1// The template and inlines for the -*- C++ -*- complex number classes. 2 3// Copyright (C) 1997-2015 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 50namespace 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 norm(const complex<_Tp>&); 74 75 /// Return complex conjugate of @a z. 76 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); 77 /// Return complex with magnitude @a rho and angle @a theta. 78 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 79 80 // Transcendentals: 81 /// Return complex cosine of @a z. 82 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 83 /// Return complex hyperbolic cosine of @a z. 84 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 85 /// Return complex base e exponential of @a z. 86 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 87 /// Return complex natural logarithm of @a z. 88 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 89 /// Return complex base 10 logarithm of @a z. 90 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 91 /// Return @a x to the @a y'th power. 92 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 93 /// Return @a x to the @a y'th power. 94 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 95 /// Return @a x to the @a y'th power. 96 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 97 const complex<_Tp>&); 98 /// Return @a x to the @a y'th power. 99 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 100 /// Return complex sine of @a z. 101 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 102 /// Return complex hyperbolic sine of @a z. 103 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 104 /// Return complex square root of @a z. 105 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 106 /// Return complex tangent of @a z. 107 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 108 /// Return complex hyperbolic tangent of @a z. 109 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 110 111 112 // 26.2.2 Primary template class complex 113 /** 114 * Template to represent complex numbers. 115 * 116 * Specializations for float, double, and long double are part of the 117 * library. Results with any other type are not guaranteed. 118 * 119 * @param Tp Type of real and imaginary values. 120 */ 121 template<typename _Tp> 122 struct complex 123 { 124 /// Value typedef. 125 typedef _Tp value_type; 126 127 /// Default constructor. First parameter is x, second parameter is y. 128 /// Unspecified parameters default to 0. 129 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 130 : _M_real(__r), _M_imag(__i) { } 131 132 // Let the compiler synthesize the copy constructor 133#if __cplusplus >= 201103L 134 constexpr complex(const complex&) = default; 135#endif 136 137 /// Converting constructor. 138 template<typename _Up> 139 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 140 : _M_real(__z.real()), _M_imag(__z.imag()) { } 141 142#if __cplusplus >= 201103L 143 // _GLIBCXX_RESOLVE_LIB_DEFECTS 144 // DR 387. std::complex over-encapsulated. 145 _GLIBCXX_ABI_TAG_CXX11 146 constexpr _Tp 147 real() const { return _M_real; } 148 149 _GLIBCXX_ABI_TAG_CXX11 150 constexpr _Tp 151 imag() const { return _M_imag; } 152#else 153 /// Return real part of complex number. 154 _Tp& 155 real() { return _M_real; } 156 157 /// Return real part of complex number. 158 const _Tp& 159 real() const { return _M_real; } 160 161 /// Return imaginary part of complex number. 162 _Tp& 163 imag() { return _M_imag; } 164 165 /// Return imaginary part of complex number. 166 const _Tp& 167 imag() const { return _M_imag; } 168#endif 169 170 // _GLIBCXX_RESOLVE_LIB_DEFECTS 171 // DR 387. std::complex over-encapsulated. 172 void 173 real(_Tp __val) { _M_real = __val; } 174 175 void 176 imag(_Tp __val) { _M_imag = __val; } 177 178 /// Assign a scalar to this complex number. 179 complex<_Tp>& operator=(const _Tp&); 180 181 /// Add a scalar to this complex number. 182 // 26.2.5/1 183 complex<_Tp>& 184 operator+=(const _Tp& __t) 185 { 186 _M_real += __t; 187 return *this; 188 } 189 190 /// Subtract a scalar from this complex number. 191 // 26.2.5/3 192 complex<_Tp>& 193 operator-=(const _Tp& __t) 194 { 195 _M_real -= __t; 196 return *this; 197 } 198 199 /// Multiply this complex number by a scalar. 200 complex<_Tp>& operator*=(const _Tp&); 201 /// Divide this complex number by a scalar. 202 complex<_Tp>& operator/=(const _Tp&); 203 204 // Let the compiler synthesize the copy assignment operator 205#if __cplusplus >= 201103L 206 complex& operator=(const complex&) = default; 207#endif 208 209 /// Assign another complex number to this one. 210 template<typename _Up> 211 complex<_Tp>& operator=(const complex<_Up>&); 212 /// Add another complex number to this one. 213 template<typename _Up> 214 complex<_Tp>& operator+=(const complex<_Up>&); 215 /// Subtract another complex number from this one. 216 template<typename _Up> 217 complex<_Tp>& operator-=(const complex<_Up>&); 218 /// Multiply this complex number by another. 219 template<typename _Up> 220 complex<_Tp>& operator*=(const complex<_Up>&); 221 /// Divide this complex number by another. 222 template<typename _Up> 223 complex<_Tp>& operator/=(const complex<_Up>&); 224 225 _GLIBCXX_CONSTEXPR complex __rep() const 226 { return *this; } 227 228 private: 229 _Tp _M_real; 230 _Tp _M_imag; 231 }; 232 233 template<typename _Tp> 234 complex<_Tp>& 235 complex<_Tp>::operator=(const _Tp& __t) 236 { 237 _M_real = __t; 238 _M_imag = _Tp(); 239 return *this; 240 } 241 242 // 26.2.5/5 243 template<typename _Tp> 244 complex<_Tp>& 245 complex<_Tp>::operator*=(const _Tp& __t) 246 { 247 _M_real *= __t; 248 _M_imag *= __t; 249 return *this; 250 } 251 252 // 26.2.5/7 253 template<typename _Tp> 254 complex<_Tp>& 255 complex<_Tp>::operator/=(const _Tp& __t) 256 { 257 _M_real /= __t; 258 _M_imag /= __t; 259 return *this; 260 } 261 262 template<typename _Tp> 263 template<typename _Up> 264 complex<_Tp>& 265 complex<_Tp>::operator=(const complex<_Up>& __z) 266 { 267 _M_real = __z.real(); 268 _M_imag = __z.imag(); 269 return *this; 270 } 271 272 // 26.2.5/9 273 template<typename _Tp> 274 template<typename _Up> 275 complex<_Tp>& 276 complex<_Tp>::operator+=(const complex<_Up>& __z) 277 { 278 _M_real += __z.real(); 279 _M_imag += __z.imag(); 280 return *this; 281 } 282 283 // 26.2.5/11 284 template<typename _Tp> 285 template<typename _Up> 286 complex<_Tp>& 287 complex<_Tp>::operator-=(const complex<_Up>& __z) 288 { 289 _M_real -= __z.real(); 290 _M_imag -= __z.imag(); 291 return *this; 292 } 293 294 // 26.2.5/13 295 // XXX: This is a grammar school implementation. 