1// The template and inlines for the -*- C++ -*- complex number classes. 2 3// Copyright (C) 1997-2014 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 // Lets the compiler synthesize the copy constructor 133 // complex (const complex<_Tp>&); 134 /// Copy constructor. 135 template<typename _Up> 136 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 137 : _M_real(__z.real()), _M_imag(__z.imag()) { } 138 139#if __cplusplus >= 201103L 140 // _GLIBCXX_RESOLVE_LIB_DEFECTS 141 // DR 387. std::complex over-encapsulated. 142 _GLIBCXX_ABI_TAG_CXX11 143 constexpr _Tp 144 real() { return _M_real; } 145 146 _GLIBCXX_ABI_TAG_CXX11 147 constexpr _Tp 148 imag() { return _M_imag; } 149#else 150 /// Return real part of complex number. 151 _Tp& 152 real() { return _M_real; } 153 154 /// Return real part of complex number. 155 const _Tp& 156 real() const { return _M_real; } 157 158 /// Return imaginary part of complex number. 159 _Tp& 160 imag() { return _M_imag; } 161 162 /// Return imaginary part of complex number. 163 const _Tp& 164 imag() const { return _M_imag; } 165#endif 166 167 // _GLIBCXX_RESOLVE_LIB_DEFECTS 168 // DR 387. std::complex over-encapsulated. 169 void 170 real(_Tp __val) { _M_real = __val; } 171 172 void 173 imag(_Tp __val) { _M_imag = __val; } 174 175 /// Assign this complex number to scalar @a t. 176 complex<_Tp>& operator=(const _Tp&); 177 178 /// Add @a t to this complex number. 179 // 26.2.5/1 180 complex<_Tp>& 181 operator+=(const _Tp& __t) 182 { 183 _M_real += __t; 184 return *this; 185 } 186 187 /// Subtract @a t from this complex number. 188 // 26.2.5/3 189 complex<_Tp>& 190 operator-=(const _Tp& __t) 191 { 192 _M_real -= __t; 193 return *this; 194 } 195 196 /// Multiply this complex number by @a t. 197 complex<_Tp>& operator*=(const _Tp&); 198 /// Divide this complex number by @a t. 199 complex<_Tp>& operator/=(const _Tp&); 200 201 // Lets the compiler synthesize the 202 // copy and assignment operator 203 // complex<_Tp>& operator= (const complex<_Tp>&); 204 /// Assign this complex number to complex @a z. 205 template<typename _Up> 206 complex<_Tp>& operator=(const complex<_Up>&); 207 /// Add @a z to this complex number. 208 template<typename _Up> 209 complex<_Tp>& operator+=(const complex<_Up>&); 210 /// Subtract @a z from this complex number. 211 template<typename _Up> 212 complex<_Tp>& operator-=(const complex<_Up>&); 213 /// Multiply this complex number by @a z. 214 template<typename _Up> 215 complex<_Tp>& operator*=(const complex<_Up>&); 216 /// Divide this complex number by @a z. 217 template<typename _Up> 218 complex<_Tp>& operator/=(const complex<_Up>&); 219 220 _GLIBCXX_USE_CONSTEXPR complex __rep() const 221 { return *this; } 222 223 private: 224 _Tp _M_real; 225 _Tp _M_imag; 226 }; 227 228 template<typename _Tp> 229 complex<_Tp>& 230 complex<_Tp>::operator=(const _Tp& __t) 231 { 232 _M_real = __t; 233 _M_imag = _Tp(); 234 return *this; 235 } 236 237 // 26.2.5/5 238 template<typename _Tp> 239 complex<_Tp>& 240 complex<_Tp>::operator*=(const _Tp& __t) 241 { 242 _M_real *= __t; 243 _M_imag *= __t; 244 return *this; 245 } 246 247 // 26.2.5/7 248 template<typename _Tp> 249 complex<_Tp>& 250 complex<_Tp>::operator/=(const _Tp& __t) 251 { 252 _M_real /= __t; 253 _M_imag /= __t; 254 return *this; 255 } 256 257 template<typename _Tp> 258 template<typename _Up> 259 complex<_Tp>& 260 complex<_Tp>::operator=(const complex<_Up>& __z) 261 { 262 _M_real = __z.real(); 263 _M_imag = __z.imag(); 264 return *this; 265 } 266 267 // 26.2.5/9 268 template<typename _Tp> 269 template<typename _Up> 270 complex<_Tp>& 271 complex<_Tp>::operator+=(const complex<_Up>& __z) 272 { 273 _M_real += __z.real(); 274 _M_imag += __z.imag(); 275 return *this; 276 } 277 278 // 26.2.5/11 279 template<typename _Tp> 280 template<typename _Up> 281 complex<_Tp>& 282 complex<_Tp>::operator-=(const complex<_Up>& __z) 283 { 284 _M_real -= __z.real(); 285 _M_imag -= __z.imag(); 286 return *this; 287 } 288 289 // 26.2.5/13 290 // XXX: This is a grammar school implementation. 291 template<typename _Tp> 292 template<typename _Up> 293 complex<_Tp>& 294 complex<_Tp>::operator*=(const complex<_Up>& __z) 295 { 296 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 297 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 298 _M_real = __r; 299 return *this; 300 } 301 302 // 26.2.5/15 303 // XXX: This is a grammar school implementation. 304 template<typename _Tp> 305 template<typename _Up> 306 complex<_Tp>& 307 complex<_Tp>::operator/=(const complex<_Up>& __z) 308 { 309 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 310 const _Tp __n = std::norm(__z); 311 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 312 _M_real = __r / __n; 313 return *this; 314 } 315 316 // Operators: 317 //@{ 318 /// Return new complex value @a x plus @a y. 319 template<typename _Tp> 320 inline complex<_Tp> 321 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 322 { 323 complex<_Tp> __r = __x; 324 __r += __y; 325 return __r; 326 } 327 328 template<typename _Tp> 329 inline complex<_Tp> 330 operator+(const complex<_Tp>& __x, const _Tp& __y) 331 { 332 complex<_Tp> __r = __x; 333 __r += __y; 334 return __r; 335 } 336 337 template<typename _Tp> 338 inline complex<_Tp> 339 operator+(const _Tp& __x, const complex<_Tp>& __y) 340 { 341 complex<_Tp> __r = __y; 342 __r += __x; 343 return __r; 344 } 345 //@} 346 347 //@{ 348 /// Return new complex value @a x minus @a y. 349 template<typename _Tp> 350 inline complex<_Tp> 351 