.real(); 280 _M_imag += __z.imag(); 281 return *this; 282 } 283 284 // 26.2.5/11 285 template<typename _Tp> 286 template<typename _Up> 287 _GLIBCXX20_CONSTEXPR complex<_Tp>& 288 complex<_Tp>::operator-=(const complex<_Up>& __z) 289 { 290 _M_real -= __z.real(); 291 _M_imag -= __z.imag(); 292 return *this; 293 } 294 295 // 26.2.5/13 296 // XXX: This is a grammar school implementation. 297 template<typename _Tp> 298 template<typename _Up> 299 _GLIBCXX20_CONSTEXPR complex<_Tp>& 300 complex<_Tp>::operator*=(const complex<_Up>& __z) 301 { 302 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 303 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 304 _M_real = __r; 305 return *this; 306 } 307 308 // 26.2.5/15 309 // XXX: This is a grammar school implementation. 310 template<typename _Tp> 311 template<typename _Up> 312 _GLIBCXX20_CONSTEXPR complex<_Tp>& 313 complex<_Tp>::operator/=(const complex<_Up>& __z) 314 { 315 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 316 const _Tp __n = std::norm(__z); 317 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 318 _M_real = __r / __n; 319 return *this; 320 } 321 322 // Operators: 323 //@{ 324 /// Return new complex value @a x plus @a y. 325 template<typename _Tp> 326 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 327 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 328 { 329 complex<_Tp> __r = __x; 330 __r += __y; 331 return __r; 332 } 333 334 template<typename _Tp> 335 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 336 operator+(const complex<_Tp>& __x, const _Tp& __y) 337 { 338 complex<_Tp> __r = __x; 339 __r += __y; 340 return __r; 341 } 342 343 template<typename _Tp> 344 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 345 operator+(const _Tp& __x, const complex<_Tp>& __y) 346 { 347 complex<_Tp> __r = __y; 348 __r += __x; 349 return __r; 350 } 351 //@} 352 353 //@{ 354 /// Return new complex value @a x minus @a y. 355 template<typename _Tp> 356 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 357 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 358 { 359 complex<_Tp> __r = __x; 360 __r -= __y; 361 return __r; 362 } 363 364 template<typename _Tp> 365 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 366 operator-(const complex<_Tp>& __x, const _Tp& __y) 367 { 368 complex<_Tp> __r = __x; 369 __r -= __y; 370 return __r; 371 } 372 373 template<typename _Tp> 374 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 375 operator-(const _Tp& __x, const complex<_Tp>& __y) 376 { 377 complex<_Tp> __r = -__y; 378 __r += __x; 379 return __r; 380 } 381 //@} 382 383 //@{ 384 /// Return new complex value @a x times @a y. 385 template<typename _Tp> 386 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 387 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 388 { 389 complex<_Tp> __r = __x; 390 __r *= __y; 391 return __r; 392 } 393 394 template<typename _Tp> 395 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 396 operator*(const complex<_Tp>& __x, const _Tp& __y) 397 { 398 complex<_Tp> __r = __x; 399 __r *= __y; 400 return __r; 401 } 402 403 template<typename _Tp> 404 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 405 operator*(const _Tp& __x, const complex<_Tp>& __y) 406 { 407 complex<_Tp> __r = __y; 408 __r *= __x; 409 return __r; 410 } 411 //@} 412 413 //@{ 414 /// Return new complex value @a x divided by @a y. 415 template<typename _Tp> 416 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 417 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 418 { 419 complex<_Tp> __r = __x; 420 __r /= __y; 421 return __r; 422 } 423 424 template<typename _Tp> 425 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 426 operator/(const complex<_Tp>& __x, const _Tp& __y) 427 { 428 complex<_Tp> __r = __x; 429 __r /= __y; 430 return __r; 431 } 432 433 template<typename _Tp> 434 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 435 operator/(const _Tp& __x, const complex<_Tp>& __y) 436 { 437 complex<_Tp> __r = __x; 438 __r /= __y; 439 return __r; 440 } 441 //@} 442 443 /// Return @a x. 444 template<typename _Tp> 445 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 446 operator+(const complex<_Tp>& __x) 447 { return __x; } 448 449 /// Return complex negation of @a x. 450 template<typename _Tp> 451 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 452 operator-(const complex<_Tp>& __x) 453 { return complex<_Tp>(-__x.real(), -__x.imag()); } 454 455 //@{ 456 /// Return true if @a x is equal to @a y. 457 template<typename _Tp> 458 inline _GLIBCXX_CONSTEXPR bool 459 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 460 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 461 462 template<typename _Tp> 463 inline _GLIBCXX_CONSTEXPR bool 464 operator==(const complex<_Tp>& __x, const _Tp& __y) 465 { return __x.real() == __y && __x.imag() == _Tp(); } 466 467 template<typename _Tp> 468 inline _GLIBCXX_CONSTEXPR bool 469 operator==(const _Tp& __x, const complex<_Tp>& __y) 470 { return __x == __y.real() && _Tp() == __y.imag(); } 471 //@} 472 473 //@{ 474 /// Return false if @a x is equal to @a y. 475 template<typename _Tp> 476 inline _GLIBCXX_CONSTEXPR bool 477 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 478 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 479 480 template<typename _Tp> 481 inline _GLIBCXX_CONSTEXPR bool 482 operator!=(const complex<_Tp>& __x, const _Tp& __y) 483 { return __x.real() != __y || __x.imag() != _Tp(); } 484 485 template<typename _Tp> 486 inline _GLIBCXX_CONSTEXPR bool 487 operator!=(const _Tp& __x, const complex<_Tp>& __y) 488 { return __x != __y.real() || _Tp() != __y.imag(); } 489 //@} 490 491 /// Extraction operator for complex values. 