296 template<typename _Tp> 297 template<typename _Up> 298 complex<_Tp>& 299 complex<_Tp>::operator*=(const complex<_Up>& __z) 300 { 301 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 302 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 303 _M_real = __r; 304 return *this; 305 } 306 307 // 26.2.5/15 308 // XXX: This is a grammar school implementation. 309 template<typename _Tp> 310 template<typename _Up> 311 complex<_Tp>& 312 complex<_Tp>::operator/=(const complex<_Up>& __z) 313 { 314 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 315 const _Tp __n = std::norm(__z); 316 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 317 _M_real = __r / __n; 318 return *this; 319 } 320 321 // Operators: 322 //@{ 323 /// Return new complex value @a x plus @a y. 324 template<typename _Tp> 325 inline complex<_Tp> 326 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 327 { 328 complex<_Tp> __r = __x; 329 __r += __y; 330 return __r; 331 } 332 333 template<typename _Tp> 334 inline complex<_Tp> 335 operator+(const complex<_Tp>& __x, const _Tp& __y) 336 { 337 complex<_Tp> __r = __x; 338 __r += __y; 339 return __r; 340 } 341 342 template<typename _Tp> 343 inline complex<_Tp> 344 operator+(const _Tp& __x, const complex<_Tp>& __y) 345 { 346 complex<_Tp> __r = __y; 347 __r += __x; 348 return __r; 349 } 350 //@} 351 352 //@{ 353 /// Return new complex value @a x minus @a y. 354 template<typename _Tp> 355 inline complex<_Tp> 356 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 357 { 358 complex<_Tp> __r = __x; 359 __r -= __y; 360 return __r; 361 } 362 363 template<typename _Tp> 364 inline complex<_Tp> 365 operator-(const complex<_Tp>& __x, const _Tp& __y) 366 { 367 complex<_Tp> __r = __x; 368 __r -= __y; 369 return __r; 370 } 371 372 template<typename _Tp> 373 inline complex<_Tp> 374 operator-(const _Tp& __x, const complex<_Tp>& __y) 375 { 376 complex<_Tp> __r(__x, -__y.imag()); 377 __r -= __y.real(); 378 return __r; 379 } 380 //@} 381 382 //@{ 383 /// Return new complex value @a x times @a y. 384 template<typename _Tp> 385 inline complex<_Tp> 386 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 387 { 388 complex<_Tp> __r = __x; 389 __r *= __y; 390 return __r; 391 } 392 393 template<typename _Tp> 394 inline complex<_Tp> 395 operator*(const complex<_Tp>& __x, const _Tp& __y) 396 { 397 complex<_Tp> __r = __x; 398 __r *= __y; 399 return __r; 400 } 401 402 template<typename _Tp> 403 inline complex<_Tp> 404 operator*(const _Tp& __x, const complex<_Tp>& __y) 405 { 406 complex<_Tp> __r = __y; 407 __r *= __x; 408 return __r; 409 } 410 //@} 411 412 //@{ 413 /// Return new complex value @a x divided by @a y. 414 template<typename _Tp> 415 inline complex<_Tp> 416 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 417 { 418 complex<_Tp> __r = __x; 419 __r /= __y; 420 return __r; 421 } 422 423 template<typename _Tp> 424 inline complex<_Tp> 425 operator/(const complex<_Tp>& __x, const _Tp& __y) 426 { 427 complex<_Tp> __r = __x; 428 __r /= __y; 429 return __r; 430 } 431 432 template<typename _Tp> 433 inline complex<_Tp> 434 operator/(const _Tp& __x, const complex<_Tp>& __y) 435 { 436 complex<_Tp> __r = __x; 437 __r /= __y; 438 return __r; 439 } 440 //@} 441 442 /// Return @a x. 443 template<typename _Tp> 444 inline complex<_Tp> 445 operator+(const complex<_Tp>& __x) 446 { return __x; } 447 448 /// Return complex negation of @a x. 449 template<typename _Tp> 450 inline complex<_Tp> 451 operator-(const complex<_Tp>& __x) 452 { return complex<_Tp>(-__x.real(), -__x.imag()); } 453 454 //@{ 455 /// Return true if @a x is equal to @a y. 456 template<typename _Tp> 457 inline _GLIBCXX_CONSTEXPR bool 458 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 459 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 460 461 template<typename _Tp> 462 inline _GLIBCXX_CONSTEXPR bool 463 operator==(const complex<_Tp>& __x, const _Tp& __y) 464 { return __x.real() == __y && __x.imag() == _Tp(); } 465 466 template<typename _Tp> 467 inline _GLIBCXX_CONSTEXPR bool 468 operator==(const _Tp& __x, const complex<_Tp>& __y) 469 { return __x == __y.real() && _Tp() == __y.imag(); } 470 //@} 471 472 //@{ 473 /// Return false if @a x is equal to @a y. 474 template<typename _Tp> 475 inline _GLIBCXX_CONSTEXPR bool 476 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 477 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 478 479 template<typename _Tp> 480 inline _GLIBCXX_CONSTEXPR bool 481 operator!=(const complex<_Tp>& __x, const _Tp& __y) 482 { return __x.real() != __y || __x.imag() != _Tp(); } 483 484 template<typename _Tp> 485 inline _GLIBCXX_CONSTEXPR bool 486 operator!=(const _Tp& __x, const complex<_Tp>& __y) 487 { return __x != __y.real() || _Tp() != __y.imag(); } 488 //@} 489 490 /// Extraction operator for complex values. 491 template<typename _Tp, typename _CharT, class _Traits> 492 basic_istream<_CharT, _Traits>& 493 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 494 { 495 _Tp __re_x, __im_x; 496 _CharT __ch; 497 __is >> __ch; 498 if (__ch == '(') 499 { 500 __is >> __re_x >> __ch; 501 if (__ch == ',') 502 { 503 __is >> __im_x >> __ch; 504 if (__ch == ')') 505 __x = complex<_Tp>(__re_x, __im_x); 506 else 507 __is.setstate(ios_base::failbit); 508 } 509 else if (__ch == ')') 510 __x = __re_x; 511 else 512 __is.setstate(ios_base::failbit); 513 } 514 else 515 { 516 __is.putback(__ch); 517 __is >> __re_x; 518 __x = __re_x; 519 } 520 return __is; 521 } 522 523 /// Insertion operator for complex values. 524 template<typename _Tp, typename _CharT, class _Traits> 525 basic_ostream<_CharT, _Traits>& 526 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 527 { 528 basic_ostringstream<_CharT, _Traits> __s; 529 __s.flags(__os.flags()); 530 __s.imbue(__os.getloc()); 531 __s.precision(__os.precision()); 532 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 533 return __os << __s.str(); 534 } 535 536 // Values 537#if __cplusplus >= 201103L 538 template<typename _Tp> 539 constexpr _Tp 540 real(const complex<_Tp>& __z) 541 { return __z.real(); } 542 543 template<typename _Tp> 544 constexpr _Tp 545 imag(const complex<_Tp>& __z) 546 { return __z.imag(); } 547#else 548 template<typename _Tp> 549 inline _Tp& 550 real(complex<_Tp>& __z) 551 { return __z.real(); } 552 553 template<typename _Tp> 554 inline const _Tp& 555 real(const complex<_Tp>& __z) 556 { return __z.real(); } 557 558 template<typename _Tp> 559 inline _Tp& 560 imag(complex<_Tp>& __z) 561 { return __z.imag(); } 562 563 template<typename _Tp> 564 inline const _Tp& 565 imag(const complex<_Tp>& __z) 566 { return __z.imag(); } 567#endif 568 569 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 570 template<typename _Tp> 571 inline _Tp 572 __complex_abs(const complex<_Tp>& __z) 573 { 574 _Tp __x = __z.real(); 575 _Tp __y = __z.imag(); 576 const _Tp __s = std::max(abs(__x), abs(__y)); 577 if (__s == _Tp()) // well ... 