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 352 { 353 complex<_Tp> __r = __x; 354 __r -= __y; 355 return __r; 356 } 357 358 template<typename _Tp> 359 inline complex<_Tp> 360 operator-(const complex<_Tp>& __x, const _Tp& __y) 361 { 362 complex<_Tp> __r = __x; 363 __r -= __y; 364 return __r; 365 } 366 367 template<typename _Tp> 368 inline complex<_Tp> 369 operator-(const _Tp& __x, const complex<_Tp>& __y) 370 { 371 complex<_Tp> __r(__x, -__y.imag()); 372 __r -= __y.real(); 373 return __r; 374 } 375 //@} 376 377 //@{ 378 /// Return new complex value @a x times @a y. 379 template<typename _Tp> 380 inline complex<_Tp> 381 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 382 { 383 complex<_Tp> __r = __x; 384 __r *= __y; 385 return __r; 386 } 387 388 template<typename _Tp> 389 inline complex<_Tp> 390 operator*(const complex<_Tp>& __x, const _Tp& __y) 391 { 392 complex<_Tp> __r = __x; 393 __r *= __y; 394 return __r; 395 } 396 397 template<typename _Tp> 398 inline complex<_Tp> 399 operator*(const _Tp& __x, const complex<_Tp>& __y) 400 { 401 complex<_Tp> __r = __y; 402 __r *= __x; 403 return __r; 404 } 405 //@} 406 407 //@{ 408 /// Return new complex value @a x divided by @a y. 409 template<typename _Tp> 410 inline complex<_Tp> 411 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 412 { 413 complex<_Tp> __r = __x; 414 __r /= __y; 415 return __r; 416 } 417 418 template<typename _Tp> 419 inline complex<_Tp> 420 operator/(const complex<_Tp>& __x, const _Tp& __y) 421 { 422 complex<_Tp> __r = __x; 423 __r /= __y; 424 return __r; 425 } 426 427 template<typename _Tp> 428 inline complex<_Tp> 429 operator/(const _Tp& __x, const complex<_Tp>& __y) 430 { 431 complex<_Tp> __r = __x; 432 __r /= __y; 433 return __r; 434 } 435 //@} 436 437 /// Return @a x. 438 template<typename _Tp> 439 inline complex<_Tp> 440 operator+(const complex<_Tp>& __x) 441 { return __x; } 442 443 /// Return complex negation of @a x. 444 template<typename _Tp> 445 inline complex<_Tp> 446 operator-(const complex<_Tp>& __x) 447 { return complex<_Tp>(-__x.real(), -__x.imag()); } 448 449 //@{ 450 /// Return true if @a x is equal to @a y. 451 template<typename _Tp> 452 inline _GLIBCXX_CONSTEXPR bool 453 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 454 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 455 456 template<typename _Tp> 457 inline _GLIBCXX_CONSTEXPR bool 458 operator==(const complex<_Tp>& __x, const _Tp& __y) 459 { return __x.real() == __y && __x.imag() == _Tp(); } 460 461 template<typename _Tp> 462 inline _GLIBCXX_CONSTEXPR bool 463 operator==(const _Tp& __x, const complex<_Tp>& __y) 464 { return __x == __y.real() && _Tp() == __y.imag(); } 465 //@} 466 467 //@{ 468 /// Return false if @a x is equal to @a y. 469 template<typename _Tp> 470 inline _GLIBCXX_CONSTEXPR bool 471 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 472 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 473 474 template<typename _Tp> 475 inline _GLIBCXX_CONSTEXPR bool 476 operator!=(const complex<_Tp>& __x, const _Tp& __y) 477 { return __x.real() != __y || __x.imag() != _Tp(); } 478 479 template<typename _Tp> 480 inline _GLIBCXX_CONSTEXPR bool 481 operator!=(const _Tp& __x, const complex<_Tp>& __y) 482 { return __x != __y.real() || _Tp() != __y.imag(); } 483 //@} 484 485 /// Extraction operator for complex values. 486 template<typename _Tp, typename _CharT, class _Traits> 487 basic_istream<_CharT, _Traits>& 488 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 489 { 490 _Tp __re_x, __im_x; 491 _CharT __ch; 492 __is >> __ch; 493 if (__ch == '(') 494 { 495 __is >> __re_x >> __ch; 496 if (__ch == ',') 497 { 498 __is >> __im_x >> __ch; 499 if (__ch == ')') 500 __x = complex<_Tp>(__re_x, __im_x); 501 else 502 __is.setstate(ios_base::failbit); 503 } 504 else if (__ch == ')') 505 __x = __re_x; 506 else 507 __is.setstate(ios_base::failbit); 508 } 509 else 510 { 511 __is.putback(__ch); 512 __is >> __re_x; 513 __x = __re_x; 514 } 515 return __is; 516 } 517 518 /// Insertion operator for complex values. 519 template<typename _Tp, typename _CharT, class _Traits> 520 basic_ostream<_CharT, _Traits>& 521 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 522 { 523 basic_ostringstream<_CharT, _Traits> __s; 524 __s.flags(__os.flags()); 525 __s.imbue(__os.getloc()); 526 __s.precision(__os.precision()); 527 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 528 return __os << __s.str(); 529 } 530 531 // Values 532#if __cplusplus >= 201103L 533 template<typename _Tp> 534 constexpr _Tp 535 real(const complex<_Tp>& __z) 536 { return __z.real(); } 537 538 template<typename _Tp> 539 constexpr _Tp 540 imag(const complex<_Tp>& __z) 541 { return __z.imag(); } 542#else 543 template<typename _Tp> 544 inline _Tp& 545 real(complex<_Tp>& __z) 546 { return __z.real(); } 547 548 template<typename _Tp> 549 inline const _Tp& 550 real(const complex<_Tp>& __z) 551 { return __z.real(); } 552 553 template<typename _Tp> 554 inline _Tp& 555 imag(complex<_Tp>& __z) 556 { return __z.imag(); } 557 558 template<typename _Tp> 559 inline const _Tp& 560 imag(const complex<_Tp>& __z) 561 { return __z.imag(); } 562#endif 563 564 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 565 template<typename _Tp> 566 inline _Tp 567 __complex_abs(const complex<_Tp>& __z) 568 { 569 _Tp __x = __z.real(); 570 _Tp __y = __z.imag(); 571 const _Tp __s = std::max(abs(__x), abs(__y)); 572 if (__s == _Tp()) // well ... 