1// The template and inlines for the -*- C++ -*- complex number classes. 2 3// Copyright (C) 1997-2020 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@cygnus.com> 33// Improved by Gabriel Dos Reis <dosreis@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#if __cplusplus > 201703L 51# define __cpp_lib_constexpr_complex 201711L 52#endif 53 54namespace std _GLIBCXX_VISIBILITY(default) 55{ 56_GLIBCXX_BEGIN_NAMESPACE_VERSION 57 58 /** 59 * @defgroup complex_numbers Complex Numbers 60 * @ingroup numerics 61 * 62 * Classes and functions for complex numbers. 63 * @{ 64 */ 65 66 // Forward declarations. 67 template<typename _Tp> class complex; 68 template<> class complex<float>; 69 template<> class complex<double>; 70 template<> class complex<long double>; 71 72 /// Return magnitude of @a z. 73 template<typename _Tp> _Tp abs(const complex<_Tp>&); 74 /// Return phase angle of @a z. 75 template<typename _Tp> _Tp arg(const complex<_Tp>&); 76 /// Return @a z magnitude squared. 77 template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&); 78 79 /// Return complex conjugate of @a z. 80 template<typename _Tp> 81 _GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&); 82 /// Return complex with magnitude @a rho and angle @a theta. 83 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 84 85 // Transcendentals: 86 /// Return complex cosine of @a z. 87 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 88 /// Return complex hyperbolic cosine of @a z. 89 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 90 /// Return complex base e exponential of @a z. 91 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 92 /// Return complex natural logarithm of @a z. 93 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 94 /// Return complex base 10 logarithm of @a z. 95 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 96 /// Return @a x to the @a y'th power. 97 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 98 /// Return @a x to the @a y'th power. 99 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 100 /// Return @a x to the @a y'th power. 101 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 102 const complex<_Tp>&); 103 /// Return @a x to the @a y'th power. 104 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 105 /// Return complex sine of @a z. 106 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 107 /// Return complex hyperbolic sine of @a z. 108 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 109 /// Return complex square root of @a z. 110 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 111 /// Return complex tangent of @a z. 112 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 113 /// Return complex hyperbolic tangent of @a z. 114 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 115 116 117 // 26.2.2 Primary template class complex 118 /** 119 * Template to represent complex numbers. 120 * 121 * Specializations for float, double, and long double are part of the 122 * library. Results with any other type are not guaranteed. 123 * 124 * @param Tp Type of real and imaginary values. 125 */ 126 template<typename _Tp> 127 struct complex 128 { 129 /// Value typedef. 130 typedef _Tp value_type; 131 132 /// Default constructor. First parameter is x, second parameter is y. 133 /// Unspecified parameters default to 0. 134 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 135 : _M_real(__r), _M_imag(__i) { } 136 137 // Let the compiler synthesize the copy constructor 138#if __cplusplus >= 201103L 139 constexpr complex(const complex&) = default; 140#endif 141 142 /// Converting constructor. 143 template<typename _Up> 144 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 145 : _M_real(__z.real()), _M_imag(__z.imag()) { } 146 147#if __cplusplus >= 201103L 148 // _GLIBCXX_RESOLVE_LIB_DEFECTS 149 // DR 387. std::complex over-encapsulated. 150 _GLIBCXX_ABI_TAG_CXX11 151 constexpr _Tp 152 real() const { return _M_real; } 153 154 _GLIBCXX_ABI_TAG_CXX11 155 constexpr _Tp 156 imag() const { return _M_imag; } 157#else 158 /// Return real part of complex number. 159 _Tp& 160 real() { return _M_real; } 161 162 /// Return real part of complex number. 163 const _Tp& 164 real() const { return _M_real; } 165 166 /// Return imaginary part of complex number. 167 _Tp& 168 imag() { return _M_imag; } 169 170 /// Return imaginary part of complex number. 171 const _Tp& 172 imag() const { return _M_imag; } 173#endif 174 175 // _GLIBCXX_RESOLVE_LIB_DEFECTS 176 // DR 387. std::complex over-encapsulated. 177 _GLIBCXX20_CONSTEXPR void 178 real(_Tp __val) { _M_real = __val; } 179 180 _GLIBCXX20_CONSTEXPR void 181 imag(_Tp __val) { _M_imag = __val; } 182 183 /// Assign a scalar to this complex number. 184 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&); 185 186 /// Add a scalar to this complex number. 187 // 26.2.5/1 188 _GLIBCXX20_CONSTEXPR complex<_Tp>& 189 operator+=(const _Tp& __t) 190 { 191 _M_real += __t; 192 return *this; 193 } 194 195 /// Subtract a scalar from this complex number. 196 // 26.2.5/3 197 _GLIBCXX20_CONSTEXPR complex<_Tp>& 198 operator-=(const _Tp& __t) 199 { 200 _M_real -= __t; 201 return *this; 202 } 203 204 /// Multiply this complex number by a scalar. 205 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&); 206 /// Divide this complex number by a scalar. 207 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&); 208 209 // Let the compiler synthesize the copy assignment operator 210#if __cplusplus >= 201103L 211 _GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default; 212#endif 213 214 /// Assign another complex number to this one. 215 template<typename _Up> 216 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&); 217 /// Add another complex number to this one. 218 template<typename _Up> 219 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&); 220 /// Subtract another complex number from this one. 221 template<typename _Up> 222 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&); 223 /// Multiply this complex number by another. 224 template<typename _Up> 225 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&); 226 /// Divide this complex number by another. 