492 template<typename _Tp, typename _CharT, class _Traits> 493 basic_istream<_CharT, _Traits>& 494 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 495 { 496 bool __fail = true; 497 _CharT __ch; 498 if (__is >> __ch) 499 { 500 if (_Traits::eq(__ch, __is.widen('('))) 501 { 502 _Tp __u; 503 if (__is >> __u >> __ch) 504 { 505 const _CharT __rparen = __is.widen(')'); 506 if (_Traits::eq(__ch, __rparen)) 507 { 508 __x = __u; 509 __fail = false; 510 } 511 else if (_Traits::eq(__ch, __is.widen(','))) 512 { 513 _Tp __v; 514 if (__is >> __v >> __ch) 515 { 516 if (_Traits::eq(__ch, __rparen)) 517 { 518 __x = complex<_Tp>(__u, __v); 519 __fail = false; 520 } 521 else 522 __is.putback(__ch); 523 } 524 } 525 else 526 __is.putback(__ch); 527 } 528 } 529 else 530 { 531 __is.putback(__ch); 532 _Tp __u; 533 if (__is >> __u) 534 { 535 __x = __u; 536 __fail = false; 537 } 538 } 539 } 540 if (__fail) 541 __is.setstate(ios_base::failbit); 542 return __is; 543 } 544 545 /// Insertion operator for complex values. 546 template<typename _Tp, typename _CharT, class _Traits> 547 basic_ostream<_CharT, _Traits>& 548 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 549 { 550 basic_ostringstream<_CharT, _Traits> __s; 551 __s.flags(__os.flags()); 552 __s.imbue(__os.getloc()); 553 __s.precision(__os.precision()); 554 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 555 return __os << __s.str(); 556 } 557 558 // Values 559 #if __cplusplus >= 201103L 560 template<typename _Tp> 561 constexpr _Tp 562 real(const complex<_Tp>& __z) 563 { return __z.real(); } 564 565 template<typename _Tp> 566 constexpr _Tp 567 imag(const complex<_Tp>& __z) 568 { return __z.imag(); } 569 #else 570 template<typename _Tp> 571 inline _Tp& 572 real(complex<_Tp>& __z) 573 { return __z.real(); } 574 575 template<typename _Tp> 576 inline const _Tp& 577 real(const complex<_Tp>& __z) 578 { return __z.real(); } 579 580 template<typename _Tp> 581 inline _Tp& 582 imag(complex<_Tp>& __z) 583 { return __z.imag(); } 584 585 template<typename _Tp> 586 inline const _Tp& 587 imag(const complex<_Tp>& __z) 588 { return __z.imag(); } 589 #endif 590 591 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 592 template<typename _Tp> 593 inline _Tp 594 __complex_abs(const complex<_Tp>& __z) 595 { 596 _Tp __x = __z.real(); 597 _Tp __y = __z.imag(); 598 const _Tp __s = std::max(abs(__x), abs(__y)); 599 if (__s == _Tp()) // well ... 600 return __s; 601 __x /= __s; 602 __y /= __s; 603 return __s * sqrt(__x * __x + __y * __y); 604 } 605 606 #if _GLIBCXX_USE_C99_COMPLEX 607 inline float 608 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 609 610 inline double 611 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 612 613 inline long double 614 __complex_abs(const __complex__ long double& __z) 615 { return __builtin_cabsl(__z); } 616 617 template<typename _Tp> 618 inline _Tp 619 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 620 #else 621 template<typename _Tp> 622 inline _Tp 623 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 624 #endif 625 626 627 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 628 template<typename _Tp> 629 inline _Tp 630 __complex_arg(const complex<_Tp>& __z) 631 { return atan2(__z.imag(), __z.real()); } 632 633 #if _GLIBCXX_USE_C99_COMPLEX 634 inline float 635 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 636 637 inline double 638 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 639 640 inline long double 641 __complex_arg(const __complex__ long double& __z) 642 { return __builtin_cargl(__z); } 643 644 template<typename _Tp> 645 inline _Tp 646 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 647 #else 648 template<typename _Tp> 649 inline _Tp 650 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 651 #endif 652 653 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 654 // As defined, norm() is -not- a norm is the common mathematical 655 // sense used in numerics. The helper class _Norm_helper<> tries to 656 // distinguish between builtin floating point and the rest, so as 657 // to deliver an answer as close as possible to the real value. 658 template<bool> 659 struct _Norm_helper 660 { 661 template<typename _Tp> 662 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) 663 { 664 const _Tp __x = __z.real(); 665 const _Tp __y = __z.imag(); 666 return __x * __x + __y * __y; 667 } 668 }; 669 670 template<> 671 struct _Norm_helper<true> 672 { 673 template<typename _Tp> 674 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) 675 { 676 //_Tp __res = std::abs(__z); 677 //return __res * __res; 678 const _Tp __x = __z.real(); 679 const _Tp __y = __z.imag(); 680 return __x * __x + __y * __y; 681 } 682 }; 683 684 template<typename _Tp> 685 inline _GLIBCXX20_CONSTEXPR _Tp 686 norm(const complex<_Tp>& __z) 687 { 688 return _Norm_helper<__is_floating<_Tp>::__value 689 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 690 } 691 692 template<typename _Tp> 693 inline complex<_Tp> 694 polar(const _Tp& __rho, const _Tp& __theta) 695 { 696 __glibcxx_assert( __rho >= 0 ); 697 return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); 698 } 699 700 template<typename _Tp> 701 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 702 conj(const complex<_Tp>& __z) 703 { return complex<_Tp>(__z.real(), -__z.imag()); } 704 705 // Transcendentals 706 707 // 26.2.8/1 cos(__z): Returns the cosine of __z. 708 template<typename _Tp> 709 inline complex<_Tp> 710 __complex_cos(const complex<_Tp>& __z) 711 { 712 const _Tp __x = __z.real(); 713 const _Tp __y = __z.imag(); 714 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 715 } 716 717 #if _GLIBCXX_USE_C99_COMPLEX 718 inline __complex__ float 719 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 720 721 inline __complex__ double 722 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 723 724 inline __complex__ long double 725 __complex_cos(const __complex__ long double& __z) 726 { return __builtin_ccosl(__z); } 727 728 template<typename _Tp> 729 inline complex<_Tp> 730 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 731 #else 732 template<typename _Tp> 733 inline complex<_Tp> 734 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 735 #endif 736 737 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 738 template<typename _Tp> 739 inline complex<_Tp> 740 __complex_cosh(const complex<_Tp>& __z) 741 { 742 const _Tp __x = __z.real(); 743 const _Tp __y = __z.imag(); 744 