578 return __s; 579 __x /= __s; 580 __y /= __s; 581 return __s * sqrt(__x * __x + __y * __y); 582 } 583 584#if _GLIBCXX_USE_C99_COMPLEX 585 inline float 586 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 587 588 inline double 589 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 590 591 inline long double 592 __complex_abs(const __complex__ long double& __z) 593 { return __builtin_cabsl(__z); } 594 595 template<typename _Tp> 596 inline _Tp 597 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 598#else 599 template<typename _Tp> 600 inline _Tp 601 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 602#endif 603 604 605 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 606 template<typename _Tp> 607 inline _Tp 608 __complex_arg(const complex<_Tp>& __z) 609 { return atan2(__z.imag(), __z.real()); } 610 611#if _GLIBCXX_USE_C99_COMPLEX 612 inline float 613 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 614 615 inline double 616 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 617 618 inline long double 619 __complex_arg(const __complex__ long double& __z) 620 { return __builtin_cargl(__z); } 621 622 template<typename _Tp> 623 inline _Tp 624 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 625#else 626 template<typename _Tp> 627 inline _Tp 628 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 629#endif 630 631 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 632 // As defined, norm() is -not- a norm is the common mathematical 633 // sense used in numerics. The helper class _Norm_helper<> tries to 634 // distinguish between builtin floating point and the rest, so as 635 // to deliver an answer as close as possible to the real value. 636 template<bool> 637 struct _Norm_helper 638 { 639 template<typename _Tp> 640 static inline _Tp _S_do_it(const complex<_Tp>& __z) 641 { 642 const _Tp __x = __z.real(); 643 const _Tp __y = __z.imag(); 644 return __x * __x + __y * __y; 645 } 646 }; 647 648 template<> 649 struct _Norm_helper<true> 650 { 651 template<typename _Tp> 652 static inline _Tp _S_do_it(const complex<_Tp>& __z) 653 { 654 _Tp __res = std::abs(__z); 655 return __res * __res; 656 } 657 }; 658 659 template<typename _Tp> 660 inline _Tp 661 norm(const complex<_Tp>& __z) 662 { 663 return _Norm_helper<__is_floating<_Tp>::__value 664 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 665 } 666 667 template<typename _Tp> 668 inline complex<_Tp> 669 polar(const _Tp& __rho, const _Tp& __theta) 670 { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } 671 672 template<typename _Tp> 673 inline complex<_Tp> 674 conj(const complex<_Tp>& __z) 675 { return complex<_Tp>(__z.real(), -__z.imag()); } 676 677 // Transcendentals 678 679 // 26.2.8/1 cos(__z): Returns the cosine of __z. 680 template<typename _Tp> 681 inline complex<_Tp> 682 __complex_cos(const complex<_Tp>& __z) 683 { 684 const _Tp __x = __z.real(); 685 const _Tp __y = __z.imag(); 686 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 687 } 688 689#if _GLIBCXX_USE_C99_COMPLEX 690 inline __complex__ float 691 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 692 693 inline __complex__ double 694 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 695 696 inline __complex__ long double 697 __complex_cos(const __complex__ long double& __z) 698 { return __builtin_ccosl(__z); } 699 700 template<typename _Tp> 701 inline complex<_Tp> 702 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 703#else 704 template<typename _Tp> 705 inline complex<_Tp> 706 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 707#endif 708 709 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 710 template<typename _Tp> 711 inline complex<_Tp> 712 __complex_cosh(const complex<_Tp>& __z) 713 { 714 const _Tp __x = __z.real(); 715 const _Tp __y = __z.imag(); 716 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 717 } 718 719#if _GLIBCXX_USE_C99_COMPLEX 720 inline __complex__ float 721 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 722 723 inline __complex__ double 724 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 725 726 inline __complex__ long double 727 __complex_cosh(const __complex__ long double& __z) 728 { return __builtin_ccoshl(__z); } 729 730 template<typename _Tp> 731 inline complex<_Tp> 732 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 733#else 734 template<typename _Tp> 735 inline complex<_Tp> 736 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 737#endif 738 739 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 740 template<typename _Tp> 741 inline complex<_Tp> 742 __complex_exp(const complex<_Tp>& __z) 743 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); } 744 745#if _GLIBCXX_USE_C99_COMPLEX 746 inline __complex__ float 747 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 748 749 inline __complex__ double 750 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 751 752 inline __complex__ long double 753 __complex_exp(const __complex__ long double& __z) 754 { return __builtin_cexpl(__z); } 755 756 template<typename _Tp> 757 inline complex<_Tp> 758 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 759#else 760 template<typename _Tp> 761 inline complex<_Tp> 762 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 763#endif 764 765 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 766 // The branch cut is along the negative axis. 767 template<typename _Tp> 768 inline complex<_Tp> 769 __complex_log(const complex<_Tp>& __z) 770 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 771 772#if _GLIBCXX_USE_C99_COMPLEX 773 inline __complex__ float 774 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 775 776 inline __complex__ double 777 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 778 779 inline __complex__ long double 780 __complex_log(const __complex__ long double& __z) 781 { return __builtin_clogl(__z); } 782 783 template<typename _Tp> 784 inline complex<_Tp> 785 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 786#else 787 template<typename _Tp> 788 inline complex<_Tp> 789 log(const complex<_Tp>& __z) { return __complex_log(__z); } 790#endif 791 792 template<typename _Tp> 793 inline complex<_Tp> 794 log10(const complex<_Tp>& __z) 795 { return std::log(__z) / log(_Tp(10.0)); } 796 797 // 26.2.8/10 sin(__z): Returns the sine of __z. 798 template<typename _Tp> 799 inline complex<_Tp> 800 __complex_sin(const complex<_Tp>& __z) 801 { 802 const _Tp __x = __z.real(); 803 const _Tp __y = __z.imag(); 804 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 805 } 806 807#if _GLIBCXX_USE_C99_COMPLEX 808 inline __complex__ float 809 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 810 811 inline __complex__ double 812 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 813 814 inline __complex__ long double 815 __complex_sin(const __complex__ long double& __z) 816 { return __builtin_csinl(__z); } 817 818 template<typename _Tp> 819 inline complex<_Tp> 820 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 821#else 822 template<typename _Tp> 823 inline complex<_Tp> 824 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 825#endif 826 827 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 828 template<typename _Tp> 829 inline complex<_Tp> 830 __complex_sinh(const complex<_Tp>& __z) 831 { 832 const _Tp __x = __z.real(); 833 const _Tp __y = __z.imag(); 834 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 835 } 836 837#if _GLIBCXX_USE_C99_COMPLEX 838 inline __complex__ float 839 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 840 841 inline __complex__ double 842 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 843 844 inline __complex__ long double 845 __complex_sinh(const __complex__ long double& __z) 846 { return __builtin_csinhl(__z); } 847 848 template<typename _Tp> 849 inline complex<_Tp> 850 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 851#else 852 template<typename _Tp> 853 inline complex<_Tp> 854 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 855#endif 856 857 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 858 // The branch cut is on the negative axis. 859 template<typename _Tp> 860 complex<_Tp> 861 __complex_sqrt(const complex<_Tp>& __z) 862 { 863 _Tp __x = __z.real(); 864 _Tp __y = __z.imag(); 865 866 if (__x == _Tp()) 867 { 868 _Tp __t = sqrt(abs(__y) / 2); 869 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 870 } 871 else 872 { 873 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 874 _Tp __u = __t / 2; 875 return __x > _Tp() 876 ? complex<_Tp>(__u, __y / __t) 877 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 878 } 879 } 880 881#if _GLIBCXX_USE_C99_COMPLEX 882 inline __complex__ float 883 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 884 885 inline __complex__ double 886 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 887 888 inline __complex__ long double 889 __complex_sqrt(const __complex__ long double& __z) 890 { return __builtin_csqrtl(__z); } 891 892 template<typename _Tp> 893 inline complex<_Tp> 894 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 895#else 896 template<typename _Tp> 897 inline complex<_Tp> 898 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 899#endif 900 901 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 902 903 template<typename _Tp> 904 inline complex<_Tp> 905 __complex_tan(const complex<_Tp>& __z) 906 { return std::sin(__z) / std::cos(__z); } 907 908#if _GLIBCXX_USE_C99_COMPLEX 909 inline __complex__ float 910 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 911 912 inline __complex__ double 913 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 914 915 inline __complex__ long double 916 __complex_tan(const __complex__ long double& __z) 917 { return __builtin_ctanl(__z); } 918 919 template<typename _Tp> 920 inline complex<_Tp> 921 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 922#else 923 template<typename _Tp> 924 inline complex<_Tp> 925 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 926#endif 927 928 929 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 930 931 template<typename _Tp> 932 inline complex<_Tp> 933 __complex_tanh(const complex<_Tp>& __z) 934 { return std::sinh(__z) / std::cosh(__z); } 935 936#if _GLIBCXX_USE_C99_COMPLEX 937 inline __complex__ float 938 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 939 940 inline __complex__ double 941 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 942 943 inline __complex__ long double 944 __complex_tanh(const __complex__ long double& __z) 945 { return __builtin_ctanhl(__z); } 946 947 template<typename _Tp> 948 inline complex<_Tp> 949 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 950#else 951 template<typename _Tp> 952 inline complex<_Tp> 953 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 954#endif 955 956 957 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 958 // raised to the __y-th power. The branch 959 // cut is on the negative axis. 960 template<typename _Tp> 961 complex<_Tp> 962 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 963 { 964 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 965 966 while (__n >>= 1) 967 { 968 __x *= __x; 969 if (__n % 2) 970 __y *= __x; 971 } 972 973 return __y; 974 } 975 976 // In C++11 mode we used to implement the resolution of 977 // DR 844. complex pow return type is ambiguous. 978 // thus the following overload was disabled in that mode. However, doing 979 // that causes all sorts of issues, see, for example: 980 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html 981 // and also PR57974. 982 template<typename _Tp> 983 inline complex<_Tp> 984 pow(const complex<_Tp>& __z, int __n) 985 { 986 return __n < 0 987 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) 988 : std::__complex_pow_unsigned(__z, __n); 989 } 990 991 template<typename _Tp> 992 complex<_Tp> 993 pow(const complex<_Tp>& __x, const _Tp& __y) 994 { 995#ifndef _GLIBCXX_USE_C99_COMPLEX 996 if (__x == _Tp()) 997 return _Tp(); 998#endif 999 if (__x.imag() == _Tp() && __x.real() > _Tp()) 1000 return pow(__x.real(), __y); 1001 1002 complex<_Tp> __t = std::log(__x); 1003 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag()); 1004 } 1005 1006 template<typename _Tp> 1007 inline complex<_Tp> 1008 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1009 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1010 1011#if _GLIBCXX_USE_C99_COMPLEX 1012 inline __complex__ float 1013 __complex_pow(__complex__ float __x, __complex__ float __y) 1014 { return __builtin_cpowf(__x, __y); } 1015 1016 inline __complex__ double 1017 __complex_pow(__complex__ double __x, __complex__ double __y) 1018 { return __builtin_cpow(__x, __y); } 1019 1020 inline __complex__ long double 1021 __complex_pow(const __complex__ long double& __x, 1022 const __complex__ long double& __y) 1023 { return __builtin_cpowl(__x, __y); } 1024 1025 template<typename _Tp> 1026 inline complex<_Tp> 1027 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1028 { return __complex_pow(__x.