227 template<typename _Up> 228 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&); 229 230 _GLIBCXX_CONSTEXPR complex __rep() const 231 { return *this; } 232 233 private: 234 _Tp _M_real; 235 _Tp _M_imag; 236 }; 237 238 template<typename _Tp> 239 _GLIBCXX20_CONSTEXPR complex<_Tp>& 240 complex<_Tp>::operator=(const _Tp& __t) 241 { 242 _M_real = __t; 243 _M_imag = _Tp(); 244 return *this; 245 } 246 247 // 26.2.5/5 248 template<typename _Tp> 249 _GLIBCXX20_CONSTEXPR complex<_Tp>& 250 complex<_Tp>::operator*=(const _Tp& __t) 251 { 252 _M_real *= __t; 253 _M_imag *= __t; 254 return *this; 255 } 256 257 // 26.2.5/7 258 template<typename _Tp> 259 _GLIBCXX20_CONSTEXPR complex<_Tp>& 260 complex<_Tp>::operator/=(const _Tp& __t) 261 { 262 _M_real /= __t; 263 _M_imag /= __t; 264 return *this; 265 } 266 267 template<typename _Tp> 268 template<typename _Up> 269 _GLIBCXX20_CONSTEXPR complex<_Tp>& 270 complex<_Tp>::operator=(const complex<_Up>& __z) 271 { 272 _M_real = __z.real(); 273 _M_imag = __z.imag(); 274 return *this; 275 } 276 277 // 26.2.5/9 278 template<typename _Tp> 279 template<typename _Up> 280 _GLIBCXX20_CONSTEXPR complex<_Tp>& 281 complex<_Tp>::operator+=(const complex<_Up>& __z) 282 { 283 _M_real += __z.real(); 284 _M_imag += __z.imag(); 285 return *this; 286 } 287 288 // 26.2.5/11 289 template<typename _Tp> 290 template<typename _Up> 291 _GLIBCXX20_CONSTEXPR complex<_Tp>& 292 complex<_Tp>::operator-=(const complex<_Up>& __z) 293 { 294 _M_real -= __z.real(); 295 _M_imag -= __z.imag(); 296 return *this; 297 } 298 299 // 26.2.5/13 300 // XXX: This is a grammar school implementation. 301 template<typename _Tp> 302 template<typename _Up> 303 _GLIBCXX20_CONSTEXPR complex<_Tp>& 304 complex<_Tp>::operator*=(const complex<_Up>& __z) 305 { 306 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 307 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 308 _M_real = __r; 309 return *this; 310 } 311 312 // 26.2.5/15 313 // XXX: This is a grammar school implementation. 314 template<typename _Tp> 315 template<typename _Up> 316 _GLIBCXX20_CONSTEXPR complex<_Tp>& 317 complex<_Tp>::operator/=(const complex<_Up>& __z) 318 { 319 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 320 const _Tp __n = std::norm(__z); 321 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 322 _M_real = __r / __n; 323 return *this; 324 } 325 326 // Operators: 327 ///@{ 328 /// Return new complex value @a x plus @a y. 329 template<typename _Tp> 330 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 331 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 332 { 333 complex<_Tp> __r = __x; 334 __r += __y; 335 return __r; 336 } 337 338 template<typename _Tp> 339 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 340 operator+(const complex<_Tp>& __x, const _Tp& __y) 341 { 342 complex<_Tp> __r = __x; 343 __r += __y; 344 return __r; 345 } 346 347 template<typename _Tp> 348 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 349 operator+(const _Tp& __x, const complex<_Tp>& __y) 350 { 351 complex<_Tp> __r = __y; 352 __r += __x; 353 return __r; 354 } 355 ///@} 356 357 ///@{ 358 /// Return new complex value @a x minus @a y. 359 template<typename _Tp> 360 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 361 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 362 { 363 complex<_Tp> __r = __x; 364 __r -= __y; 365 return __r; 366 } 367 368 template<typename _Tp> 369 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 370 operator-(const complex<_Tp>& __x, const _Tp& __y) 371 { 372 complex<_Tp> __r = __x; 373 __r -= __y; 374 return __r; 375 } 376 377 template<typename _Tp> 378 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 379 operator-(const _Tp& __x, const complex<_Tp>& __y) 380 { 381 complex<_Tp> __r = -__y; 382 __r += __x; 383 return __r; 384 } 385 ///@} 386 387 ///@{ 388 /// Return new complex value @a x times @a y. 389 template<typename _Tp> 390 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 391 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 392 { 393 complex<_Tp> __r = __x; 394 __r *= __y; 395 return __r; 396 } 397 398 template<typename _Tp> 399 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 400 operator*(const complex<_Tp>& __x, const _Tp& __y) 401 { 402 complex<_Tp> __r = __x; 403 __r *= __y; 404 return __r; 405 } 406 407 template<typename _Tp> 408 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 409 operator*(const _Tp& __x, const complex<_Tp>& __y) 410 { 411 complex<_Tp> __r = __y; 412 __r *= __x; 413 return __r; 414 } 415 ///@} 416 417 ///@{ 418 /// Return new complex value @a x divided by @a y. 419 template<typename _Tp> 420 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 421 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 422 { 423 complex<_Tp> __r = __x; 424 __r /= __y; 425 return __r; 426 } 427 428 template<typename _Tp> 429 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 430 operator/(const complex<_Tp>& __x, const _Tp& __y) 431 { 432 complex<_Tp> __r = __x; 433 __r /= __y; 434 return __r; 435 } 436 437 template<typename _Tp> 438 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 439 operator/(const _Tp& __x, const complex<_Tp>& __y) 440 { 441 complex<_Tp> __r = __x; 442 __r /= __y; 443 return __r; 444 } 445 ///@} 446 447 /// Return @a x. 448 template<typename _Tp> 449 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 450 operator+(const complex<_Tp>& __x) 451 { return __x; } 452 453 /// Return complex negation of @a x. 454 template<typename _Tp> 455 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 456 operator-(const complex<_Tp>& __x) 457 { return complex<_Tp>(-__x.real(), -__x.imag()); } 458 459 ///@{ 460 /// Return true if @a x is equal to @a y. 461 template<typename _Tp> 462 inline _GLIBCXX_CONSTEXPR bool 463 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 464 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 465 466 template<typename _Tp> 467 inline _GLIBCXX_CONSTEXPR bool 468 operator==(const complex<_Tp>& __x, const _Tp& __y) 469 { return __x.real() == __y && __x.imag() == _Tp(); } 470 471#if !(__cpp_impl_three_way_comparison >= 201907L) 472 template<typename _Tp> 473 inline _GLIBCXX_CONSTEXPR bool 474 operator==(const _Tp& __x, const complex<_Tp>& __y) 475 { return __x == __y.real() && _Tp() == __y.imag(); } 476 ///@} 477 478 ///@{ 479 /// Return false if @a x is equal to @a y. 480 template<typename _Tp> 481 inline _GLIBCXX_CONSTEXPR bool 482 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 483 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 484 485 template<typename _Tp> 486 inline _GLIBCXX_CONSTEXPR bool 487 operator!=(const complex<_Tp>& __x, const _Tp& __y) 488 { return __x.real() != __y || __x.imag() != _Tp(); } 489 490 template<typename _Tp> 491 inline _GLIBCXX_CONSTEXPR bool 492 operator!=(const _Tp& __x, const complex<_Tp>& __y) 493 { return __x != __y.real() || _Tp() != __y.imag(); } 494#endif 495 ///@} 496 497 /// Extraction operator for complex values. 498 template<typename _Tp, typename _CharT, class _Traits> 499 basic_istream<_CharT, _Traits>& 500 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 501 { 502 bool __fail = true; 503 _CharT __ch; 504 if (__is >> __ch) 505 { 506 if (_Traits::eq(__ch, __is.widen('('))) 507 { 508 _Tp __u; 509 if (__is >> __u >> __ch) 510 { 511 const _CharT __rparen = __is.widen(')'); 512 if (_Traits::eq(__ch, __rparen)) 513 { 514 __x = __u; 515 __fail = false; 516 } 517 else if (_Traits::eq(__ch, __is.widen(','))) 518 { 519 _Tp __v; 520 if (__is >> __v >> __ch) 521 { 522 if (_Traits::eq(__ch, __rparen)) 523 { 524 __x = complex<_Tp>(__u, __v); 525 __fail = false; 526 } 527 else 528 __is.putback(__ch); 529 } 530 } 531 else 532 __is.putback(__ch); 533 } 534 } 535 else 536 { 537 __is.putback(__ch); 538 _Tp __u; 539 if (__is >> __u) 540 { 541 __x = __u; 542 __fail = false; 543 } 544 } 545 } 546 if (__fail) 547 __is.setstate(ios_base::failbit); 548 return __is; 549 } 550 551 /// Insertion operator for complex values. 