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 745 } 746 747 #if _GLIBCXX_USE_C99_COMPLEX 748 inline __complex__ float 749 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 750 751 inline __complex__ double 752 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 753 754 inline __complex__ long double 755 __complex_cosh(const __complex__ long double& __z) 756 { return __builtin_ccoshl(__z); } 757 758 template<typename _Tp> 759 inline complex<_Tp> 760 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 761 #else 762 template<typename _Tp> 763 inline complex<_Tp> 764 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 765 #endif 766 767 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 768 template<typename _Tp> 769 inline complex<_Tp> 770 __complex_exp(const complex<_Tp>& __z) 771 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); } 772 773 #if _GLIBCXX_USE_C99_COMPLEX 774 inline __complex__ float 775 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 776 777 inline __complex__ double 778 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 779 780 inline __complex__ long double 781 __complex_exp(const __complex__ long double& __z) 782 { return __builtin_cexpl(__z); } 783 784 template<typename _Tp> 785 inline complex<_Tp> 786 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 787 #else 788 template<typename _Tp> 789 inline complex<_Tp> 790 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 791 #endif 792 793 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 794 // The branch cut is along the negative axis. 795 template<typename _Tp> 796 inline complex<_Tp> 797 __complex_log(const complex<_Tp>& __z) 798 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 799 800 #if _GLIBCXX_USE_C99_COMPLEX 801 inline __complex__ float 802 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 803 804 inline __complex__ double 805 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 806 807 inline __complex__ long double 808 __complex_log(const __complex__ long double& __z) 809 { return __builtin_clogl(__z); } 810 811 template<typename _Tp> 812 inline complex<_Tp> 813 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 814 #else 815 template<typename _Tp> 816 inline complex<_Tp> 817 log(const complex<_Tp>& __z) { return __complex_log(__z); } 818 #endif 819 820 template<typename _Tp> 821 inline complex<_Tp> 822 log10(const complex<_Tp>& __z) 823 { return std::log(__z) / log(_Tp(10.0)); } 824 825 // 26.2.8/10 sin(__z): Returns the sine of __z. 826 template<typename _Tp> 827 inline complex<_Tp> 828 __complex_sin(const complex<_Tp>& __z) 829 { 830 const _Tp __x = __z.real(); 831 const _Tp __y = __z.imag(); 832 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 833 } 834 835 #if _GLIBCXX_USE_C99_COMPLEX 836 inline __complex__ float 837 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 838 839 inline __complex__ double 840 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 841 842 inline __complex__ long double 843 __complex_sin(const __complex__ long double& __z) 844 { return __builtin_csinl(__z); } 845 846 template<typename _Tp> 847 inline complex<_Tp> 848 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 849 #else 850 template<typename _Tp> 851 inline complex<_Tp> 852 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 853 #endif 854 855 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 856 template<typename _Tp> 857 inline complex<_Tp> 858 __complex_sinh(const complex<_Tp>& __z) 859 { 860 const _Tp __x = __z.real(); 861 const _Tp __y = __z.imag(); 862 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 863 } 864 865 #if _GLIBCXX_USE_C99_COMPLEX 866 inline __complex__ float 867 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 868 869 inline __complex__ double 870 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 871 872 inline __complex__ long double 873 __complex_sinh(const __complex__ long double& __z) 874 { return __builtin_csinhl(__z); } 875 876 template<typename _Tp> 877 inline complex<_Tp> 878 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 879 #else 880 template<typename _Tp> 881 inline complex<_Tp> 882 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 883 #endif 884 885 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 886 // The branch cut is on the negative axis. 887 template<typename _Tp> 888 complex<_Tp> 889 __complex_sqrt(const complex<_Tp>& __z) 890 { 891 _Tp __x = __z.real(); 892 _Tp __y = __z.imag(); 893 894 if (__x == _Tp()) 895 { 896 _Tp __t = sqrt(abs(__y) / 2); 897 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 898 } 899 else 900 { 901 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 902 _Tp __u = __t / 2; 903 return __x > _Tp() 904 ? complex<_Tp>(__u, __y / __t) 905 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 906 } 907 } 908 909 #if _GLIBCXX_USE_C99_COMPLEX 910 inline __complex__ float 911 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 912 913 inline __complex__ double 914 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 915 916 inline __complex__ long double 917 __complex_sqrt(const __complex__ long double& __z) 918 { return __builtin_csqrtl(__z); } 919 920 template<typename _Tp> 921 inline complex<_Tp> 922 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 923 #else 924 template<typename _Tp> 925 inline complex<_Tp> 926 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 927 #endif 928 929 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 930 931 template<typename _Tp> 932 inline complex<_Tp> 933 __complex_tan(const complex<_Tp>& __z) 934 { return std::sin(__z) / std::cos(__z); } 935 936 #if _GLIBCXX_USE_C99_COMPLEX 937 inline __complex__ float 938 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 939 940 inline __complex__ double 941 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 942 943 inline __complex__ long double 944 __complex_tan(const __complex__ long double& __z) 945 { return __builtin_ctanl(__z); } 946 947 template<typename _Tp> 948 inline complex<_Tp> 949 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 950 #else 951 template<typename _Tp> 952 inline complex<_Tp> 953 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 954 #endif 955 956 957 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 958 959 template<typename _Tp> 960 inline complex<_Tp> 961 __complex_tanh(const complex<_Tp>& __z) 962 { return std::sinh(__z) / std::cosh(__z); } 963 964 #if _GLIBCXX_USE_C99_COMPLEX 965 inline __complex__ float 966 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 967 968 inline __complex__ double 969 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 970 971 inline __complex__ long double 972 __complex_tanh(const __complex__ long double& __z) 973 { return __builtin_ctanhl(__z); } 974 975 template<typename _Tp> 976 inline complex<_Tp> 977 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 978 #else 979 template<typename _Tp> 980 inline complex<_Tp> 981 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 982 #endif 983 984 985 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 986 // raised to the __y-th power. The branch 987 // cut is on the negative axis. 988 template<typename _Tp> 989 complex<_Tp> 990 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 991 { 992 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 993 994 while (__n >>= 1) 995 { 996 __x *= __x; 997 if (__n % 2) 998 __y *= __x; 999 } 1000 1001 return __y; 1002 } 1003 1004 // In C++11 mode we used to implement the resolution of 1005 // DR 844. complex pow return type is ambiguous. 1006 // thus the following overload was disabled in that mode. However, doing 1007 // that causes all sorts of issues, see, for example: 1008 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html 1009 // and also PR57974. 1010 template<typename _Tp> 1011 inline complex<_Tp> 1012 pow(const complex<_Tp>& __z, int __n) 1013 { 1014 return __n < 0 1015 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) 1016 : std::__complex_pow_unsigned(__z, __n); 1017 } 1018 1019 template<typename _Tp> 1020 complex<_Tp> 1021 pow(const complex<_Tp>& __x, const _Tp& __y) 1022 { 1023 #if ! _GLIBCXX_USE_C99_COMPLEX 1024 if (__x == _Tp()) 1025 return _Tp(); 1026 #endif 1027 if (__x.imag() == _Tp() && __x.real() > _Tp()) 1028 return pow(__x.real(), __y); 1029 1030 complex<_Tp> __t = std::log(__x); 1031 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag()); 1032 } 1033 1034 template<typename _Tp> 1035 inline complex<_Tp> 1036 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1037 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1038 1039 #if _GLIBCXX_USE_C99_COMPLEX 1040 inline __complex__ float 1041 __complex_pow(__complex__ float __x, __complex__ float __y) 1042 { return __builtin_cpowf(__x, __y); } 1043 1044 inline __complex__ double 1045 __complex_pow(__complex__ double __x, __complex__ double __y) 1046 { return __builtin_cpow(__x, __y); } 1047 1048 inline __complex__ long double 1049 __complex_pow(const __complex__ long double& __x, 1050 const __complex__ long double& __y) 1051 { return __builtin_cpowl(__x, __y); } 1052 1053 template<typename _Tp> 1054 inline complex<_Tp> 1055 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1056 { return __complex_pow(__x.__rep(), __y.__rep()); } 1057 #else 1058 template<typename _Tp> 1059 inline complex<_Tp> 1060 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1061 { return __complex_pow(__x, __y); } 1062 #endif 1063 1064 template<typename _Tp> 1065 inline complex<_Tp> 1066 pow(const _Tp& __x, const complex<_Tp>& __y) 1067 { 1068 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()), 1069 __y.imag() * log(__x)) 1070 : std::pow(complex<_Tp>(__x), __y); 1071 } 1072 1073 /// 26.2.3 complex specializations 1074 /// complex<float> specialization 1075 template<> 1076 struct complex<float> 1077 { 1078 typedef float value_type; 1079 typedef __complex__ float _ComplexT; 1080 1081 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1082 1083 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1084 #if __cplusplus >= 201103L 1085 : _M_value{ __r, __i } { } 1086 #else 1087 { 1088 __real__ _M_value = __r; 1089 __imag__ _M_value = __i; 1090 } 1091 #endif 1092 1093 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1094 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1095 1096 #if __cplusplus >= 201103L 1097 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1098 // DR 387. std::complex over-encapsulated. 1099 __attribute ((__abi_tag__ ("cxx11"))) 1100 constexpr float 1101 real() const { return __real__ _M_value; } 1102 1103 __attribute ((__abi_tag__ ("cxx11"))) 1104 constexpr float 1105 imag() const { return __imag__ _M_value; } 1106 #else 1107 float& 1108 real() { return __real__ _M_value; } 1109 1110 const float& 1111 real() const { return __real__ _M_value; } 1112 1113 float& 1114 imag() { return __imag__ _M_value; } 1115 1116 const float& 1117 imag() const { return __imag__ _M_value; } 1118 #endif 1119 1120 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1121 // DR 387. std::complex over-encapsulated. 1122 _GLIBCXX20_CONSTEXPR void 1123 real(float __val) { __real__ _M_value = __val; } 1124 1125 _GLIBCXX20_CONSTEXPR void 1126 imag(float __val) { __imag__ _M_value = __val; } 1127 1128 _GLIBCXX20_CONSTEXPR complex& 1129 operator=(float __f) 1130 { 1131 _M_value = __f; 1132 return *this; 1133 } 1134 1135 _GLIBCXX20_CONSTEXPR complex& 1136 operator+=(float __f) 1137 { 1138 _M_value += __f; 1139 return *this; 1140 } 1141 1142 _GLIBCXX20_CONSTEXPR complex& 1143 operator-=(float __f) 1144 { 1145 _M_value -= __f; 1146 return *this; 1147 } 1148 1149 _GLIBCXX20_CONSTEXPR complex& 1150 operator*=(float __f) 1151 { 1152 _M_value *= __f; 1153 return *this; 1154 } 1155 1156 _GLIBCXX20_CONSTEXPR complex& 1157 operator/=(float __f) 1158 { 1159 _M_value /= __f; 1160 return *this; 1161 } 1162 1163 // Let the compiler synthesize the copy and assignment 1164 // operator. It always does a pretty good job. 1165 #if __cplusplus >= 201103L 1166 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1167 #endif 1168 1169 template<typename _Tp> 1170 _GLIBCXX20_CONSTEXPR complex& 1171 operator=(const complex<_Tp>& __z) 1172 { 1173 __real__ _M_value = __z.real(); 1174 __imag__ _M_value = __z.imag(); 1175 return *this; 1176 } 1177 1178 template<typename _Tp> 1179 _GLIBCXX20_CONSTEXPR complex& 1180 operator+=(const complex<_Tp>& __z) 1181 { 1182 _M_value += __z.