573 return __s; 574 __x /= __s; 575 __y /= __s; 576 return __s * sqrt(__x * __x + __y * __y); 577 } 578 579#if _GLIBCXX_USE_C99_COMPLEX 580 inline float 581 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 582 583 inline double 584 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 585 586 inline long double 587 __complex_abs(const __complex__ long double& __z) 588 { return __builtin_cabsl(__z); } 589 590 template<typename _Tp> 591 inline _Tp 592 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 593#else 594 template<typename _Tp> 595 inline _Tp 596 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 597#endif 598 599 600 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 601 template<typename _Tp> 602 inline _Tp 603 __complex_arg(const complex<_Tp>& __z) 604 { return atan2(__z.imag(), __z.real()); } 605 606#if _GLIBCXX_USE_C99_COMPLEX 607 inline float 608 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 609 610 inline double 611 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 612 613 inline long double 614 __complex_arg(const __complex__ long double& __z) 615 { return __builtin_cargl(__z); } 616 617 template<typename _Tp> 618 inline _Tp 619 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 620#else 621 template<typename _Tp> 622 inline _Tp 623 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 624#endif 625 626 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 627 // As defined, norm() is -not- a norm is the common mathematical 628 // sens used in numerics. The helper class _Norm_helper<> tries to 629 // distinguish between builtin floating point and the rest, so as 630 // to deliver an answer as close as possible to the real value. 631 template<bool> 632 struct _Norm_helper 633 { 634 template<typename _Tp> 635 static inline _Tp _S_do_it(const complex<_Tp>& __z) 636 { 637 const _Tp __x = __z.real(); 638 const _Tp __y = __z.imag(); 639 return __x * __x + __y * __y; 640 } 641 }; 642 643 template<> 644 struct _Norm_helper<true> 645 { 646 template<typename _Tp> 647 static inline _Tp _S_do_it(const complex<_Tp>& __z) 648 { 649 _Tp __res = std::abs(__z); 650 return __res * __res; 651 } 652 }; 653 654 template<typename _Tp> 655 inline _Tp 656 norm(const complex<_Tp>& __z) 657 { 658 return _Norm_helper<__is_floating<_Tp>::__value 659 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 660 } 661 662 template<typename _Tp> 663 inline complex<_Tp> 664 polar(const _Tp& __rho, const _Tp& __theta) 665 { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } 666 667 template<typename _Tp> 668 inline complex<_Tp> 669 conj(const complex<_Tp>& __z) 670 { return complex<_Tp>(__z.real(), -__z.imag()); } 671 672 // Transcendentals 673 674 // 26.2.8/1 cos(__z): Returns the cosine of __z. 675 template<typename _Tp> 676 inline complex<_Tp> 677 __complex_cos(const complex<_Tp>& __z) 678 { 679 const _Tp __x = __z.real(); 680 const _Tp __y = __z.imag(); 681 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 682 } 683 684#if _GLIBCXX_USE_C99_COMPLEX 685 inline __complex__ float 686 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 687 688 inline __complex__ double 689 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 690 691 inline __complex__ long double 692 __complex_cos(const __complex__ long double& __z) 693 { return __builtin_ccosl(__z); } 694 695 template<typename _Tp> 696 inline complex<_Tp> 697 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 698#else 699 template<typename _Tp> 700 inline complex<_Tp> 701 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 702#endif 703 704 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 705 template<typename _Tp> 706 inline complex<_Tp> 707 __complex_cosh(const complex<_Tp>& __z) 708 { 709 const _Tp __x = __z.real(); 710 const _Tp __y = __z.imag(); 711 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 712 } 713 714#if _GLIBCXX_USE_C99_COMPLEX 715 inline __complex__ float 716 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 717 718 inline __complex__ double 719 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 720 721 inline __complex__ long double 722 __complex_cosh(const __complex__ long double& __z) 723 { return __builtin_ccoshl(__z); } 724 725 template<typename _Tp> 726 inline complex<_Tp> 727 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 728#else 729 template<typename _Tp> 730 inline complex<_Tp> 731 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 732#endif 733 734 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 735 template<typename _Tp> 736 inline complex<_Tp> 737 __complex_exp(const complex<_Tp>& __z) 738 { return std::polar(exp(__z.real()), __z.imag()); } 739 740#if _GLIBCXX_USE_C99_COMPLEX 741 inline __complex__ float 742 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 743 744 inline __complex__ double 745 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 746 747 inline __complex__ long double 748 __complex_exp(const __complex__ long double& __z) 749 { return __builtin_cexpl(__z); } 750 751 template<typename _Tp> 752 inline complex<_Tp> 753 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 754#else 755 template<typename _Tp> 756 inline complex<_Tp> 757 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 758#endif 759 760 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 761 // The branch cut is along the negative axis. 762 template<typename _Tp> 763 inline complex<_Tp> 764 __complex_log(const complex<_Tp>& __z) 765 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 766 767#if _GLIBCXX_USE_C99_COMPLEX 