552 template<typename _Tp, typename _CharT, class _Traits> 553 basic_ostream<_CharT, _Traits>& 554 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 555 { 556 basic_ostringstream<_CharT, _Traits> __s; 557 __s.flags(__os.flags()); 558 __s.imbue(__os.getloc()); 559 __s.precision(__os.precision()); 560 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 561 return __os << __s.str(); 562 } 563 564 // Values 565#if __cplusplus >= 201103L 566 template<typename _Tp> 567 constexpr _Tp 568 real(const complex<_Tp>& __z) 569 { return __z.real(); } 570 571 template<typename _Tp> 572 constexpr _Tp 573 imag(const complex<_Tp>& __z) 574 { return __z.imag(); } 575#else 576 template<typename _Tp> 577 inline _Tp& 578 real(complex<_Tp>& __z) 579 { return __z.real(); } 580 581 template<typename _Tp> 582 inline const _Tp& 583 real(const complex<_Tp>& __z) 584 { return __z.real(); } 585 586 template<typename _Tp> 587 inline _Tp& 588 imag(complex<_Tp>& __z) 589 { return __z.imag(); } 590 591 template<typename _Tp> 592 inline const _Tp& 593 imag(const complex<_Tp>& __z) 594 { return __z.imag(); } 595#endif 596 597 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 598 template<typename _Tp> 599 inline _Tp 600 __complex_abs(const complex<_Tp>& __z) 601 { 602 _Tp __x = __z.real(); 603 _Tp __y = __z.imag(); 604 const _Tp __s = std::max(abs(__x), abs(__y)); 605 if (__s == _Tp()) // well ... 606 return __s; 607 __x /= __s; 608 __y /= __s; 609 return __s * sqrt(__x * __x + __y * __y); 610 } 611 612#if _GLIBCXX_USE_C99_COMPLEX 613 inline float 614 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 615 616 inline double 617 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 618 619 inline long double 620 __complex_abs(const __complex__ long double& __z) 621 { return __builtin_cabsl(__z); } 622 623 template<typename _Tp> 624 inline _Tp 625 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 626#else 627 template<typename _Tp> 628 inline _Tp 629 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 630#endif 631 632 633 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 634 template<typename _Tp> 635 inline _Tp 636 __complex_arg(const complex<_Tp>& __z) 637 { return atan2(__z.imag(), __z.real()); } 638 639#if _GLIBCXX_USE_C99_COMPLEX 640 inline float 641 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 642 643 inline double 644 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 645 646 inline long double 647 __complex_arg(const __complex__ long double& __z) 648 { return __builtin_cargl(__z); } 649 650 template<typename _Tp> 651 inline _Tp 652 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 653#else 654 template<typename _Tp> 655 inline _Tp 656 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 657#endif 658 659 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 660 // As defined, norm() is -not- a norm is the common mathematical 661 // sense used in numerics. The helper class _Norm_helper<> tries to 662 // distinguish between builtin floating point and the rest, so as 663 // to deliver an answer as close as possible to the real value. 664 template<bool> 665 struct _Norm_helper 666 { 667 template<typename _Tp> 668 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) 669 { 670 const _Tp __x = __z.real(); 671 const _Tp __y = __z.imag(); 672 return __x * __x + __y * __y; 673 } 674 }; 675 676 template<> 677 struct _Norm_helper<true> 678 { 679 template<typename _Tp> 680 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) 681 { 682 //_Tp __res = std::abs(__z); 683 //return __res * __res; 684 const _Tp __x = __z.real(); 685 const _Tp __y = __z.imag(); 686 return __x * __x + __y * __y; 687 } 688 }; 689 690 template<typename _Tp> 691 inline _GLIBCXX20_CONSTEXPR _Tp 692 norm(const complex<_Tp>& __z) 693 { 694 return _Norm_helper<__is_floating<_Tp>::__value 695 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 696 } 697 698 template<typename _Tp> 699 inline complex<_Tp> 700 polar(const _Tp& __rho, const _Tp& __theta) 701 { 702 __glibcxx_assert( __rho >= 0 ); 703 return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); 704 } 705 706 template<typename _Tp> 707 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 708 conj(const complex<_Tp>& __z) 709 { return complex<_Tp>(__z.real(), -__z.imag()); } 710 711 // Transcendentals 712 713 // 26.2.8/1 cos(__z): Returns the cosine of __z. 714 template<typename _Tp> 715 inline complex<_Tp> 716 __complex_cos(const complex<_Tp>& __z) 717 { 718 const _Tp __x = __z.real(); 719 const _Tp __y = __z.imag(); 720 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 721 } 722 723#if _GLIBCXX_USE_C99_COMPLEX 724 inline __complex__ float 725 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 726 727 inline __complex__ double 728 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 729 730 inline __complex__ long double 731 __complex_cos(const __complex__ long double& __z) 732 { return __builtin_ccosl(__z); } 733 734 template<typename _Tp> 735 inline complex<_Tp> 736 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 737#else 738 template<typename _Tp> 739 inline complex<_Tp> 740 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 741#endif 742 743 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 744 template<typename _Tp> 745 inline complex<_Tp> 746 __complex_cosh(const complex<_Tp>& __z) 747 { 748 const _Tp __x = __z.real(); 749 const _Tp __y = __z.imag(); 750 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 751 } 752 753#if _GLIBCXX_USE_C99_COMPLEX 754 inline __complex__ float 755 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 756 757 inline __complex__ double 758 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 759 760 inline __complex__ long double 761 __complex_cosh(const __complex__ long double& __z) 762 { return __builtin_ccoshl(__z); } 763 764 template<typename _Tp> 765 inline complex<_Tp> 766 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 767#else 768 template<typename _Tp> 769 inline complex<_Tp> 770 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 771#endif 772 773 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 774 template<typename _Tp> 775 inline complex<_Tp> 776 __complex_exp(const complex<_Tp>& __z) 777 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); } 778 779#if _GLIBCXX_USE_C99_COMPLEX 780 inline __complex__ float 781 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 782 783 inline __complex__ double 784 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 785 786 inline __complex__ long double 787 __complex_exp(const __complex__ long double& __z) 788 { return __builtin_cexpl(__z); } 789 790 template<typename _Tp> 791 inline complex<_Tp> 792 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 