__rep(); 1183 return *this; 1184 } 1185 1186 template<class _Tp> 1187 _GLIBCXX20_CONSTEXPR complex& 1188 operator-=(const complex<_Tp>& __z) 1189 { 1190 _M_value -= __z.__rep(); 1191 return *this; 1192 } 1193 1194 template<class _Tp> 1195 _GLIBCXX20_CONSTEXPR complex& 1196 operator*=(const complex<_Tp>& __z) 1197 { 1198 const _ComplexT __t = __z.__rep(); 1199 _M_value *= __t; 1200 return *this; 1201 } 1202 1203 template<class _Tp> 1204 _GLIBCXX20_CONSTEXPR complex& 1205 operator/=(const complex<_Tp>& __z) 1206 { 1207 const _ComplexT __t = __z.__rep(); 1208 _M_value /= __t; 1209 return *this; 1210 } 1211 1212 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1213 1214 private: 1215 _ComplexT _M_value; 1216 }; 1217 1218 /// 26.2.3 complex specializations 1219 /// complex<double> specialization 1220 template<> 1221 struct complex<double> 1222 { 1223 typedef double value_type; 1224 typedef __complex__ double _ComplexT; 1225 1226 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1227 1228 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1229 #if __cplusplus >= 201103L 1230 : _M_value{ __r, __i } { } 1231 #else 1232 { 1233 __real__ _M_value = __r; 1234 __imag__ _M_value = __i; 1235 } 1236 #endif 1237 1238 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1239 : _M_value(__z.__rep()) { } 1240 1241 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1242 1243 #if __cplusplus >= 201103L 1244 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1245 // DR 387. std::complex over-encapsulated. 1246 __attribute ((__abi_tag__ ("cxx11"))) 1247 constexpr double 1248 real() const { return __real__ _M_value; } 1249 1250 __attribute ((__abi_tag__ ("cxx11"))) 1251 constexpr double 1252 imag() const { return __imag__ _M_value; } 1253 #else 1254 double& 1255 real() { return __real__ _M_value; } 1256 1257 const double& 1258 real() const { return __real__ _M_value; } 1259 1260 double& 1261 imag() { return __imag__ _M_value; } 1262 1263 const double& 1264 imag() const { return __imag__ _M_value; } 1265 #endif 1266 1267 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1268 // DR 387. std::complex over-encapsulated. 1269 _GLIBCXX20_CONSTEXPR void 1270 real(double __val) { __real__ _M_value = __val; } 1271 1272 _GLIBCXX20_CONSTEXPR void 1273 imag(double __val) { __imag__ _M_value = __val; } 1274 1275 _GLIBCXX20_CONSTEXPR complex& 1276 operator=(double __d) 1277 { 1278 _M_value = __d; 1279 return *this; 1280 } 1281 1282 _GLIBCXX20_CONSTEXPR complex& 1283 operator+=(double __d) 1284 { 1285 _M_value += __d; 1286 return *this; 1287 } 1288 1289 _GLIBCXX20_CONSTEXPR complex& 1290 operator-=(double __d) 1291 { 1292 _M_value -= __d; 1293 return *this; 1294 } 1295 1296 _GLIBCXX20_CONSTEXPR complex& 1297 operator*=(double __d) 1298 { 1299 _M_value *= __d; 1300 return *this; 1301 } 1302 1303 _GLIBCXX20_CONSTEXPR complex& 1304 operator/=(double __d) 1305 { 1306 _M_value /= __d; 1307 return *this; 1308 } 1309 1310 // The compiler will synthesize this, efficiently. 1311 #if __cplusplus >= 201103L 1312 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1313 #endif 1314 1315 template<typename _Tp> 1316 _GLIBCXX20_CONSTEXPR complex& 1317 operator=(const complex<_Tp>& __z) 1318 { 1319 _M_value = __z.__rep(); 1320 return *this; 1321 } 1322 1323 template<typename _Tp> 1324 _GLIBCXX20_CONSTEXPR complex& 1325 operator+=(const complex<_Tp>& __z) 1326 { 1327 _M_value += __z.__rep(); 1328 return *this; 1329 } 1330 1331 template<typename _Tp> 1332 _GLIBCXX20_CONSTEXPR complex& 1333 operator-=(const complex<_Tp>& __z) 1334 { 1335 _M_value -= __z.__rep(); 1336 return *this; 1337 } 1338 1339 template<typename _Tp> 1340 _GLIBCXX20_CONSTEXPR complex& 1341 operator*=(const complex<_Tp>& __z) 1342 { 1343 const _ComplexT __t = __z.__rep(); 1344 _M_value *= __t; 1345 return *this; 1346 } 1347 1348 template<typename _Tp> 1349 _GLIBCXX20_CONSTEXPR complex& 1350 operator/=(const complex<_Tp>& __z) 1351 { 1352 const _ComplexT __t = __z.__rep(); 1353 _M_value /= __t; 1354 return *this; 1355 } 1356 1357 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1358 1359 private: 1360 _ComplexT _M_value; 1361 }; 1362 1363 /// 26.2.3 complex specializations 1364 /// complex<long double> specialization 1365 template<> 1366 struct complex<long double> 1367 { 1368 typedef long double value_type; 1369 typedef __complex__ long double _ComplexT; 1370 1371 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1372 1373 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1374 long double __i = 0.0L) 1375 #if __cplusplus >= 201103L 1376 : _M_value{ __r, __i } { } 1377 #else 1378 { 1379 __real__ _M_value = __r; 1380 __imag__ _M_value = __i; 1381 } 1382 #endif 1383 1384 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1385 : _M_value(__z.__rep()) { } 1386 1387 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1388 : _M_value(__z.__rep()) { } 1389 1390 #if __cplusplus >= 201103L 1391 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1392 // DR 387. std::complex over-encapsulated. 1393 __attribute ((__abi_tag__ ("cxx11"))) 1394 constexpr long double 1395 real() const { return __real__ _M_value; } 1396 1397 __attribute ((__abi_tag__ ("cxx11"))) 1398 constexpr long double 1399 imag() const { return __imag__ _M_value; } 1400 #else 1401 long double& 1402 real() { return __real__ _M_value; } 1403 1404 const long double& 1405 real() const { return __real__ _M_value; } 1406 1407 long double& 1408 imag() { return __imag__ _M_value; } 1409 1410 const long double& 1411 imag() const { return __imag__ _M_value; } 1412 #endif 1413 1414 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1415 // DR 387. std::complex over-encapsulated. 