__rep(), __y.__rep()); } 1029#else 1030 template<typename _Tp> 1031 inline complex<_Tp> 1032 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1033 { return __complex_pow(__x, __y); } 1034#endif 1035 1036 template<typename _Tp> 1037 inline complex<_Tp> 1038 pow(const _Tp& __x, const complex<_Tp>& __y) 1039 { 1040 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()), 1041 __y.imag() * log(__x)) 1042 : std::pow(complex<_Tp>(__x), __y); 1043 } 1044 1045 /// 26.2.3 complex specializations 1046 /// complex<float> specialization 1047 template<> 1048 struct complex<float> 1049 { 1050 typedef float value_type; 1051 typedef __complex__ float _ComplexT; 1052 1053 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1054 1055 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1056#if __cplusplus >= 201103L 1057 : _M_value{ __r, __i } { } 1058#else 1059 { 1060 __real__ _M_value = __r; 1061 __imag__ _M_value = __i; 1062 } 1063#endif 1064 1065 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1066 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1067 1068#if __cplusplus >= 201103L 1069 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1070 // DR 387. std::complex over-encapsulated. 1071 __attribute ((__abi_tag__ ("cxx11"))) 1072 constexpr float 1073 real() const { return __real__ _M_value; } 1074 1075 __attribute ((__abi_tag__ ("cxx11"))) 1076 constexpr float 1077 imag() const { return __imag__ _M_value; } 1078#else 1079 float& 1080 real() { return __real__ _M_value; } 1081 1082 const float& 1083 real() const { return __real__ _M_value; } 1084 1085 float& 1086 imag() { return __imag__ _M_value; } 1087 1088 const float& 1089 imag() const { return __imag__ _M_value; } 1090#endif 1091 1092 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1093 // DR 387. std::complex over-encapsulated. 1094 void 1095 real(float __val) { __real__ _M_value = __val; } 1096 1097 void 1098 imag(float __val) { __imag__ _M_value = __val; } 1099 1100 complex& 1101 operator=(float __f) 1102 { 1103 _M_value = __f; 1104 return *this; 1105 } 1106 1107 complex& 1108 operator+=(float __f) 1109 { 1110 _M_value += __f; 1111 return *this; 1112 } 1113 1114 complex& 1115 operator-=(float __f) 1116 { 1117 _M_value -= __f; 1118 return *this; 1119 } 1120 1121 complex& 1122 operator*=(float __f) 1123 { 1124 _M_value *= __f; 1125 return *this; 1126 } 1127 1128 complex& 1129 operator/=(float __f) 1130 { 1131 _M_value /= __f; 1132 return *this; 1133 } 1134 1135 // Let the compiler synthesize the copy and assignment 1136 // operator. It always does a pretty good job. 1137 // complex& operator=(const complex&); 1138 1139 template<typename _Tp> 1140 complex& 1141 operator=(const complex<_Tp>& __z) 1142 { 1143 __real__ _M_value = __z.real(); 1144 __imag__ _M_value = __z.imag(); 1145 return *this; 1146 } 1147 1148 template<typename _Tp> 1149 complex& 1150 operator+=(const complex<_Tp>& __z) 1151 { 1152 __real__ _M_value += __z.real(); 1153 __imag__ _M_value += __z.imag(); 1154 return *this; 1155 } 1156 1157 template<class _Tp> 1158 complex& 1159 operator-=(const complex<_Tp>& __z) 1160 { 1161 __real__ _M_value -= __z.real(); 1162 __imag__ _M_value -= __z.imag(); 1163 return *this; 1164 } 1165 1166 template<class _Tp> 1167 complex& 1168 operator*=(const complex<_Tp>& __z) 1169 { 1170 _ComplexT __t; 1171 __real__ __t = __z.real(); 1172 __imag__ __t = __z.imag(); 1173 _M_value *= __t; 1174 return *this; 1175 } 1176 1177 template<class _Tp> 1178 complex& 1179 operator/=(const complex<_Tp>& __z) 1180 { 1181 _ComplexT __t; 1182 __real__ __t = __z.real(); 1183 __imag__ __t = __z.imag(); 1184 _M_value /= __t; 1185 return *this; 1186 } 1187 1188 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1189 1190 private: 1191 _ComplexT _M_value; 1192 }; 1193 1194 /// 26.2.3 complex specializations 1195 /// complex<double> specialization 1196 template<> 1197 struct complex<double> 1198 { 1199 typedef double value_type; 1200 typedef __complex__ double _ComplexT; 1201 1202 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1203 1204 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1205#if __cplusplus >= 201103L 1206 : _M_value{ __r, __i } { } 1207#else 1208 { 1209 __real__ _M_value = __r; 1210 __imag__ _M_value = __i; 1211 } 1212#endif 1213 1214 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1215 : _M_value(__z.__rep()) { } 1216 1217 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1218 1219#if __cplusplus >= 201103L 1220 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1221 // DR 387. std::complex over-encapsulated. 1222 __attribute ((__abi_tag__ ("cxx11"))) 1223 constexpr double 1224 real() const { return __real__ _M_value; } 1225 1226 __attribute ((__abi_tag__ ("cxx11"))) 1227 constexpr double 1228 imag() const { return __imag__ _M_value; } 1229#else 1230 double& 1231 real() { return __real__ _M_value; } 1232 1233 const double& 1234 real() const { return __real__ _M_value; } 1235 1236 double& 1237 imag() { return __imag__ _M_value; } 1238 1239 const double& 1240 imag() const { return __imag__ _M_value; } 1241#endif 1242 1243 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1244 // DR 387. std::complex over-encapsulated. 1245 void 1246 real(double __val) { __real__ _M_value = __val; } 1247 1248 void 1249 imag(double __val) { __imag__ _M_value = __val; } 1250 1251 complex& 1252 operator=(double __d) 1253 { 1254 _M_value = __d; 1255 return *this; 1256 } 1257 1258 complex& 1259 operator+=(double __d) 1260 { 1261 _M_value += __d; 1262 return *this; 1263 } 1264 1265 complex& 1266 operator-=(double __d) 1267 { 1268 _M_value -= __d; 1269 return *this; 1270 } 1271 1272 complex& 1273 operator*=(double __d) 1274 { 1275 _M_value *= __d; 1276 return *this; 1277 } 1278 1279 complex& 1280 operator/=(double __d) 1281 { 1282 _M_value /= __d; 1283 return *this; 1284 } 1285 1286 // The compiler will synthesize this, efficiently. 