793#else 794 template<typename _Tp> 795 inline complex<_Tp> 796 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 797#endif 798 799 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 800 // The branch cut is along the negative axis. 801 template<typename _Tp> 802 inline complex<_Tp> 803 __complex_log(const complex<_Tp>& __z) 804 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 805 806#if _GLIBCXX_USE_C99_COMPLEX 807 inline __complex__ float 808 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 809 810 inline __complex__ double 811 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 812 813 inline __complex__ long double 814 __complex_log(const __complex__ long double& __z) 815 { return __builtin_clogl(__z); } 816 817 template<typename _Tp> 818 inline complex<_Tp> 819 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 820#else 821 template<typename _Tp> 822 inline complex<_Tp> 823 log(const complex<_Tp>& __z) { return __complex_log(__z); } 824#endif 825 826 template<typename _Tp> 827 inline complex<_Tp> 828 log10(const complex<_Tp>& __z) 829 { return std::log(__z) / log(_Tp(10.0)); } 830 831 // 26.2.8/10 sin(__z): Returns the sine of __z. 832 template<typename _Tp> 833 inline complex<_Tp> 834 __complex_sin(const complex<_Tp>& __z) 835 { 836 const _Tp __x = __z.real(); 837 const _Tp __y = __z.imag(); 838 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 839 } 840 841#if _GLIBCXX_USE_C99_COMPLEX 842 inline __complex__ float 843 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 844 845 inline __complex__ double 846 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 847 848 inline __complex__ long double 849 __complex_sin(const __complex__ long double& __z) 850 { return __builtin_csinl(__z); } 851 852 template<typename _Tp> 853 inline complex<_Tp> 854 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 855#else 856 template<typename _Tp> 857 inline complex<_Tp> 858 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 859#endif 860 861 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 862 template<typename _Tp> 863 inline complex<_Tp> 864 __complex_sinh(const complex<_Tp>& __z) 865 { 866 const _Tp __x = __z.real(); 867 const _Tp __y = __z.imag(); 868 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 869 } 870 871#if _GLIBCXX_USE_C99_COMPLEX 872 inline __complex__ float 873 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 874 875 inline __complex__ double 876 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 877 878 inline __complex__ long double 879 __complex_sinh(const __complex__ long double& __z) 880 { return __builtin_csinhl(__z); } 881 882 template<typename _Tp> 883 inline complex<_Tp> 884 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 885#else 886 template<typename _Tp> 887 inline complex<_Tp> 888 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 889#endif 890 891 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 892 // The branch cut is on the negative axis. 893 template<typename _Tp> 894 complex<_Tp> 895 __complex_sqrt(const complex<_Tp>& __z) 896 { 897 _Tp __x = __z.real(); 898 _Tp __y = __z.imag(); 899 900 if (__x == _Tp()) 901 { 902 _Tp __t = sqrt(abs(__y) / 2); 903 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 904 } 905 else 906 { 907 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 908 _Tp __u = __t / 2; 909 return __x > _Tp() 910 ? complex<_Tp>(__u, __y / __t) 911 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 912 } 913 } 914 915#if _GLIBCXX_USE_C99_COMPLEX 916 inline __complex__ float 917 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 918 919 inline __complex__ double 920 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 921 922 inline __complex__ long double 923 __complex_sqrt(const __complex__ long double& __z) 924 { return __builtin_csqrtl(__z); } 925 926 template<typename _Tp> 927 inline complex<_Tp> 928 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 929#else 930 template<typename _Tp> 931 inline complex<_Tp> 932 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 933#endif 934 935 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 936 937 template<typename _Tp> 938 inline complex<_Tp> 939 __complex_tan(const complex<_Tp>& __z) 940 { return std::sin(__z) / std::cos(__z); } 941 942#if _GLIBCXX_USE_C99_COMPLEX 943 inline __complex__ float 944 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 945 946 inline __complex__ double 947 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 948 949 inline __complex__ long double 950 __complex_tan(const __complex__ long double& __z) 951 { return __builtin_ctanl(__z); } 952 953 template<typename _Tp> 954 inline complex<_Tp> 955 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 956#else 957 template<typename _Tp> 958 inline complex<_Tp> 959 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 960#endif 961 962 963 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 964 965 template<typename _Tp> 966 inline complex<_Tp> 967 __complex_tanh(const complex<_Tp>& __z) 968 { return std::sinh(__z) / std::cosh(__z); } 969 970#if _GLIBCXX_USE_C99_COMPLEX 971 inline __complex__ float 972 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 973 974 inline __complex__ double 975 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 976 977 inline __complex__ long double 978 __complex_tanh(const __complex__ long double& __z) 979 { return __builtin_ctanhl(__z); } 980 981 template<typename _Tp> 982 inline complex<_Tp> 983 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 984#else 985 template<typename _Tp> 986 inline complex<_Tp> 987 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 988#endif 989 990 991 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 992 // raised to the __y-th power. The branch 993 // cut is on the negative axis. 994 template<typename _Tp> 995 complex<_Tp> 996 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 997 { 998 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 999 1000 while (__n >>= 1) 1001 { 1002 __x *= __x; 1003 if (__n % 2) 1004 __y *= __x; 1005 } 1006 1007 return __y; 1008 } 1009 1010 // In C++11 mode we used to implement the resolution of 1011 // DR 844. complex pow return type is ambiguous. 1012 // thus the following overload was disabled in that mode. However, doing 1013 // that causes all sorts of issues, see, for example: 1014 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html 1015 // and also PR57974. 