1416 _GLIBCXX20_CONSTEXPR void 1417 real(long double __val) { __real__ _M_value = __val; } 1418 1419 _GLIBCXX20_CONSTEXPR void 1420 imag(long double __val) { __imag__ _M_value = __val; } 1421 1422 _GLIBCXX20_CONSTEXPR complex& 1423 operator=(long double __r) 1424 { 1425 _M_value = __r; 1426 return *this; 1427 } 1428 1429 _GLIBCXX20_CONSTEXPR complex& 1430 operator+=(long double __r) 1431 { 1432 _M_value += __r; 1433 return *this; 1434 } 1435 1436 _GLIBCXX20_CONSTEXPR complex& 1437 operator-=(long double __r) 1438 { 1439 _M_value -= __r; 1440 return *this; 1441 } 1442 1443 _GLIBCXX20_CONSTEXPR complex& 1444 operator*=(long double __r) 1445 { 1446 _M_value *= __r; 1447 return *this; 1448 } 1449 1450 _GLIBCXX20_CONSTEXPR complex& 1451 operator/=(long double __r) 1452 { 1453 _M_value /= __r; 1454 return *this; 1455 } 1456 1457 // The compiler knows how to do this efficiently 1458 #if __cplusplus >= 201103L 1459 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1460 #endif 1461 1462 template<typename _Tp> 1463 _GLIBCXX20_CONSTEXPR complex& 1464 operator=(const complex<_Tp>& __z) 1465 { 1466 _M_value = __z.__rep(); 1467 return *this; 1468 } 1469 1470 template<typename _Tp> 1471 _GLIBCXX20_CONSTEXPR complex& 1472 operator+=(const complex<_Tp>& __z) 1473 { 1474 _M_value += __z.__rep(); 1475 return *this; 1476 } 1477 1478 template<typename _Tp> 1479 _GLIBCXX20_CONSTEXPR complex& 1480 operator-=(const complex<_Tp>& __z) 1481 { 1482 _M_value -= __z.__rep(); 1483 return *this; 1484 } 1485 1486 template<typename _Tp> 1487 _GLIBCXX20_CONSTEXPR complex& 1488 operator*=(const complex<_Tp>& __z) 1489 { 1490 const _ComplexT __t = __z.__rep(); 1491 _M_value *= __t; 1492 return *this; 1493 } 1494 1495 template<typename _Tp> 1496 _GLIBCXX20_CONSTEXPR complex& 1497 operator/=(const complex<_Tp>& __z) 1498 { 1499 const _ComplexT __t = __z.__rep(); 1500 _M_value /= __t; 1501 return *this; 1502 } 1503 1504 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1505 1506 private: 1507 _ComplexT _M_value; 1508 }; 1509 1510 // These bits have to be at the end of this file, so that the 1511 // specializations have all been defined. 1512 inline _GLIBCXX_CONSTEXPR 1513 complex<float>::complex(const complex<double>& __z) 1514 : _M_value(__z.__rep()) { } 1515 1516 inline _GLIBCXX_CONSTEXPR 1517 complex<float>::complex(const complex<long double>& __z) 1518 : _M_value(__z.__rep()) { } 1519 1520 inline _GLIBCXX_CONSTEXPR 1521 complex<double>::complex(const complex<long double>& __z) 1522 : _M_value(__z.__rep()) { } 1523 1524 // Inhibit implicit instantiations for required instantiations, 1525 // which are defined via explicit instantiations elsewhere. 1526 // NB: This syntax is a GNU extension. 1527 #if _GLIBCXX_EXTERN_TEMPLATE 1528 extern template istream& operator>>(istream&, complex<float>&); 1529 extern template ostream& operator<<(ostream&, const complex<float>&); 1530 extern template istream& operator>>(istream&, complex<double>&); 1531 extern template ostream& operator<<(ostream&, const complex<double>&); 1532 extern template istream& operator>>(istream&, complex<long double>&); 1533 extern template ostream& operator<<(ostream&, const complex<long double>&); 1534 1535 #ifdef _GLIBCXX_USE_WCHAR_T 1536 extern template wistream& operator>>(wistream&, complex<float>&); 1537 extern template wostream& operator<<(wostream&, const complex<float>&); 1538 extern template wistream& operator>>(wistream&, complex<double>&); 1539 extern template wostream& operator<<(wostream&, const complex<double>&); 1540 extern template wistream& operator>>(wistream&, complex<long double>&); 1541 extern template wostream& operator<<(wostream&, const complex<long double>&); 1542 #endif 1543 #endif 1544 1545 // @} group complex_numbers 1546 1547 _GLIBCXX_END_NAMESPACE_VERSION 1548 } // namespace 1549 1550 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1551 { 1552 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1553 1554 // See ext/type_traits.h for the primary template. 1555 template<typename _Tp, typename _Up> 1556 struct __promote_2<std::complex<_Tp>, _Up> 1557 { 1558 public: 1559 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1560 }; 1561 1562 template<typename _Tp, typename _Up> 1563 struct __promote_2<_Tp, std::complex<_Up> > 1564 { 1565 public: 1566 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1567 }; 1568 1569 template<typename _Tp, typename _Up> 1570 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1571 { 1572 public: 1573 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1574 }; 1575 1576 _GLIBCXX_END_NAMESPACE_VERSION 1577 } // namespace 1578 1579 #if __cplusplus >= 201103L 1580 1581 namespace std _GLIBCXX_VISIBILITY(default) 1582 { 1583 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1584 1585 // Forward declarations. 1586 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1587 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1588 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1589 1590 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1591 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1592 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1593 // DR 595. 1594 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1595 1596 template<typename _Tp> 1597 inline std::complex<_Tp> 1598 __complex_acos(const std::complex<_Tp>& __z) 1599 { 1600 const std::complex<_Tp> __t = std::asin(__z); 1601 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1602 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1603 } 1604 1605 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1606 inline __complex__ float 1607 __complex_acos(__complex__ float __z) 1608 { return __builtin_cacosf(__z); } 1609 1610 inline __complex__ double 1611 __complex_acos(__complex__ double __z) 1612 { return __builtin_cacos(__z); } 1613 1614 inline __complex__ long double 1615 __complex_acos(const __complex__ long double& __z) 1616 { return __builtin_cacosl(__z); } 1617 1618 template<typename _Tp> 1619 inline std::complex<_Tp> 1620 acos(const std::complex<_Tp>& __z) 1621 { return __complex_acos(__z.__rep()); } 1622 #else 1623 /// acos(__z) [8.1.2]. 