1287 // complex& operator=(const complex&); 1288 1289 template<typename _Tp> 1290 complex& 1291 operator=(const complex<_Tp>& __z) 1292 { 1293 __real__ _M_value = __z.real(); 1294 __imag__ _M_value = __z.imag(); 1295 return *this; 1296 } 1297 1298 template<typename _Tp> 1299 complex& 1300 operator+=(const complex<_Tp>& __z) 1301 { 1302 __real__ _M_value += __z.real(); 1303 __imag__ _M_value += __z.imag(); 1304 return *this; 1305 } 1306 1307 template<typename _Tp> 1308 complex& 1309 operator-=(const complex<_Tp>& __z) 1310 { 1311 __real__ _M_value -= __z.real(); 1312 __imag__ _M_value -= __z.imag(); 1313 return *this; 1314 } 1315 1316 template<typename _Tp> 1317 complex& 1318 operator*=(const complex<_Tp>& __z) 1319 { 1320 _ComplexT __t; 1321 __real__ __t = __z.real(); 1322 __imag__ __t = __z.imag(); 1323 _M_value *= __t; 1324 return *this; 1325 } 1326 1327 template<typename _Tp> 1328 complex& 1329 operator/=(const complex<_Tp>& __z) 1330 { 1331 _ComplexT __t; 1332 __real__ __t = __z.real(); 1333 __imag__ __t = __z.imag(); 1334 _M_value /= __t; 1335 return *this; 1336 } 1337 1338 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1339 1340 private: 1341 _ComplexT _M_value; 1342 }; 1343 1344 /// 26.2.3 complex specializations 1345 /// complex<long double> specialization 1346 template<> 1347 struct complex<long double> 1348 { 1349 typedef long double value_type; 1350 typedef __complex__ long double _ComplexT; 1351 1352 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1353 1354 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1355 long double __i = 0.0L) 1356#if __cplusplus >= 201103L 1357 : _M_value{ __r, __i } { } 1358#else 1359 { 1360 __real__ _M_value = __r; 1361 __imag__ _M_value = __i; 1362 } 1363#endif 1364 1365 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1366 : _M_value(__z.__rep()) { } 1367 1368 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1369 : _M_value(__z.__rep()) { } 1370 1371#if __cplusplus >= 201103L 1372 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1373 // DR 387. std::complex over-encapsulated. 1374 __attribute ((__abi_tag__ ("cxx11"))) 1375 constexpr long double 1376 real() const { return __real__ _M_value; } 1377 1378 __attribute ((__abi_tag__ ("cxx11"))) 1379 constexpr long double 1380 imag() const { return __imag__ _M_value; } 1381#else 1382 long double& 1383 real() { return __real__ _M_value; } 1384 1385 const long double& 1386 real() const { return __real__ _M_value; } 1387 1388 long double& 1389 imag() { return __imag__ _M_value; } 1390 1391 const long double& 1392 imag() const { return __imag__ _M_value; } 1393#endif 1394 1395 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1396 // DR 387. std::complex over-encapsulated. 1397 void 1398 real(long double __val) { __real__ _M_value = __val; } 1399 1400 void 1401 imag(long double __val) { __imag__ _M_value = __val; } 1402 1403 complex& 1404 operator=(long double __r) 1405 { 1406 _M_value = __r; 1407 return *this; 1408 } 1409 1410 complex& 1411 operator+=(long double __r) 1412 { 1413 _M_value += __r; 1414 return *this; 1415 } 1416 1417 complex& 1418 operator-=(long double __r) 1419 { 1420 _M_value -= __r; 1421 return *this; 1422 } 1423 1424 complex& 1425 operator*=(long double __r) 1426 { 1427 _M_value *= __r; 1428 return *this; 1429 } 1430 1431 complex& 1432 operator/=(long double __r) 1433 { 1434 _M_value /= __r; 1435 return *this; 1436 } 1437 1438 // The compiler knows how to do this efficiently 1439 // complex& operator=(const complex&); 1440 1441 template<typename _Tp> 1442 complex& 1443 operator=(const complex<_Tp>& __z) 1444 { 1445 __real__ _M_value = __z.real(); 1446 __imag__ _M_value = __z.imag(); 1447 return *this; 1448 } 1449 1450 template<typename _Tp> 1451 complex& 1452 operator+=(const complex<_Tp>& __z) 1453 { 1454 __real__ _M_value += __z.real(); 1455 __imag__ _M_value += __z.imag(); 1456 return *this; 1457 } 1458 1459 template<typename _Tp> 1460 complex& 1461 operator-=(const complex<_Tp>& __z) 1462 { 1463 __real__ _M_value -= __z.real(); 1464 __imag__ _M_value -= __z.imag(); 1465 return *this; 1466 } 1467 1468 template<typename _Tp> 1469 complex& 1470 operator*=(const complex<_Tp>& __z) 1471 { 1472 _ComplexT __t; 1473 __real__ __t = __z.real(); 1474 __imag__ __t = __z.imag(); 1475 _M_value *= __t; 1476 return *this; 1477 } 1478 1479 template<typename _Tp> 1480 complex& 1481 operator/=(const complex<_Tp>& __z) 1482 { 1483 _ComplexT __t; 1484 __real__ __t = __z.real(); 1485 __imag__ __t = __z.imag(); 1486 _M_value /= __t; 1487 return *this; 1488 } 1489 1490 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1491 1492 private: 1493 _ComplexT _M_value; 1494 }; 1495 1496 // These bits have to be at the end of this file, so that the 1497 // specializations have all been defined. 1498 inline _GLIBCXX_CONSTEXPR 1499 complex<float>::complex(const complex<double>& __z) 1500 : _M_value(__z.__rep()) { } 1501 1502 inline _GLIBCXX_CONSTEXPR 1503 complex<float>::complex(const complex<long double>& __z) 1504 : _M_value(__z.__rep()) { } 1505 1506 inline _GLIBCXX_CONSTEXPR 1507 complex<double>::complex(const complex<long double>& __z) 1508 : _M_value(__z.__rep()) { } 1509 1510 // Inhibit implicit instantiations for required instantiations, 1511 // which are defined via explicit instantiations elsewhere. 1512 // NB: This syntax is a GNU extension. 1513#if _GLIBCXX_EXTERN_TEMPLATE 1514 extern template istream& operator>>(istream&, complex<float>&); 1515 extern template ostream& operator<<(ostream&, const complex<float>&); 1516 extern template istream& operator>>(istream&, complex<double>&); 1517 extern template ostream& operator<<(ostream&, const complex<double>&); 1518 extern template istream& operator>>(istream&, complex<long double>&); 1519 extern template ostream& operator<<(ostream&, const complex<long double>&); 1520 1521#ifdef _GLIBCXX_USE_WCHAR_T 1522 extern template wistream& operator>>(wistream&, complex<float>&); 1523 extern template wostream& operator<<(wostream&, const complex<float>&); 1524 extern template wistream& operator>>(wistream&, complex<double>&); 1525 extern template wostream& operator<<(wostream&, const complex<double>&); 1526 extern template wistream& operator>>(wistream&, complex<long double>&); 1527 extern template wostream& operator<<(wostream&, const complex<long double>&); 1528#endif 1529#endif 1530 1531 // @} group complex_numbers 1532 1533_GLIBCXX_END_NAMESPACE_VERSION 1534} // namespace 1535 1536namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1537{ 1538_GLIBCXX_BEGIN_NAMESPACE_VERSION 1539 1540 // See ext/type_traits.h for the primary template. 