1016 template<typename _Tp> 1017 inline complex<_Tp> 1018 pow(const complex<_Tp>& __z, int __n) 1019 { 1020 return __n < 0 1021 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) 1022 : std::__complex_pow_unsigned(__z, __n); 1023 } 1024 1025 template<typename _Tp> 1026 complex<_Tp> 1027 pow(const complex<_Tp>& __x, const _Tp& __y) 1028 { 1029#if ! _GLIBCXX_USE_C99_COMPLEX 1030 if (__x == _Tp()) 1031 return _Tp(); 1032#endif 1033 if (__x.imag() == _Tp() && __x.real() > _Tp()) 1034 return pow(__x.real(), __y); 1035 1036 complex<_Tp> __t = std::log(__x); 1037 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag()); 1038 } 1039 1040 template<typename _Tp> 1041 inline complex<_Tp> 1042 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1043 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1044 1045#if _GLIBCXX_USE_C99_COMPLEX 1046 inline __complex__ float 1047 __complex_pow(__complex__ float __x, __complex__ float __y) 1048 { return __builtin_cpowf(__x, __y); } 1049 1050 inline __complex__ double 1051 __complex_pow(__complex__ double __x, __complex__ double __y) 1052 { return __builtin_cpow(__x, __y); } 1053 1054 inline __complex__ long double 1055 __complex_pow(const __complex__ long double& __x, 1056 const __complex__ long double& __y) 1057 { return __builtin_cpowl(__x, __y); } 1058 1059 template<typename _Tp> 1060 inline complex<_Tp> 1061 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1062 { return __complex_pow(__x.__rep(), __y.__rep()); } 1063#else 1064 template<typename _Tp> 1065 inline complex<_Tp> 1066 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1067 { return __complex_pow(__x, __y); } 1068#endif 1069 1070 template<typename _Tp> 1071 inline complex<_Tp> 1072 pow(const _Tp& __x, const complex<_Tp>& __y) 1073 { 1074 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()), 1075 __y.imag() * log(__x)) 1076 : std::pow(complex<_Tp>(__x), __y); 1077 } 1078 1079 /// 26.2.3 complex specializations 1080 /// complex<float> specialization 1081 template<> 1082 struct complex<float> 1083 { 1084 typedef float value_type; 1085 typedef __complex__ float _ComplexT; 1086 1087 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1088 1089 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1090#if __cplusplus >= 201103L 1091 : _M_value{ __r, __i } { } 1092#else 1093 { 1094 __real__ _M_value = __r; 1095 __imag__ _M_value = __i; 1096 } 1097#endif 1098 1099 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1100 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1101 1102#if __cplusplus >= 201103L 1103 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1104 // DR 387. std::complex over-encapsulated. 1105 __attribute ((__abi_tag__ ("cxx11"))) 1106 constexpr float 1107 real() const { return __real__ _M_value; } 1108 1109 __attribute ((__abi_tag__ ("cxx11"))) 1110 constexpr float 1111 imag() const { return __imag__ _M_value; } 1112#else 1113 float& 1114 real() { return __real__ _M_value; } 1115 1116 const float& 1117 real() const { return __real__ _M_value; } 1118 1119 float& 1120 imag() { return __imag__ _M_value; } 1121 1122 const float& 1123 imag() const { return __imag__ _M_value; } 1124#endif 1125 1126 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1127 // DR 387. std::complex over-encapsulated. 1128 _GLIBCXX20_CONSTEXPR void 1129 real(float __val) { __real__ _M_value = __val; } 1130 1131 _GLIBCXX20_CONSTEXPR void 1132 imag(float __val) { __imag__ _M_value = __val; } 1133 1134 _GLIBCXX20_CONSTEXPR complex& 1135 operator=(float __f) 1136 { 1137 _M_value = __f; 1138 return *this; 1139 } 1140 1141 _GLIBCXX20_CONSTEXPR complex& 1142 operator+=(float __f) 1143 { 1144 _M_value += __f; 1145 return *this; 1146 } 1147 1148 _GLIBCXX20_CONSTEXPR complex& 1149 operator-=(float __f) 1150 { 1151 _M_value -= __f; 1152 return *this; 1153 } 1154 1155 _GLIBCXX20_CONSTEXPR complex& 1156 operator*=(float __f) 1157 { 1158 _M_value *= __f; 1159 return *this; 1160 } 1161 1162 _GLIBCXX20_CONSTEXPR complex& 1163 operator/=(float __f) 1164 { 1165 _M_value /= __f; 1166 return *this; 1167 } 1168 1169 // Let the compiler synthesize the copy and assignment 1170 // operator. It always does a pretty good job. 1171#if __cplusplus >= 201103L 1172 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1173#endif 1174 1175 template<typename _Tp> 1176 _GLIBCXX20_CONSTEXPR complex& 1177 operator=(const complex<_Tp>& __z) 1178 { 1179 __real__ _M_value = __z.real(); 1180 __imag__ _M_value = __z.imag(); 1181 return *this; 1182 } 1183 1184 template<typename _Tp> 1185 _GLIBCXX20_CONSTEXPR complex& 1186 operator+=(const complex<_Tp>& __z) 1187 { 1188 _M_value += __z.__rep(); 1189 return *this; 1190 } 1191 1192 template<class _Tp> 1193 _GLIBCXX20_CONSTEXPR complex& 1194 operator-=(const complex<_Tp>& __z) 1195 { 1196 _M_value -= __z.__rep(); 1197 return *this; 1198 } 1199 1200 template<class _Tp> 1201 _GLIBCXX20_CONSTEXPR complex& 1202 operator*=(const complex<_Tp>& __z) 1203 { 1204 const _ComplexT __t = __z.__rep(); 1205 _M_value *= __t; 1206 return *this; 1207 } 1208 1209 template<class _Tp> 1210 _GLIBCXX20_CONSTEXPR complex& 1211 operator/=(const complex<_Tp>& __z) 1212 { 1213 const _ComplexT __t = __z.__rep(); 1214 _M_value /= __t; 1215 return *this; 1216 } 1217 1218 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1219 1220 private: 1221 _ComplexT _M_value; 1222 }; 1223 1224 /// 26.2.3 complex specializations 1225 /// complex<double> specialization 1226 template<> 1227 struct complex<double> 1228 { 1229 typedef double value_type; 1230 typedef __complex__ double _ComplexT; 1231 1232 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1233 1234 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1235#if __cplusplus >= 201103L 1236 : _M_value{ __r, __i } { } 1237#else 1238 { 1239 __real__ _M_value = __r; 1240 __imag__ _M_value = __i; 1241 } 1242#endif 1243 1244 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1245 : _M_value(__z.__rep()) { } 1246 1247 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1248 1249#if __cplusplus >= 201103L 1250 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1251 // DR 387. std::complex over-encapsulated. 1252 __attribute ((__abi_tag__ ("cxx11"))) 1253 constexpr double 1254 real() const { return __real__ _M_value; } 1255 1256 __attribute ((__abi_tag__ ("cxx11"))) 1257 constexpr double 1258 imag() const { return __imag__ _M_value; } 1259#else 1260 double& 1261 real() { return __real__ _M_value; } 1262 1263 const double& 1264 real() const { return __real__ _M_value; } 1265 1266 double& 1267 imag() { return __imag__ _M_value; } 1268 1269 const double& 1270 imag() const { return __imag__ _M_value; } 1271#endif 1272 1273 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1274 // DR 387. std::complex over-encapsulated. 1275 _GLIBCXX20_CONSTEXPR void 1276 real(double __val) { __real__ _M_value = __val; } 1277 1278 _GLIBCXX20_CONSTEXPR void 1279 imag(double __val) { __imag__ _M_value = __val; } 1280 1281 _GLIBCXX20_CONSTEXPR complex& 1282 operator=(double __d) 1283 { 1284 _M_value = __d; 1285 return *this; 1286 } 1287 1288 _GLIBCXX20_CONSTEXPR complex& 1289 operator+=(double __d) 1290 { 1291 _M_value += __d; 1292 return *this; 1293 } 1294 1295 _GLIBCXX20_CONSTEXPR complex& 1296 operator-=(double __d) 1297 { 1298 _M_value -= __d; 1299 return *this; 1300 } 1301 1302 _GLIBCXX20_CONSTEXPR complex& 1303 operator*=(double __d) 1304 { 1305 _M_value *= __d; 1306 return *this; 1307 } 1308 1309 _GLIBCXX20_CONSTEXPR complex& 1310 operator/=(double __d) 1311 { 1312 _M_value /= __d; 1313 return *this; 1314 } 1315 1316 // The compiler will synthesize this, efficiently. 