768 inline __complex__ float 769 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 770 771 inline __complex__ double 772 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 773 774 inline __complex__ long double 775 __complex_log(const __complex__ long double& __z) 776 { return __builtin_clogl(__z); } 777 778 template<typename _Tp> 779 inline complex<_Tp> 780 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 781#else 782 template<typename _Tp> 783 inline complex<_Tp> 784 log(const complex<_Tp>& __z) { return __complex_log(__z); } 785#endif 786 787 template<typename _Tp> 788 inline complex<_Tp> 789 log10(const complex<_Tp>& __z) 790 { return std::log(__z) / log(_Tp(10.0)); } 791 792 // 26.2.8/10 sin(__z): Returns the sine of __z. 793 template<typename _Tp> 794 inline complex<_Tp> 795 __complex_sin(const complex<_Tp>& __z) 796 { 797 const _Tp __x = __z.real(); 798 const _Tp __y = __z.imag(); 799 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 800 } 801 802#if _GLIBCXX_USE_C99_COMPLEX 803 inline __complex__ float 804 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 805 806 inline __complex__ double 807 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 808 809 inline __complex__ long double 810 __complex_sin(const __complex__ long double& __z) 811 { return __builtin_csinl(__z); } 812 813 template<typename _Tp> 814 inline complex<_Tp> 815 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 816#else 817 template<typename _Tp> 818 inline complex<_Tp> 819 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 820#endif 821 822 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 823 template<typename _Tp> 824 inline complex<_Tp> 825 __complex_sinh(const complex<_Tp>& __z) 826 { 827 const _Tp __x = __z.real(); 828 const _Tp __y = __z.imag(); 829 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 830 } 831 832#if _GLIBCXX_USE_C99_COMPLEX 833 inline __complex__ float 834 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 835 836 inline __complex__ double 837 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 838 839 inline __complex__ long double 840 __complex_sinh(const __complex__ long double& __z) 841 { return __builtin_csinhl(__z); } 842 843 template<typename _Tp> 844 inline complex<_Tp> 845 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 846#else 847 template<typename _Tp> 848 inline complex<_Tp> 849 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 850#endif 851 852 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 853 // The branch cut is on the negative axis. 854 template<typename _Tp> 855 complex<_Tp> 856 __complex_sqrt(const complex<_Tp>& __z) 857 { 858 _Tp __x = __z.real(); 859 _Tp __y = __z.imag(); 860 861 if (__x == _Tp()) 862 { 863 _Tp __t = sqrt(abs(__y) / 2); 864 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 865 } 866 else 867 { 868 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 869 _Tp __u = __t / 2; 870 return __x > _Tp() 871 ? complex<_Tp>(__u, __y / __t) 872 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 873 } 874 } 875 876#if _GLIBCXX_USE_C99_COMPLEX 877 inline __complex__ float 878 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 879 880 inline __complex__ double 881 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 882 883 inline __complex__ long double 884 __complex_sqrt(const __complex__ long double& __z) 885 { return __builtin_csqrtl(__z); } 886 887 template<typename _Tp> 888 inline complex<_Tp> 889 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 890#else 891 template<typename _Tp> 892 inline complex<_Tp> 893 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 894#endif 895 896 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 897 898 template<typename _Tp> 899 inline complex<_Tp> 900 __complex_tan(const complex<_Tp>& __z) 901 { return std::sin(__z) / std::cos(__z); } 902 903#if _GLIBCXX_USE_C99_COMPLEX 904 inline __complex__ float 905 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 906 907 inline __complex__ double 908 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 909 910 inline __complex__ long double 911 __complex_tan(const __complex__ long double& __z) 912 { return __builtin_ctanl(__z); } 913 914 template<typename _Tp> 915 inline complex<_Tp> 916 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 917#else 918 template<typename _Tp> 919 inline complex<_Tp> 920 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 921#endif 922 923 924 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 925 926 template<typename _Tp> 927 inline complex<_Tp> 928 __complex_tanh(const complex<_Tp>& __z) 929 { return std::sinh(__z) / std::cosh(__z); } 930 931#if _GLIBCXX_USE_C99_COMPLEX 932 inline __complex__ float 933 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 934 935 inline __complex__ double 936 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 937 938 inline __complex__ long double 939 __complex_tanh(const __complex__ long double& __z) 940 { return __builtin_ctanhl(__z); } 941 942 template<typename _Tp> 943 inline complex<_Tp> 944 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 945#else 946 template<typename _Tp> 947 inline complex<_Tp> 948 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 949#endif 950 951 952 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 953 // raised to the __y-th power. The branch 954 // cut is on the negative axis. 955 template<typename _Tp> 956 complex<_Tp> 957 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 958 { 959 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 960 961 while (__n >>= 1) 962 { 963 __x *= __x; 964 if (__n % 2) 965 __y *= __x; 966 } 967 968 return __y; 969 } 970 971 // In C++11 mode we used to implement the resolution of 972 // DR 844. complex pow return type is ambiguous. 