1624 // Effects: Behaves the same as C99 function cacos, defined 1625 // in subclause 7.3.5.1. 1626 template<typename _Tp> 1627 inline std::complex<_Tp> 1628 acos(const std::complex<_Tp>& __z) 1629 { return __complex_acos(__z); } 1630 #endif 1631 1632 template<typename _Tp> 1633 inline std::complex<_Tp> 1634 __complex_asin(const std::complex<_Tp>& __z) 1635 { 1636 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1637 __t = std::asinh(__t); 1638 return std::complex<_Tp>(__t.imag(), -__t.real()); 1639 } 1640 1641 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1642 inline __complex__ float 1643 __complex_asin(__complex__ float __z) 1644 { return __builtin_casinf(__z); } 1645 1646 inline __complex__ double 1647 __complex_asin(__complex__ double __z) 1648 { return __builtin_casin(__z); } 1649 1650 inline __complex__ long double 1651 __complex_asin(const __complex__ long double& __z) 1652 { return __builtin_casinl(__z); } 1653 1654 template<typename _Tp> 1655 inline std::complex<_Tp> 1656 asin(const std::complex<_Tp>& __z) 1657 { return __complex_asin(__z.__rep()); } 1658 #else 1659 /// asin(__z) [8.1.3]. 1660 // Effects: Behaves the same as C99 function casin, defined 1661 // in subclause 7.3.5.2. 1662 template<typename _Tp> 1663 inline std::complex<_Tp> 1664 asin(const std::complex<_Tp>& __z) 1665 { return __complex_asin(__z); } 1666 #endif 1667 1668 template<typename _Tp> 1669 std::complex<_Tp> 1670 __complex_atan(const std::complex<_Tp>& __z) 1671 { 1672 const _Tp __r2 = __z.real() * __z.real(); 1673 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1674 1675 _Tp __num = __z.imag() + _Tp(1.0); 1676 _Tp __den = __z.imag() - _Tp(1.0); 1677 1678 __num = __r2 + __num * __num; 1679 __den = __r2 + __den * __den; 1680 1681 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1682 _Tp(0.25) * log(__num / __den)); 1683 } 1684 1685 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1686 inline __complex__ float 1687 __complex_atan(__complex__ float __z) 1688 { return __builtin_catanf(__z); } 1689 1690 inline __complex__ double 1691 __complex_atan(__complex__ double __z) 1692 { return __builtin_catan(__z); } 1693 1694 inline __complex__ long double 1695 __complex_atan(const __complex__ long double& __z) 1696 { return __builtin_catanl(__z); } 1697 1698 template<typename _Tp> 1699 inline std::complex<_Tp> 1700 atan(const std::complex<_Tp>& __z) 1701 { return __complex_atan(__z.__rep()); } 1702 #else 1703 /// atan(__z) [8.1.4]. 1704 // Effects: Behaves the same as C99 function catan, defined 1705 // in subclause 7.3.5.3. 1706 template<typename _Tp> 1707 inline std::complex<_Tp> 1708 atan(const std::complex<_Tp>& __z) 1709 { return __complex_atan(__z); } 1710 #endif 1711 1712 template<typename _Tp> 1713 std::complex<_Tp> 1714 __complex_acosh(const std::complex<_Tp>& __z) 1715 { 1716 // Kahan's formula. 1717 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1718 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1719 } 1720 1721 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1722 inline __complex__ float 1723 __complex_acosh(__complex__ float __z) 1724 { return __builtin_cacoshf(__z); } 1725 1726 inline __complex__ double 1727 __complex_acosh(__complex__ double __z) 1728 { return __builtin_cacosh(__z); } 1729 1730 inline __complex__ long double 1731 __complex_acosh(const __complex__ long double& __z) 1732 { return __builtin_cacoshl(__z); } 1733 1734 template<typename _Tp> 1735 inline std::complex<_Tp> 1736 acosh(const std::complex<_Tp>& __z) 1737 { return __complex_acosh(__z.__rep()); } 1738 #else 1739 /// acosh(__z) [8.1.5]. 1740 // Effects: Behaves the same as C99 function cacosh, defined 1741 // in subclause 7.3.6.1. 1742 template<typename _Tp> 1743 inline std::complex<_Tp> 1744 acosh(const std::complex<_Tp>& __z) 1745 { return __complex_acosh(__z); } 1746 #endif 1747 1748 template<typename _Tp> 1749 std::complex<_Tp> 1750 __complex_asinh(const std::complex<_Tp>& __z) 1751 { 1752 std::complex<_Tp> __t((__z.real() - __z.imag()) 1753 * (__z.real() + __z.imag()) + _Tp(1.0), 1754 _Tp(2.0) * __z.real() * __z.imag()); 1755 __t = std::sqrt(__t); 1756 1757 return std::log(__t + __z); 1758 } 1759 1760 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1761 inline __complex__ float 1762 __complex_asinh(__complex__ float __z) 1763 { return __builtin_casinhf(__z); } 1764 1765 inline __complex__ double 1766 __complex_asinh(__complex__ double __z) 1767 { return __builtin_casinh(__z); } 1768 1769 inline __complex__ long double 1770 __complex_asinh(const __complex__ long double& __z) 1771 { return __builtin_casinhl(__z); } 1772 1773 template<typename _Tp> 1774 inline std::complex<_Tp> 1775 asinh(const std::complex<_Tp>& __z) 1776 { return __complex_asinh(__z.__rep()); } 1777 #else 1778 /// asinh(__z) [8.1.6]. 1779 // Effects: Behaves the same as C99 function casin, defined 1780 // in subclause 7.3.6.2. 1781 template<typename _Tp> 1782 inline std::complex<_Tp> 1783 asinh(const std::complex<_Tp>& __z) 1784 { return __complex_asinh(__z); } 1785 #endif 1786 1787 template<typename _Tp> 1788 std::complex<_Tp> 1789 __complex_atanh(const std::complex<_Tp>& __z) 1790 { 1791 const _Tp __i2 = __z.imag() * __z.imag(); 1792 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1793 1794 _Tp __num = _Tp(1.0) + __z.real(); 1795 _Tp __den = _Tp(1.0) - __z.real(); 1796 1797 __num = __i2 + __num * __num; 1798 __den = __i2 + __den * __den; 1799 1800 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1801 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1802 } 1803 1804 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1805 inline __complex__ float 1806 __complex_atanh(__complex__ float __z) 1807 { return __builtin_catanhf(__z); } 1808 1809 inline __complex__ double 1810 __complex_atanh(__complex__ double __z) 1811 { return __builtin_catanh(__z); } 1812 1813 inline __complex__ long double 1814 __complex_atanh(const __complex__ long double& __z) 1815 { return __builtin_catanhl(__z); } 1816 1817 template<typename _Tp> 1818 inline std::complex<_Tp> 1819 atanh(const std::complex<_Tp>& __z) 1820 { return __complex_atanh(__z.