1317#if __cplusplus >= 201103L 1318 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1319#endif 1320 1321 template<typename _Tp> 1322 _GLIBCXX20_CONSTEXPR complex& 1323 operator=(const complex<_Tp>& __z) 1324 { 1325 _M_value = __z.__rep(); 1326 return *this; 1327 } 1328 1329 template<typename _Tp> 1330 _GLIBCXX20_CONSTEXPR complex& 1331 operator+=(const complex<_Tp>& __z) 1332 { 1333 _M_value += __z.__rep(); 1334 return *this; 1335 } 1336 1337 template<typename _Tp> 1338 _GLIBCXX20_CONSTEXPR complex& 1339 operator-=(const complex<_Tp>& __z) 1340 { 1341 _M_value -= __z.__rep(); 1342 return *this; 1343 } 1344 1345 template<typename _Tp> 1346 _GLIBCXX20_CONSTEXPR complex& 1347 operator*=(const complex<_Tp>& __z) 1348 { 1349 const _ComplexT __t = __z.__rep(); 1350 _M_value *= __t; 1351 return *this; 1352 } 1353 1354 template<typename _Tp> 1355 _GLIBCXX20_CONSTEXPR complex& 1356 operator/=(const complex<_Tp>& __z) 1357 { 1358 const _ComplexT __t = __z.__rep(); 1359 _M_value /= __t; 1360 return *this; 1361 } 1362 1363 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1364 1365 private: 1366 _ComplexT _M_value; 1367 }; 1368 1369 /// 26.2.3 complex specializations 1370 /// complex<long double> specialization 1371 template<> 1372 struct complex<long double> 1373 { 1374 typedef long double value_type; 1375 typedef __complex__ long double _ComplexT; 1376 1377 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1378 1379 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1380 long double __i = 0.0L) 1381#if __cplusplus >= 201103L 1382 : _M_value{ __r, __i } { } 1383#else 1384 { 1385 __real__ _M_value = __r; 1386 __imag__ _M_value = __i; 1387 } 1388#endif 1389 1390 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1391 : _M_value(__z.__rep()) { } 1392 1393 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1394 : _M_value(__z.__rep()) { } 1395 1396#if __cplusplus >= 201103L 1397 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1398 // DR 387. std::complex over-encapsulated. 1399 __attribute ((__abi_tag__ ("cxx11"))) 1400 constexpr long double 1401 real() const { return __real__ _M_value; } 1402 1403 __attribute ((__abi_tag__ ("cxx11"))) 1404 constexpr long double 1405 imag() const { return __imag__ _M_value; } 1406#else 1407 long double& 1408 real() { return __real__ _M_value; } 1409 1410 const long double& 1411 real() const { return __real__ _M_value; } 1412 1413 long double& 1414 imag() { return __imag__ _M_value; } 1415 1416 const long double& 1417 imag() const { return __imag__ _M_value; } 1418#endif 1419 1420 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1421 // DR 387. std::complex over-encapsulated. 1422 _GLIBCXX20_CONSTEXPR void 1423 real(long double __val) { __real__ _M_value = __val; } 1424 1425 _GLIBCXX20_CONSTEXPR void 1426 imag(long double __val) { __imag__ _M_value = __val; } 1427 1428 _GLIBCXX20_CONSTEXPR complex& 1429 operator=(long double __r) 1430 { 1431 _M_value = __r; 1432 return *this; 1433 } 1434 1435 _GLIBCXX20_CONSTEXPR complex& 1436 operator+=(long double __r) 1437 { 1438 _M_value += __r; 1439 return *this; 1440 } 1441 1442 _GLIBCXX20_CONSTEXPR complex& 1443 operator-=(long double __r) 1444 { 1445 _M_value -= __r; 1446 return *this; 1447 } 1448 1449 _GLIBCXX20_CONSTEXPR complex& 1450 operator*=(long double __r) 1451 { 1452 _M_value *= __r; 1453 return *this; 1454 } 1455 1456 _GLIBCXX20_CONSTEXPR complex& 1457 operator/=(long double __r) 1458 { 1459 _M_value /= __r; 1460 return *this; 1461 } 1462 1463 // The compiler knows how to do this efficiently 1464#if __cplusplus >= 201103L 1465 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1466#endif 1467 1468 template<typename _Tp> 1469 _GLIBCXX20_CONSTEXPR complex& 1470 operator=(const complex<_Tp>& __z) 1471 { 1472 _M_value = __z.__rep(); 1473 return *this; 1474 } 1475 1476 template<typename _Tp> 1477 _GLIBCXX20_CONSTEXPR complex& 1478 operator+=(const complex<_Tp>& __z) 1479 { 1480 _M_value += __z.__rep(); 1481 return *this; 1482 } 1483 1484 template<typename _Tp> 1485 _GLIBCXX20_CONSTEXPR complex& 1486 operator-=(const complex<_Tp>& __z) 1487 { 1488 _M_value -= __z.__rep(); 1489 return *this; 1490 } 1491 1492 template<typename _Tp> 1493 _GLIBCXX20_CONSTEXPR complex& 1494 operator*=(const complex<_Tp>& __z) 1495 { 1496 const _ComplexT __t = __z.__rep(); 1497 _M_value *= __t; 1498 return *this; 1499 } 1500 1501 template<typename _Tp> 1502 _GLIBCXX20_CONSTEXPR complex& 1503 operator/=(const complex<_Tp>& __z) 1504 { 1505 const _ComplexT __t = __z.__rep(); 1506 _M_value /= __t; 1507 return *this; 1508 } 1509 1510 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1511 1512 private: 1513 _ComplexT _M_value; 1514 }; 1515 1516 // These bits have to be at the end of this file, so that the 1517 // specializations have all been defined. 1518 inline _GLIBCXX_CONSTEXPR 1519 complex<float>::complex(const complex<double>& __z) 1520 : _M_value(__z.__rep()) { } 1521 1522 inline _GLIBCXX_CONSTEXPR 1523 complex<float>::complex(const complex<long double>& __z) 1524 : _M_value(__z.__rep()) { } 1525 1526 inline _GLIBCXX_CONSTEXPR 1527 complex<double>::complex(const complex<long double>& __z) 1528 : _M_value(__z.__rep()) { } 1529 1530 // Inhibit implicit instantiations for required instantiations, 1531 // which are defined via explicit instantiations elsewhere. 1532 // NB: This syntax is a GNU extension. 1533#if _GLIBCXX_EXTERN_TEMPLATE 1534 extern template istream& operator>>(istream&, complex<float>&); 1535 extern template ostream& operator<<(ostream&, const complex<float>&); 1536 extern template istream& operator>>(istream&, complex<double>&); 1537 extern template ostream& operator<<(ostream&, const complex<double>&); 1538 extern template istream& operator>>(istream&, complex<long double>&); 1539 extern template ostream& operator<<(ostream&, const complex<long double>&); 1540 1541#ifdef _GLIBCXX_USE_WCHAR_T 1542 extern template wistream& operator>>(wistream&, complex<float>&); 1543 extern template wostream& operator<<(wostream&, const complex<float>&); 1544 extern template wistream& operator>>(wistream&, complex<double>&); 1545 extern template wostream& operator<<(wostream&, const complex<double>&); 1546 extern template wistream& operator>>(wistream&, complex<long double>&); 1547 extern template wostream& operator<<(wostream&, const complex<long double>&); 1548#endif 1549#endif 1550 1551 /// @} group complex_numbers 1552 1553_GLIBCXX_END_NAMESPACE_VERSION 1554} // namespace 1555 1556namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1557{ 1558_GLIBCXX_BEGIN_NAMESPACE_VERSION 1559 1560 // See ext/type_traits.h for the primary template. 