973 // thus the following overload was disabled in that mode. However, doing 974 // that causes all sorts of issues, see, for example: 975 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html 976 // and also PR57974. 977 template<typename _Tp> 978 inline complex<_Tp> 979 pow(const complex<_Tp>& __z, int __n) 980 { 981 return __n < 0 982 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) 983 : std::__complex_pow_unsigned(__z, __n); 984 } 985 986 template<typename _Tp> 987 complex<_Tp> 988 pow(const complex<_Tp>& __x, const _Tp& __y) 989 { 990#ifndef _GLIBCXX_USE_C99_COMPLEX 991 if (__x == _Tp()) 992 return _Tp(); 993#endif 994 if (__x.imag() == _Tp() && __x.real() > _Tp()) 995 return pow(__x.real(), __y); 996 997 complex<_Tp> __t = std::log(__x); 998 return std::polar(exp(__y * __t.real()), __y * __t.imag()); 999 } 1000 1001 template<typename _Tp> 1002 inline complex<_Tp> 1003 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1004 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1005 1006#if _GLIBCXX_USE_C99_COMPLEX 1007 inline __complex__ float 1008 __complex_pow(__complex__ float __x, __complex__ float __y) 1009 { return __builtin_cpowf(__x, __y); } 1010 1011 inline __complex__ double 1012 __complex_pow(__complex__ double __x, __complex__ double __y) 1013 { return __builtin_cpow(__x, __y); } 1014 1015 inline __complex__ long double 1016 __complex_pow(const __complex__ long double& __x, 1017 const __complex__ long double& __y) 1018 { return __builtin_cpowl(__x, __y); } 1019 1020 template<typename _Tp> 1021 inline complex<_Tp> 1022 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1023 { return __complex_pow(__x.__rep(), __y.__rep()); } 1024#else 1025 template<typename _Tp> 1026 inline complex<_Tp> 1027 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1028 { return __complex_pow(__x, __y); } 1029#endif 1030 1031 template<typename _Tp> 1032 inline complex<_Tp> 1033 pow(const _Tp& __x, const complex<_Tp>& __y) 1034 { 1035 return __x > _Tp() ? std::polar(pow(__x, __y.real()), 1036 __y.imag() * log(__x)) 1037 : std::pow(complex<_Tp>(__x), __y); 1038 } 1039 1040 /// 26.2.3 complex specializations 1041 /// complex<float> specialization 1042 template<> 1043 struct complex<float> 1044 { 1045 typedef float value_type; 1046 typedef __complex__ float _ComplexT; 1047 1048 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1049 1050 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1051#if __cplusplus >= 201103L 1052 : _M_value{ __r, __i } { } 1053#else 1054 { 1055 __real__ _M_value = __r; 1056 __imag__ _M_value = __i; 1057 } 1058#endif 1059 1060 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1061 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1062 1063#if __cplusplus >= 201103L 1064 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1065 // DR 387. std::complex over-encapsulated. 1066 __attribute ((__abi_tag__ ("cxx11"))) 1067 constexpr float 1068 real() const { return __real__ _M_value; } 1069 1070 __attribute ((__abi_tag__ ("cxx11"))) 1071 constexpr float 1072 imag() const { return __imag__ _M_value; } 1073#else 1074 float& 1075 real() { return __real__ _M_value; } 1076 1077 const float& 1078 real() const { return __real__ _M_value; } 1079 1080 float& 1081 imag() { return __imag__ _M_value; } 1082 1083 const float& 1084 imag() const { return __imag__ _M_value; } 1085#endif 1086 1087 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1088 // DR 387. std::complex over-encapsulated. 1089 void 1090 real(float __val) { __real__ _M_value = __val; } 1091 1092 void 1093 imag(float __val) { __imag__ _M_value = __val; } 1094 1095 complex& 1096 operator=(float __f) 1097 { 1098 _M_value = __f; 1099 return *this; 1100 } 1101 1102 complex& 1103 operator+=(float __f) 1104 { 1105 _M_value += __f; 1106 return *this; 1107 } 1108 1109 complex& 1110 operator-=(float __f) 1111 { 1112 _M_value -= __f; 1113 return *this; 1114 } 1115 1116 complex& 1117 operator*=(float __f) 1118 { 1119 _M_value *= __f; 1120 return *this; 1121 } 1122 1123 complex& 1124 operator/=(float __f) 1125 { 1126 _M_value /= __f; 1127 return *this; 1128 } 1129 1130 // Let the compiler synthesize the copy and assignment 1131 // operator. It always does a pretty good job. 1132 // complex& operator=(const complex&); 1133 1134 template<typename _Tp> 1135 complex& 1136 operator=(const complex<_Tp>& __z) 1137 { 1138 __real__ _M_value = __z.real(); 1139 __imag__ _M_value = __z.imag(); 1140 return *this; 1141 } 1142 1143 template<typename _Tp> 1144 complex& 1145 operator+=(const complex<_Tp>& __z) 1146 { 1147 __real__ _M_value += __z.real(); 1148 __imag__ _M_value += __z.imag(); 1149 return *this; 1150 } 1151 1152 template<class _Tp> 1153 complex& 1154 operator-=(const complex<_Tp>& __z) 1155 { 1156 __real__ _M_value -= __z.real(); 1157 __imag__ _M_value -= __z.imag(); 1158 return *this; 1159 } 1160 1161 template<class _Tp> 1162 complex& 1163 operator*=(const complex<_Tp>& __z) 1164 { 1165 _ComplexT __t; 1166 __real__ __t = __z.real(); 1167 __imag__ __t = __z.imag(); 1168 _M_value *= __t; 1169 return *this; 1170 } 1171 1172 template<class _Tp> 1173 complex& 1174 operator/=(const complex<_Tp>& __z) 1175 { 1176 _ComplexT __t; 1177 __real__ __t = __z.real(); 1178 __imag__ __t = __z.imag(); 1179 _M_value /= __t; 1180 return *this; 1181 } 1182 1183 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1184 1185 private: 1186 _ComplexT _M_value; 1187 }; 1188 1189 /// 26.2.3 complex specializations 1190 /// complex<double> specialization 1191 template<> 1192 struct complex<double> 1193 { 1194 typedef double value_type; 1195 typedef __complex__ double _ComplexT; 1196 1197 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1198 1199 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1200#if __cplusplus >= 201103L 1201 : _M_value{ __r, __i } { } 1202#else 1203 { 1204 __real__ _M_value = __r; 1205 __imag__ _M_value = __i; 1206 } 1207#endif 1208 1209 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1210 : _M_value(__z.