1541 template<typename _Tp, typename _Up> 1542 struct __promote_2<std::complex<_Tp>, _Up> 1543 { 1544 public: 1545 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1546 }; 1547 1548 template<typename _Tp, typename _Up> 1549 struct __promote_2<_Tp, std::complex<_Up> > 1550 { 1551 public: 1552 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1553 }; 1554 1555 template<typename _Tp, typename _Up> 1556 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1557 { 1558 public: 1559 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1560 }; 1561 1562_GLIBCXX_END_NAMESPACE_VERSION 1563} // namespace 1564 1565#if __cplusplus >= 201103L 1566 1567namespace std _GLIBCXX_VISIBILITY(default) 1568{ 1569_GLIBCXX_BEGIN_NAMESPACE_VERSION 1570 1571 // Forward declarations. 1572 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1573 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1574 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1575 1576 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1577 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1578 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1579 // DR 595. 1580 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1581 1582 template<typename _Tp> 1583 inline std::complex<_Tp> 1584 __complex_acos(const std::complex<_Tp>& __z) 1585 { 1586 const std::complex<_Tp> __t = std::asin(__z); 1587 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1588 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1589 } 1590 1591#if _GLIBCXX_USE_C99_COMPLEX_TR1 1592 inline __complex__ float 1593 __complex_acos(__complex__ float __z) 1594 { return __builtin_cacosf(__z); } 1595 1596 inline __complex__ double 1597 __complex_acos(__complex__ double __z) 1598 { return __builtin_cacos(__z); } 1599 1600 inline __complex__ long double 1601 __complex_acos(const __complex__ long double& __z) 1602 { return __builtin_cacosl(__z); } 1603 1604 template<typename _Tp> 1605 inline std::complex<_Tp> 1606 acos(const std::complex<_Tp>& __z) 1607 { return __complex_acos(__z.__rep()); } 1608#else 1609 /// acos(__z) [8.1.2]. 1610 // Effects: Behaves the same as C99 function cacos, defined 1611 // in subclause 7.3.5.1. 1612 template<typename _Tp> 1613 inline std::complex<_Tp> 1614 acos(const std::complex<_Tp>& __z) 1615 { return __complex_acos(__z); } 1616#endif 1617 1618 template<typename _Tp> 1619 inline std::complex<_Tp> 1620 __complex_asin(const std::complex<_Tp>& __z) 1621 { 1622 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1623 __t = std::asinh(__t); 1624 return std::complex<_Tp>(__t.imag(), -__t.real()); 1625 } 1626 1627#if _GLIBCXX_USE_C99_COMPLEX_TR1 1628 inline __complex__ float 1629 __complex_asin(__complex__ float __z) 1630 { return __builtin_casinf(__z); } 1631 1632 inline __complex__ double 1633 __complex_asin(__complex__ double __z) 1634 { return __builtin_casin(__z); } 1635 1636 inline __complex__ long double 1637 __complex_asin(const __complex__ long double& __z) 1638 { return __builtin_casinl(__z); } 1639 1640 template<typename _Tp> 1641 inline std::complex<_Tp> 1642 asin(const std::complex<_Tp>& __z) 1643 { return __complex_asin(__z.__rep()); } 1644#else 1645 /// asin(__z) [8.1.3]. 1646 // Effects: Behaves the same as C99 function casin, defined 1647 // in subclause 7.3.5.2. 1648 template<typename _Tp> 1649 inline std::complex<_Tp> 1650 asin(const std::complex<_Tp>& __z) 1651 { return __complex_asin(__z); } 1652#endif 1653 1654 template<typename _Tp> 1655 std::complex<_Tp> 1656 __complex_atan(const std::complex<_Tp>& __z) 1657 { 1658 const _Tp __r2 = __z.real() * __z.real(); 1659 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1660 1661 _Tp __num = __z.imag() + _Tp(1.0); 1662 _Tp __den = __z.imag() - _Tp(1.0); 1663 1664 __num = __r2 + __num * __num; 1665 __den = __r2 + __den * __den; 1666 1667 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1668 _Tp(0.25) * log(__num / __den)); 1669 } 1670 1671#if _GLIBCXX_USE_C99_COMPLEX_TR1 1672 inline __complex__ float 1673 __complex_atan(__complex__ float __z) 1674 { return __builtin_catanf(__z); } 1675 1676 inline __complex__ double 1677 __complex_atan(__complex__ double __z) 1678 { return __builtin_catan(__z); } 1679 1680 inline __complex__ long double 1681 __complex_atan(const __complex__ long double& __z) 1682 { return __builtin_catanl(__z); } 1683 1684 template<typename _Tp> 1685 inline std::complex<_Tp> 1686 atan(const std::complex<_Tp>& __z) 1687 { return __complex_atan(__z.__rep()); } 1688#else 1689 /// atan(__z) [8.1.4]. 1690 // Effects: Behaves the same as C99 function catan, defined 1691 // in subclause 7.3.5.3. 1692 template<typename _Tp> 1693 inline std::complex<_Tp> 1694 atan(const std::complex<_Tp>& __z) 1695 { return __complex_atan(__z); } 1696#endif 1697 1698 template<typename _Tp> 1699 std::complex<_Tp> 1700 __complex_acosh(const std::complex<_Tp>& __z) 1701 { 1702 // Kahan's formula. 1703 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1704 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1705 } 1706 1707#if _GLIBCXX_USE_C99_COMPLEX_TR1 1708 inline __complex__ float 1709 __complex_acosh(__complex__ float __z) 1710 { return __builtin_cacoshf(__z); } 1711 1712 inline __complex__ double 1713 __complex_acosh(__complex__ double __z) 1714 { return __builtin_cacosh(__z); } 1715 1716 inline __complex__ long double 1717 __complex_acosh(const __complex__ long double& __z) 1718 { return __builtin_cacoshl(__z); } 1719 1720 template<typename _Tp> 1721 inline std::complex<_Tp> 1722 acosh(const std::complex<_Tp>& __z) 1723 { return __complex_acosh(__z.__rep()); } 1724#else 1725 /// acosh(__z) [8.1.5]. 1726 // Effects: Behaves the same as C99 function cacosh, defined 1727 // in subclause 7.3.6.1. 1728 template<typename _Tp> 1729 inline std::complex<_Tp> 1730 acosh(const std::complex<_Tp>& __z) 1731 { return __complex_acosh(__z); } 1732#endif 1733 1734 template<typename _Tp> 1735 std::complex<_Tp> 1736 __complex_asinh(const std::complex<_Tp>& __z) 1737 { 1738 std::complex<_Tp> __t((__z.real() - __z.imag()) 1739 * (__z.real() + __z.imag()) + _Tp(1.0), 1740 _Tp(2.0) * __z.real() * __z.imag()); 1741 __t = std::sqrt(__t); 1742 1743 return std::log(__t + __z); 1744 } 1745 1746#if _GLIBCXX_USE_C99_COMPLEX_TR1 1747 inline __complex__ float 1748 __complex_asinh(__complex__ float __z) 1749 { return __builtin_casinhf(__z); } 1750 1751 inline __complex__ double 1752 __complex_asinh(__complex__ double __z) 1753 { return __builtin_casinh(__z); } 1754 1755 inline __complex__ long double 1756 __complex_asinh(const __complex__ long double& __z) 1757 { return __builtin_casinhl(__z); } 1758 1759 template<typename _Tp> 1760 inline std::complex<_Tp> 1761 asinh(const std::complex<_Tp>& __z) 1762 { return __complex_asinh(__z.