1561 template<typename _Tp, typename _Up> 1562 struct __promote_2<std::complex<_Tp>, _Up> 1563 { 1564 public: 1565 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1566 }; 1567 1568 template<typename _Tp, typename _Up> 1569 struct __promote_2<_Tp, std::complex<_Up> > 1570 { 1571 public: 1572 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1573 }; 1574 1575 template<typename _Tp, typename _Up> 1576 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1577 { 1578 public: 1579 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1580 }; 1581 1582_GLIBCXX_END_NAMESPACE_VERSION 1583} // namespace 1584 1585#if __cplusplus >= 201103L 1586 1587namespace std _GLIBCXX_VISIBILITY(default) 1588{ 1589_GLIBCXX_BEGIN_NAMESPACE_VERSION 1590 1591 // Forward declarations. 1592 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1593 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1594 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1595 1596 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1597 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1598 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1599 // DR 595. 1600 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1601 1602 template<typename _Tp> 1603 inline std::complex<_Tp> 1604 __complex_acos(const std::complex<_Tp>& __z) 1605 { 1606 const std::complex<_Tp> __t = std::asin(__z); 1607 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1608 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1609 } 1610 1611#if _GLIBCXX_USE_C99_COMPLEX_TR1 1612 inline __complex__ float 1613 __complex_acos(__complex__ float __z) 1614 { return __builtin_cacosf(__z); } 1615 1616 inline __complex__ double 1617 __complex_acos(__complex__ double __z) 1618 { return __builtin_cacos(__z); } 1619 1620 inline __complex__ long double 1621 __complex_acos(const __complex__ long double& __z) 1622 { return __builtin_cacosl(__z); } 1623 1624 template<typename _Tp> 1625 inline std::complex<_Tp> 1626 acos(const std::complex<_Tp>& __z) 1627 { return __complex_acos(__z.__rep()); } 1628#else 1629 /// acos(__z) [8.1.2]. 1630 // Effects: Behaves the same as C99 function cacos, defined 1631 // in subclause 7.3.5.1. 1632 template<typename _Tp> 1633 inline std::complex<_Tp> 1634 acos(const std::complex<_Tp>& __z) 1635 { return __complex_acos(__z); } 1636#endif 1637 1638 template<typename _Tp> 1639 inline std::complex<_Tp> 1640 __complex_asin(const std::complex<_Tp>& __z) 1641 { 1642 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1643 __t = std::asinh(__t); 1644 return std::complex<_Tp>(__t.imag(), -__t.real()); 1645 } 1646 1647#if _GLIBCXX_USE_C99_COMPLEX_TR1 1648 inline __complex__ float 1649 __complex_asin(__complex__ float __z) 1650 { return __builtin_casinf(__z); } 1651 1652 inline __complex__ double 1653 __complex_asin(__complex__ double __z) 1654 { return __builtin_casin(__z); } 1655 1656 inline __complex__ long double 1657 __complex_asin(const __complex__ long double& __z) 1658 { return __builtin_casinl(__z); } 1659 1660 template<typename _Tp> 1661 inline std::complex<_Tp> 1662 asin(const std::complex<_Tp>& __z) 1663 { return __complex_asin(__z.__rep()); } 1664#else 1665 /// asin(__z) [8.1.3]. 1666 // Effects: Behaves the same as C99 function casin, defined 1667 // in subclause 7.3.5.2. 1668 template<typename _Tp> 1669 inline std::complex<_Tp> 1670 asin(const std::complex<_Tp>& __z) 1671 { return __complex_asin(__z); } 1672#endif 1673 1674 template<typename _Tp> 1675 std::complex<_Tp> 1676 __complex_atan(const std::complex<_Tp>& __z) 1677 { 1678 const _Tp __r2 = __z.real() * __z.real(); 1679 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1680 1681 _Tp __num = __z.imag() + _Tp(1.0); 1682 _Tp __den = __z.imag() - _Tp(1.0); 1683 1684 __num = __r2 + __num * __num; 1685 __den = __r2 + __den * __den; 1686 1687 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1688 _Tp(0.25) * log(__num / __den)); 1689 } 1690 1691#if _GLIBCXX_USE_C99_COMPLEX_TR1 1692 inline __complex__ float 1693 __complex_atan(__complex__ float __z) 1694 { return __builtin_catanf(__z); } 1695 1696 inline __complex__ double 1697 __complex_atan(__complex__ double __z) 1698 { return __builtin_catan(__z); } 1699 1700 inline __complex__ long double 1701 __complex_atan(const __complex__ long double& __z) 1702 { return __builtin_catanl(__z); } 1703 1704 template<typename _Tp> 1705 inline std::complex<_Tp> 1706 atan(const std::complex<_Tp>& __z) 1707 { return __complex_atan(__z.__rep()); } 1708#else 1709 /// atan(__z) [8.1.4]. 1710 // Effects: Behaves the same as C99 function catan, defined 1711 // in subclause 7.3.5.3. 1712 template<typename _Tp> 1713 inline std::complex<_Tp> 1714 atan(const std::complex<_Tp>& __z) 1715 { return __complex_atan(__z); } 1716#endif 1717 1718 template<typename _Tp> 1719 std::complex<_Tp> 1720 __complex_acosh(const std::complex<_Tp>& __z) 1721 { 1722 // Kahan's formula. 1723 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1724 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1725 } 1726 1727#if _GLIBCXX_USE_C99_COMPLEX_TR1 1728 inline __complex__ float 1729 __complex_acosh(__complex__ float __z) 1730 { return __builtin_cacoshf(__z); } 1731 1732 inline __complex__ double 1733 __complex_acosh(__complex__ double __z) 1734 { return __builtin_cacosh(__z); } 1735 1736 inline __complex__ long double 1737 __complex_acosh(const __complex__ long double& __z) 1738 { return __builtin_cacoshl(__z); } 1739 1740 template<typename _Tp> 1741 inline std::complex<_Tp> 1742 acosh(const std::complex<_Tp>& __z) 1743 { return __complex_acosh(__z.__rep()); } 1744#else 1745 /// acosh(__z) [8.1.5]. 1746 // Effects: Behaves the same as C99 function cacosh, defined 1747 // in subclause 7.3.6.1. 1748 template<typename _Tp> 1749 inline std::complex<_Tp> 1750 acosh(const std::complex<_Tp>& __z) 1751 { return __complex_acosh(__z); } 1752#endif 1753 1754 template<typename _Tp> 1755 std::complex<_Tp> 1756 __complex_asinh(const std::complex<_Tp>& __z) 1757 { 1758 std::complex<_Tp> __t((__z.real() - __z.imag()) 1759 * (__z.real() + __z.imag()) + _Tp(1.0), 1760 _Tp(2.0) * __z.real() * __z.imag()); 1761 __t = std::sqrt(__t); 1762 1763 return std::log(__t + __z); 1764 } 1765 1766#if _GLIBCXX_USE_C99_COMPLEX_TR1 1767 inline __complex__ float 1768 __complex_asinh(__complex__ float __z) 1769 { return __builtin_casinhf(__z); } 1770 1771 inline __complex__ double 1772 __complex_asinh(__complex__ double __z) 1773 { return __builtin_casinh(__z); } 1774 1775 inline __complex__ long double 1776 __complex_asinh(const __complex__ long double& __z) 1777 { return __builtin_casinhl(__z); } 1778 1779 template<typename _Tp> 1780 inline std::complex<_Tp> 1781 asinh(const std::complex<_Tp>& __z) 1782 { return __complex_asinh(__z.__rep()); } 1783#else 1784 /// asinh(__z) [8.1.6]. 1785 // Effects: Behaves the same as C99 function casin, defined 1786 // in subclause 7.3.6.2. 