__rep()) { } 1211 1212 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1213 1214#if __cplusplus >= 201103L 1215 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1216 // DR 387. std::complex over-encapsulated. 1217 __attribute ((__abi_tag__ ("cxx11"))) 1218 constexpr double 1219 real() const { return __real__ _M_value; } 1220 1221 __attribute ((__abi_tag__ ("cxx11"))) 1222 constexpr double 1223 imag() const { return __imag__ _M_value; } 1224#else 1225 double& 1226 real() { return __real__ _M_value; } 1227 1228 const double& 1229 real() const { return __real__ _M_value; } 1230 1231 double& 1232 imag() { return __imag__ _M_value; } 1233 1234 const double& 1235 imag() const { return __imag__ _M_value; } 1236#endif 1237 1238 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1239 // DR 387. std::complex over-encapsulated. 1240 void 1241 real(double __val) { __real__ _M_value = __val; } 1242 1243 void 1244 imag(double __val) { __imag__ _M_value = __val; } 1245 1246 complex& 1247 operator=(double __d) 1248 { 1249 _M_value = __d; 1250 return *this; 1251 } 1252 1253 complex& 1254 operator+=(double __d) 1255 { 1256 _M_value += __d; 1257 return *this; 1258 } 1259 1260 complex& 1261 operator-=(double __d) 1262 { 1263 _M_value -= __d; 1264 return *this; 1265 } 1266 1267 complex& 1268 operator*=(double __d) 1269 { 1270 _M_value *= __d; 1271 return *this; 1272 } 1273 1274 complex& 1275 operator/=(double __d) 1276 { 1277 _M_value /= __d; 1278 return *this; 1279 } 1280 1281 // The compiler will synthesize this, efficiently. 1282 // complex& operator=(const complex&); 1283 1284 template<typename _Tp> 1285 complex& 1286 operator=(const complex<_Tp>& __z) 1287 { 1288 __real__ _M_value = __z.real(); 1289 __imag__ _M_value = __z.imag(); 1290 return *this; 1291 } 1292 1293 template<typename _Tp> 1294 complex& 1295 operator+=(const complex<_Tp>& __z) 1296 { 1297 __real__ _M_value += __z.real(); 1298 __imag__ _M_value += __z.imag(); 1299 return *this; 1300 } 1301 1302 template<typename _Tp> 1303 complex& 1304 operator-=(const complex<_Tp>& __z) 1305 { 1306 __real__ _M_value -= __z.real(); 1307 __imag__ _M_value -= __z.imag(); 1308 return *this; 1309 } 1310 1311 template<typename _Tp> 1312 complex& 1313 operator*=(const complex<_Tp>& __z) 1314 { 1315 _ComplexT __t; 1316 __real__ __t = __z.real(); 1317 __imag__ __t = __z.imag(); 1318 _M_value *= __t; 1319 return *this; 1320 } 1321 1322 template<typename _Tp> 1323 complex& 1324 operator/=(const complex<_Tp>& __z) 1325 { 1326 _ComplexT __t; 1327 __real__ __t = __z.real(); 1328 __imag__ __t = __z.imag(); 1329 _M_value /= __t; 1330 return *this; 1331 } 1332 1333 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1334 1335 private: 1336 _ComplexT _M_value; 1337 }; 1338 1339 /// 26.2.3 complex specializations 1340 /// complex<long double> specialization 1341 template<> 1342 struct complex<long double> 1343 { 1344 typedef long double value_type; 1345 typedef __complex__ long double _ComplexT; 1346 1347 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1348 1349 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1350 long double __i = 0.0L) 1351#if __cplusplus >= 201103L 1352 : _M_value{ __r, __i } { } 1353#else 1354 { 1355 __real__ _M_value = __r; 1356 __imag__ _M_value = __i; 1357 } 1358#endif 1359 1360 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1361 : _M_value(__z.__rep()) { } 1362 1363 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1364 : _M_value(__z.__rep()) { } 1365 1366#if __cplusplus >= 201103L 1367 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1368 // DR 387. std::complex over-encapsulated. 1369 __attribute ((__abi_tag__ ("cxx11"))) 1370 constexpr long double 1371 real() const { return __real__ _M_value; } 1372 1373 __attribute ((__abi_tag__ ("cxx11"))) 1374 constexpr long double 1375 imag() const { return __imag__ _M_value; } 1376#else 1377 long double& 1378 real() { return __real__ _M_value; } 1379 1380 const long double& 1381 real() const { return __real__ _M_value; } 1382 1383 long double& 1384 imag() { return __imag__ _M_value; } 1385 1386 const long double& 1387 imag() const { return __imag__ _M_value; } 1388#endif 1389 1390 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1391 // DR 387. std::complex over-encapsulated. 