__rep()); } 1821 #else 1822 /// atanh(__z) [8.1.7]. 1823 // Effects: Behaves the same as C99 function catanh, defined 1824 // in subclause 7.3.6.3. 1825 template<typename _Tp> 1826 inline std::complex<_Tp> 1827 atanh(const std::complex<_Tp>& __z) 1828 { return __complex_atanh(__z); } 1829 #endif 1830 1831 template<typename _Tp> 1832 inline _Tp 1833 /// fabs(__z) [8.1.8]. 1834 // Effects: Behaves the same as C99 function cabs, defined 1835 // in subclause 7.3.8.1. 1836 fabs(const std::complex<_Tp>& __z) 1837 { return std::abs(__z); } 1838 1839 /// Additional overloads [8.1.9]. 1840 template<typename _Tp> 1841 inline typename __gnu_cxx::__promote<_Tp>::__type 1842 arg(_Tp __x) 1843 { 1844 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1845 #if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1846 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1847 : __type(); 1848 #else 1849 return std::arg(std::complex<__type>(__x)); 1850 #endif 1851 } 1852 1853 template<typename _Tp> 1854 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1855 imag(_Tp) 1856 { return _Tp(); } 1857 1858 template<typename _Tp> 1859 _GLIBCXX20_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1860 norm(_Tp __x) 1861 { 1862 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1863 return __type(__x) * __type(__x); 1864 } 1865 1866 template<typename _Tp> 1867 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1868 real(_Tp __x) 1869 { return __x; } 1870 1871 template<typename _Tp, typename _Up> 1872 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1873 pow(const std::complex<_Tp>& __x, const _Up& __y) 1874 { 1875 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1876 return std::pow(std::complex<__type>(__x), __type(__y)); 1877 } 1878 1879 template<typename _Tp, typename _Up> 1880 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1881 pow(const _Tp& __x, const std::complex<_Up>& __y) 1882 { 1883 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1884 return std::pow(__type(__x), std::complex<__type>(__y)); 1885 } 1886 1887 template<typename _Tp, typename _Up> 1888 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1889 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1890 { 1891 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1892 return std::pow(std::complex<__type>(__x), 1893 std::complex<__type>(__y)); 1894 } 1895 1896 // Forward declarations. 1897 // DR 781. 1898 template<typename _Tp> 1899 std::complex<_Tp> proj(const std::complex<_Tp>&); 1900 1901 // Generic implementation of std::proj, does not work for infinities. 1902 template<typename _Tp> 1903 inline std::complex<_Tp> 1904 __complex_proj(const std::complex<_Tp>& __z) 1905 { return __z; } 1906 1907 #if _GLIBCXX_USE_C99_COMPLEX 1908 inline complex<float> 1909 __complex_proj(const complex<float>& __z) 1910 { return __builtin_cprojf(__z.__rep()); } 1911 1912 inline complex<double> 1913 __complex_proj(const complex<double>& __z) 1914 { return __builtin_cproj(__z.__rep()); } 1915 1916 inline complex<long double> 1917 __complex_proj(const complex<long double>& __z) 1918 { return __builtin_cprojl(__z.__rep()); } 1919 #elif defined _GLIBCXX_USE_C99_MATH_TR1 1920 inline complex<float> 1921 __complex_proj(const complex<float>& __z) 1922 { 1923 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1924 return complex<float>(__builtin_inff(), 1925 __builtin_copysignf(0.0f, __z.imag())); 1926 return __z; 1927 } 1928 1929 inline complex<double> 1930 __complex_proj(const complex<double>& __z) 1931 { 1932 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1933 return complex<double>(__builtin_inf(), 1934 __builtin_copysign(0.0, __z.imag())); 1935 return __z; 1936 } 1937 1938 inline complex<long double> 1939 __complex_proj(const complex<long double>& __z) 1940 { 1941 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1942 return complex<long double>(__builtin_infl(), 1943 __builtin_copysignl(0.0l, __z.imag())); 1944 return __z; 1945 } 1946 #endif 1947 1948 template<typename _Tp> 1949 inline std::complex<_Tp> 1950 proj(const std::complex<_Tp>& __z) 1951 { return __complex_proj(__z); } 1952 1953 // Overload for scalars 1954 template<typename _Tp> 1955 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 1956 proj(_Tp __x) 1957 { 1958 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1959 return std::proj(std::complex<__type>(__x)); 1960 } 1961 1962 template<typename _Tp> 1963 inline _GLIBCXX20_CONSTEXPR 1964 std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 1965 conj(_Tp __x) 1966 { 1967 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1968 return std::complex<__type>(__x, -__type()); 1969 } 1970 1971 #if __cplusplus > 201103L 1972 1973 inline namespace literals { 1974 inline namespace complex_literals { 1975 #pragma GCC diagnostic push 1976 #pragma GCC diagnostic ignored "-Wliteral-suffix" 1977 #define __cpp_lib_complex_udls 201309 1978 1979 constexpr std::complex<float> 1980 operator""if(long double __num) 1981 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1982 1983 constexpr std::complex<float> 1984 operator""if(unsigned long long __num) 1985 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1986 1987 constexpr std::complex<double> 1988 operator""i(long double __num) 1989 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1990 1991 constexpr std::complex<double> 1992 operator""i(unsigned long long __num) 1993 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1994 1995 constexpr std::complex<long double> 1996 operator""il(long double __num) 1997 { return std::complex<long double>{0.0L, __num}; } 1998 1999 constexpr std::complex<long double> 2000 operator""il(unsigned long long __num) 2001 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } 2002 2003 #pragma GCC diagnostic pop 2004 } // inline namespace complex_literals 2005 } // inline namespace literals 2006 2007 #endif // C++14 2008 2009 _GLIBCXX_END_NAMESPACE_VERSION 2010 } // namespace 2011 2012 #endif // C++11 2013 2014 #endif /* _GLIBCXX_COMPLEX */ 2015
Indexes created Tue Sep 08 00:25:21 UTC 2026