1787 template<typename _Tp> 1788 inline std::complex<_Tp> 1789 asinh(const std::complex<_Tp>& __z) 1790 { return __complex_asinh(__z); } 1791#endif 1792 1793 template<typename _Tp> 1794 std::complex<_Tp> 1795 __complex_atanh(const std::complex<_Tp>& __z) 1796 { 1797 const _Tp __i2 = __z.imag() * __z.imag(); 1798 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1799 1800 _Tp __num = _Tp(1.0) + __z.real(); 1801 _Tp __den = _Tp(1.0) - __z.real(); 1802 1803 __num = __i2 + __num * __num; 1804 __den = __i2 + __den * __den; 1805 1806 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1807 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1808 } 1809 1810#if _GLIBCXX_USE_C99_COMPLEX_TR1 1811 inline __complex__ float 1812 __complex_atanh(__complex__ float __z) 1813 { return __builtin_catanhf(__z); } 1814 1815 inline __complex__ double 1816 __complex_atanh(__complex__ double __z) 1817 { return __builtin_catanh(__z); } 1818 1819 inline __complex__ long double 1820 __complex_atanh(const __complex__ long double& __z) 1821 { return __builtin_catanhl(__z); } 1822 1823 template<typename _Tp> 1824 inline std::complex<_Tp> 1825 atanh(const std::complex<_Tp>& __z) 1826 { return __complex_atanh(__z.__rep()); } 1827#else 1828 /// atanh(__z) [8.1.7]. 1829 // Effects: Behaves the same as C99 function catanh, defined 1830 // in subclause 7.3.6.3. 1831 template<typename _Tp> 1832 inline std::complex<_Tp> 1833 atanh(const std::complex<_Tp>& __z) 1834 { return __complex_atanh(__z); } 1835#endif 1836 1837 template<typename _Tp> 1838 inline _Tp 1839 /// fabs(__z) [8.1.8]. 1840 // Effects: Behaves the same as C99 function cabs, defined 1841 // in subclause 7.3.8.1. 1842 fabs(const std::complex<_Tp>& __z) 1843 { return std::abs(__z); } 1844 1845 /// Additional overloads [8.1.9]. 1846 template<typename _Tp> 1847 inline typename __gnu_cxx::__promote<_Tp>::__type 1848 arg(_Tp __x) 1849 { 1850 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1851#if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1852 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1853 : __type(); 1854#else 1855 return std::arg(std::complex<__type>(__x)); 1856#endif 1857 } 1858 1859 template<typename _Tp> 1860 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1861 imag(_Tp) 1862 { return _Tp(); } 1863 1864 template<typename _Tp> 1865 _GLIBCXX20_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1866 norm(_Tp __x) 1867 { 1868 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1869 return __type(__x) * __type(__x); 1870 } 1871 1872 template<typename _Tp> 1873 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1874 real(_Tp __x) 1875 { return __x; } 1876 1877 template<typename _Tp, typename _Up> 1878 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1879 pow(const std::complex<_Tp>& __x, const _Up& __y) 1880 { 1881 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1882 return std::pow(std::complex<__type>(__x), __type(__y)); 1883 } 1884 1885 template<typename _Tp, typename _Up> 1886 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1887 pow(const _Tp& __x, const std::complex<_Up>& __y) 1888 { 1889 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1890 return std::pow(__type(__x), std::complex<__type>(__y)); 1891 } 1892 1893 template<typename _Tp, typename _Up> 1894 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1895 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1896 { 1897 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1898 return std::pow(std::complex<__type>(__x), 1899 std::complex<__type>(__y)); 1900 } 1901 1902 // Forward declarations. 1903 // DR 781. 1904 template<typename _Tp> 1905 std::complex<_Tp> proj(const std::complex<_Tp>&); 1906 1907 // Generic implementation of std::proj, does not work for infinities. 1908 template<typename _Tp> 1909 inline std::complex<_Tp> 1910 __complex_proj(const std::complex<_Tp>& __z) 1911 { return __z; } 1912 1913#if _GLIBCXX_USE_C99_COMPLEX 1914 inline complex<float> 1915 __complex_proj(const complex<float>& __z) 1916 { return __builtin_cprojf(__z.__rep()); } 1917 1918 inline complex<double> 1919 __complex_proj(const complex<double>& __z) 1920 { return __builtin_cproj(__z.__rep()); } 1921 1922 inline complex<long double> 1923 __complex_proj(const complex<long double>& __z) 1924 { return __builtin_cprojl(__z.__rep()); } 1925#elif defined _GLIBCXX_USE_C99_MATH_TR1 1926 inline complex<float> 1927 __complex_proj(const complex<float>& __z) 1928 { 1929 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1930 return complex<float>(__builtin_inff(), 1931 __builtin_copysignf(0.0f, __z.imag())); 1932 return __z; 1933 } 1934 1935 inline complex<double> 1936 __complex_proj(const complex<double>& __z) 1937 { 1938 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1939 return complex<double>(__builtin_inf(), 1940 __builtin_copysign(0.0, __z.imag())); 1941 return __z; 1942 } 1943 1944 inline complex<long double> 1945 __complex_proj(const complex<long double>& __z) 1946 { 1947 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1948 return complex<long double>(__builtin_infl(), 1949 __builtin_copysignl(0.0l, __z.imag())); 1950 return __z; 1951 } 1952#endif 1953 1954 template<typename _Tp> 1955 inline std::complex<_Tp> 1956 proj(const std::complex<_Tp>& __z) 1957 { return __complex_proj(__z); } 1958 1959 // Overload for scalars 1960 template<typename _Tp> 1961 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 1962 proj(_Tp __x) 1963 { 1964 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1965 return std::proj(std::complex<__type>(__x)); 1966 } 1967 1968 template<typename _Tp> 1969 inline _GLIBCXX20_CONSTEXPR 1970 std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 1971 conj(_Tp __x) 1972 { 1973 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1974 return std::complex<__type>(__x, -__type()); 1975 } 1976 1977#if __cplusplus > 201103L 1978 1979inline namespace literals { 1980inline namespace complex_literals { 1981#pragma GCC diagnostic push 1982#pragma GCC diagnostic ignored "-Wliteral-suffix" 1983#define __cpp_lib_complex_udls 201309 1984 1985 constexpr std::complex<float> 1986 operator""if(long double __num) 1987 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1988 1989 constexpr std::complex<float> 1990 operator""if(unsigned long long __num) 1991 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1992 1993 constexpr std::complex<double> 1994 operator""i(long double __num) 1995 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1996 1997 constexpr std::complex<double> 1998 operator""i(unsigned long long __num) 1999 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 2000 2001 constexpr std::complex<long double> 2002 operator""il(long double __num) 2003 { return std::complex<long double>{0.0L, __num}; } 2004 2005 constexpr std::complex<long double> 2006 operator""il(unsigned long long __num) 2007 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } 2008 2009#pragma GCC diagnostic pop 2010} // inline namespace complex_literals 2011} // inline namespace literals 2012 2013#endif // C++14 2014 2015_GLIBCXX_END_NAMESPACE_VERSION 2016} // namespace 2017 2018#endif // C++11 2019 2020#endif /* _GLIBCXX_COMPLEX */ 2021