1392 void 1393 real(long double __val) { __real__ _M_value = __val; } 1394 1395 void 1396 imag(long double __val) { __imag__ _M_value = __val; } 1397 1398 complex& 1399 operator=(long double __r) 1400 { 1401 _M_value = __r; 1402 return *this; 1403 } 1404 1405 complex& 1406 operator+=(long double __r) 1407 { 1408 _M_value += __r; 1409 return *this; 1410 } 1411 1412 complex& 1413 operator-=(long double __r) 1414 { 1415 _M_value -= __r; 1416 return *this; 1417 } 1418 1419 complex& 1420 operator*=(long double __r) 1421 { 1422 _M_value *= __r; 1423 return *this; 1424 } 1425 1426 complex& 1427 operator/=(long double __r) 1428 { 1429 _M_value /= __r; 1430 return *this; 1431 } 1432 1433 // The compiler knows how to do this efficiently 1434 // complex& operator=(const complex&); 1435 1436 template<typename _Tp> 1437 complex& 1438 operator=(const complex<_Tp>& __z) 1439 { 1440 __real__ _M_value = __z.real(); 1441 __imag__ _M_value = __z.imag(); 1442 return *this; 1443 } 1444 1445 template<typename _Tp> 1446 complex& 1447 operator+=(const complex<_Tp>& __z) 1448 { 1449 __real__ _M_value += __z.real(); 1450 __imag__ _M_value += __z.imag(); 1451 return *this; 1452 } 1453 1454 template<typename _Tp> 1455 complex& 1456 operator-=(const complex<_Tp>& __z) 1457 { 1458 __real__ _M_value -= __z.real(); 1459 __imag__ _M_value -= __z.imag(); 1460 return *this; 1461 } 1462 1463 template<typename _Tp> 1464 complex& 1465 operator*=(const complex<_Tp>& __z) 1466 { 1467 _ComplexT __t; 1468 __real__ __t = __z.real(); 1469 __imag__ __t = __z.imag(); 1470 _M_value *= __t; 1471 return *this; 1472 } 1473 1474 template<typename _Tp> 1475 complex& 1476 operator/=(const complex<_Tp>& __z) 1477 { 1478 _ComplexT __t; 1479 __real__ __t = __z.real(); 1480 __imag__ __t = __z.imag(); 1481 _M_value /= __t; 1482 return *this; 1483 } 1484 1485 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1486 1487 private: 1488 _ComplexT _M_value; 1489 }; 1490 1491 // These bits have to be at the end of this file, so that the 1492 // specializations have all been defined. 1493 inline _GLIBCXX_CONSTEXPR 1494 complex<float>::complex(const complex<double>& __z) 1495 : _M_value(__z.__rep()) { } 1496 1497 inline _GLIBCXX_CONSTEXPR 1498 complex<float>::complex(const complex<long double>& __z) 1499 : _M_value(__z.__rep()) { } 1500 1501 inline _GLIBCXX_CONSTEXPR 1502 complex<double>::complex(const complex<long double>& __z) 1503 : _M_value(__z.__rep()) { } 1504 1505 // Inhibit implicit instantiations for required instantiations, 1506 // which are defined via explicit instantiations elsewhere. 1507 // NB: This syntax is a GNU extension. 1508#if _GLIBCXX_EXTERN_TEMPLATE 1509 extern template istream& operator>>(istream&, complex<float>&); 1510 extern template ostream& operator<<(ostream&, const complex<float>&); 1511 extern template istream& operator>>(istream&, complex<double>&); 1512 extern template ostream& operator<<(ostream&, const complex<double>&); 1513 extern template istream& operator>>(istream&, complex<long double>&); 1514 extern template ostream& operator<<(ostream&, const complex<long double>&); 1515 1516#ifdef _GLIBCXX_USE_WCHAR_T 1517 extern template wistream& operator>>(wistream&, complex<float>&); 1518 extern template wostream& operator<<(wostream&, const complex<float>&); 1519 extern template wistream& operator>>(wistream&, complex<double>&); 1520 extern template wostream& operator<<(wostream&, const complex<double>&); 1521 extern template wistream& operator>>(wistream&, complex<long double>&); 1522 extern template wostream& operator<<(wostream&, const complex<long double>&); 1523#endif 1524#endif 1525 1526 // @} group complex_numbers 1527 1528_GLIBCXX_END_NAMESPACE_VERSION 1529} // namespace 1530 1531namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1532{ 1533_GLIBCXX_BEGIN_NAMESPACE_VERSION 1534 1535 // See ext/type_traits.h for the primary template. 1536 template<typename _Tp, typename _Up> 1537 struct __promote_2<std::complex<_Tp>, _Up> 1538 { 1539 public: 1540 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1541 }; 1542 1543 template<typename _Tp, typename _Up> 1544 struct __promote_2<_Tp, std::complex<_Up> > 1545 { 1546 public: 1547 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1548 }; 1549 1550 template<typename _Tp, typename _Up> 1551 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1552 { 1553 public: 1554 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1555 }; 1556 1557_GLIBCXX_END_NAMESPACE_VERSION 1558} // namespace 1559 1560#if __cplusplus >= 201103L 1561 1562namespace std _GLIBCXX_VISIBILITY(default) 1563{ 1564_GLIBCXX_BEGIN_NAMESPACE_VERSION 1565 1566 // Forward declarations. 1567 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1568 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1569 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1570 1571 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1572 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1573 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1574 // DR 595. 1575 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1576 1577 template<typename _Tp> 1578 inline std::complex<_Tp> 1579 __complex_acos(const std::complex<_Tp>& __z) 1580 { 1581 const std::complex<_Tp> __t = std::asin(__z); 1582 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1583 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1584 } 1585 1586#if _GLIBCXX_USE_C99_COMPLEX_TR1 1587 inline __complex__ float 1588 __complex_acos(__complex__ float __z) 1589 { return __builtin_cacosf(__z); } 1590 1591 inline __complex__ double 1592 __complex_acos(__complex__ double __z) 1593 { return __builtin_cacos(__z); } 1594 1595 inline __complex__ long double 1596 __complex_acos(const __complex__ long double& __z) 1597 { return __builtin_cacosl(__z); } 1598 1599 template<typename _Tp> 1600 inline std::complex<_Tp> 1601 acos(const std::complex<_Tp>& __z) 1602 { return __complex_acos(__z.