__rep()); } 1763#else 1764 /// asinh(__z) [8.1.6]. 1765 // Effects: Behaves the same as C99 function casin, defined 1766 // in subclause 7.3.6.2. 1767 template<typename _Tp> 1768 inline std::complex<_Tp> 1769 asinh(const std::complex<_Tp>& __z) 1770 { return __complex_asinh(__z); } 1771#endif 1772 1773 template<typename _Tp> 1774 std::complex<_Tp> 1775 __complex_atanh(const std::complex<_Tp>& __z) 1776 { 1777 const _Tp __i2 = __z.imag() * __z.imag(); 1778 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1779 1780 _Tp __num = _Tp(1.0) + __z.real(); 1781 _Tp __den = _Tp(1.0) - __z.real(); 1782 1783 __num = __i2 + __num * __num; 1784 __den = __i2 + __den * __den; 1785 1786 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1787 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1788 } 1789 1790#if _GLIBCXX_USE_C99_COMPLEX_TR1 1791 inline __complex__ float 1792 __complex_atanh(__complex__ float __z) 1793 { return __builtin_catanhf(__z); } 1794 1795 inline __complex__ double 1796 __complex_atanh(__complex__ double __z) 1797 { return __builtin_catanh(__z); } 1798 1799 inline __complex__ long double 1800 __complex_atanh(const __complex__ long double& __z) 1801 { return __builtin_catanhl(__z); } 1802 1803 template<typename _Tp> 1804 inline std::complex<_Tp> 1805 atanh(const std::complex<_Tp>& __z) 1806 { return __complex_atanh(__z.__rep()); } 1807#else 1808 /// atanh(__z) [8.1.7]. 1809 // Effects: Behaves the same as C99 function catanh, defined 1810 // in subclause 7.3.6.3. 1811 template<typename _Tp> 1812 inline std::complex<_Tp> 1813 atanh(const std::complex<_Tp>& __z) 1814 { return __complex_atanh(__z); } 1815#endif 1816 1817 template<typename _Tp> 1818 inline _Tp 1819 /// fabs(__z) [8.1.8]. 1820 // Effects: Behaves the same as C99 function cabs, defined 1821 // in subclause 7.3.8.1. 1822 fabs(const std::complex<_Tp>& __z) 1823 { return std::abs(__z); } 1824 1825 /// Additional overloads [8.1.9]. 1826 template<typename _Tp> 1827 inline typename __gnu_cxx::__promote<_Tp>::__type 1828 arg(_Tp __x) 1829 { 1830 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1831#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1832 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1833 : __type(); 1834#else 1835 return std::arg(std::complex<__type>(__x)); 1836#endif 1837 } 1838 1839 template<typename _Tp> 1840 inline typename __gnu_cxx::__promote<_Tp>::__type 1841 imag(_Tp) 1842 { return _Tp(); } 1843 1844 template<typename _Tp> 1845 inline typename __gnu_cxx::__promote<_Tp>::__type 1846 norm(_Tp __x) 1847 { 1848 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1849 return __type(__x) * __type(__x); 1850 } 1851 1852 template<typename _Tp> 1853 inline typename __gnu_cxx::__promote<_Tp>::__type 1854 real(_Tp __x) 1855 { return __x; } 1856 1857 template<typename _Tp, typename _Up> 1858 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1859 pow(const std::complex<_Tp>& __x, const _Up& __y) 1860 { 1861 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1862 return std::pow(std::complex<__type>(__x), __type(__y)); 1863 } 1864 1865 template<typename _Tp, typename _Up> 1866 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1867 pow(const _Tp& __x, const std::complex<_Up>& __y) 1868 { 1869 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1870 return std::pow(__type(__x), std::complex<__type>(__y)); 1871 } 1872 1873 template<typename _Tp, typename _Up> 1874 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1875 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1876 { 1877 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1878 return std::pow(std::complex<__type>(__x), 1879 std::complex<__type>(__y)); 1880 } 1881 1882 // Forward declarations. 1883 // DR 781. 1884 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); 1885 1886 template<typename _Tp> 1887 std::complex<_Tp> 1888 __complex_proj(const std::complex<_Tp>& __z) 1889 { 1890 const _Tp __den = (__z.real() * __z.real() 1891 + __z.imag() * __z.imag() + _Tp(1.0)); 1892 1893 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, 1894 (_Tp(2.0) * __z.imag()) / __den); 1895 } 1896 1897#if _GLIBCXX_USE_C99_COMPLEX 1898 inline __complex__ float 1899 __complex_proj(__complex__ float __z) 1900 { return __builtin_cprojf(__z); } 1901 1902 inline __complex__ double 1903 __complex_proj(__complex__ double __z) 1904 { return __builtin_cproj(__z); } 1905 1906 inline __complex__ long double 1907 __complex_proj(const __complex__ long double& __z) 1908 { return __builtin_cprojl(__z); } 1909 1910 template<typename _Tp> 1911 inline std::complex<_Tp> 1912 proj(const std::complex<_Tp>& __z) 1913 { return __complex_proj(__z.__rep()); } 1914#else 1915 template<typename _Tp> 1916 inline std::complex<_Tp> 1917 proj(const std::complex<_Tp>& __z) 1918 { return __complex_proj(__z); } 1919#endif 1920 1921 // DR 1137. 1922 template<typename _Tp> 1923 inline typename __gnu_cxx::__promote<_Tp>::__type 1924 proj(_Tp __x) 1925 { return __x; } 1926 1927 template<typename _Tp> 1928 inline typename __gnu_cxx::__promote<_Tp>::__type 1929 conj(_Tp __x) 1930 { return __x; } 1931 1932_GLIBCXX_END_NAMESPACE_VERSION 1933 1934#if __cplusplus > 201103L 1935 1936inline namespace literals { 1937inline namespace complex_literals { 1938_GLIBCXX_BEGIN_NAMESPACE_VERSION 1939 1940#define __cpp_lib_complex_udls 201309 1941 1942 constexpr std::complex<float> 1943 operator""if(long double __num) 1944 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1945 1946 constexpr std::complex<float> 1947 operator""if(unsigned long long __num) 1948 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1949 1950 constexpr std::complex<double> 1951 operator""i(long double __num) 1952 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1953 1954 constexpr std::complex<double> 1955 operator""i(unsigned long long __num) 1956 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1957 1958 constexpr std::complex<long double> 1959 operator""il(long double __num) 1960 { return std::complex<long double>{0.0L, __num}; } 1961 1962 constexpr std::complex<long double> 1963 operator""il(unsigned long long __num) 1964 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } 1965 1966_GLIBCXX_END_NAMESPACE_VERSION 1967} // inline namespace complex_literals 1968} // inline namespace literals 1969 1970#endif // C++14 1971 1972} // namespace 1973 1974#endif // C++11 1975 1976#endif /* _GLIBCXX_COMPLEX */ 1977