__rep()); } 1603#else 1604 /// acos(__z) [8.1.2]. 1605 // Effects: Behaves the same as C99 function cacos, defined 1606 // in subclause 7.3.5.1. 1607 template<typename _Tp> 1608 inline std::complex<_Tp> 1609 acos(const std::complex<_Tp>& __z) 1610 { return __complex_acos(__z); } 1611#endif 1612 1613 template<typename _Tp> 1614 inline std::complex<_Tp> 1615 __complex_asin(const std::complex<_Tp>& __z) 1616 { 1617 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1618 __t = std::asinh(__t); 1619 return std::complex<_Tp>(__t.imag(), -__t.real()); 1620 } 1621 1622#if _GLIBCXX_USE_C99_COMPLEX_TR1 1623 inline __complex__ float 1624 __complex_asin(__complex__ float __z) 1625 { return __builtin_casinf(__z); } 1626 1627 inline __complex__ double 1628 __complex_asin(__complex__ double __z) 1629 { return __builtin_casin(__z); } 1630 1631 inline __complex__ long double 1632 __complex_asin(const __complex__ long double& __z) 1633 { return __builtin_casinl(__z); } 1634 1635 template<typename _Tp> 1636 inline std::complex<_Tp> 1637 asin(const std::complex<_Tp>& __z) 1638 { return __complex_asin(__z.__rep()); } 1639#else 1640 /// asin(__z) [8.1.3]. 1641 // Effects: Behaves the same as C99 function casin, defined 1642 // in subclause 7.3.5.2. 1643 template<typename _Tp> 1644 inline std::complex<_Tp> 1645 asin(const std::complex<_Tp>& __z) 1646 { return __complex_asin(__z); } 1647#endif 1648 1649 template<typename _Tp> 1650 std::complex<_Tp> 1651 __complex_atan(const std::complex<_Tp>& __z) 1652 { 1653 const _Tp __r2 = __z.real() * __z.real(); 1654 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1655 1656 _Tp __num = __z.imag() + _Tp(1.0); 1657 _Tp __den = __z.imag() - _Tp(1.0); 1658 1659 __num = __r2 + __num * __num; 1660 __den = __r2 + __den * __den; 1661 1662 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1663 _Tp(0.25) * log(__num / __den)); 1664 } 1665 1666#if _GLIBCXX_USE_C99_COMPLEX_TR1 1667 inline __complex__ float 1668 __complex_atan(__complex__ float __z) 1669 { return __builtin_catanf(__z); } 1670 1671 inline __complex__ double 1672 __complex_atan(__complex__ double __z) 1673 { return __builtin_catan(__z); } 1674 1675 inline __complex__ long double 1676 __complex_atan(const __complex__ long double& __z) 1677 { return __builtin_catanl(__z); } 1678 1679 template<typename _Tp> 1680 inline std::complex<_Tp> 1681 atan(const std::complex<_Tp>& __z) 1682 { return __complex_atan(__z.__rep()); } 1683#else 1684 /// atan(__z) [8.1.4]. 1685 // Effects: Behaves the same as C99 function catan, defined 1686 // in subclause 7.3.5.3. 1687 template<typename _Tp> 1688 inline std::complex<_Tp> 1689 atan(const std::complex<_Tp>& __z) 1690 { return __complex_atan(__z); } 1691#endif 1692 1693 template<typename _Tp> 1694 std::complex<_Tp> 1695 __complex_acosh(const std::complex<_Tp>& __z) 1696 { 1697 // Kahan's formula. 1698 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1699 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1700 } 1701 1702#if _GLIBCXX_USE_C99_COMPLEX_TR1 1703 inline __complex__ float 1704 __complex_acosh(__complex__ float __z) 1705 { return __builtin_cacoshf(__z); } 1706 1707 inline __complex__ double 1708 __complex_acosh(__complex__ double __z) 1709 { return __builtin_cacosh(__z); } 1710 1711 inline __complex__ long double 1712 __complex_acosh(const __complex__ long double& __z) 1713 { return __builtin_cacoshl(__z); } 1714 1715 template<typename _Tp> 1716 inline std::complex<_Tp> 1717 acosh(const std::complex<_Tp>& __z) 1718 { return __complex_acosh(__z.__rep()); } 1719#else 1720 /// acosh(__z) [8.1.5]. 1721 // Effects: Behaves the same as C99 function cacosh, defined 1722 // in subclause 7.3.6.1. 1723 template<typename _Tp> 1724 inline std::complex<_Tp> 1725 acosh(const std::complex<_Tp>& __z) 1726 { return __complex_acosh(__z); } 1727#endif 1728 1729 template<typename _Tp> 1730 std::complex<_Tp> 1731 __complex_asinh(const std::complex<_Tp>& __z) 1732 { 1733 std::complex<_Tp> __t((__z.real() - __z.imag()) 1734 * (__z.real() + __z.imag()) + _Tp(1.0), 1735 _Tp(2.0) * __z.real() * __z.imag()); 1736 __t = std::sqrt(__t); 1737 1738 return std::log(__t + __z); 1739 } 1740 1741#if _GLIBCXX_USE_C99_COMPLEX_TR1 1742 inline __complex__ float 1743 __complex_asinh(__complex__ float __z) 1744 { return __builtin_casinhf(__z); } 1745 1746 inline __complex__ double 1747 __complex_asinh(__complex__ double __z) 1748 { return __builtin_casinh(__z); } 1749 1750 inline __complex__ long double 1751 __complex_asinh(const __complex__ long double& __z) 1752 { return __builtin_casinhl(__z); } 1753 1754 template<typename _Tp> 1755 inline std::complex<_Tp> 1756 asinh(const std::complex<_Tp>& __z) 1757 { return __complex_asinh(__z.__rep()); } 1758#else 1759 /// asinh(__z) [8.1.6]. 1760 // Effects: Behaves the same as C99 function casin, defined 1761 // in subclause 7.3.6.2. 1762 template<typename _Tp> 1763 inline std::complex<_Tp> 1764 asinh(const std::complex<_Tp>& __z) 1765 { return __complex_asinh(__z); } 1766#endif 1767 1768 template<typename _Tp> 1769 std::complex<_Tp> 1770 __complex_atanh(const std::complex<_Tp>& __z) 1771 { 1772 const _Tp __i2 = __z.imag() * __z.imag(); 1773 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1774 1775 _Tp __num = _Tp(1.0) + __z.real(); 1776 _Tp __den = _Tp(1.0) - __z.real(); 1777 1778 __num = __i2 + __num * __num; 1779 __den = __i2 + __den * __den; 1780 1781 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1782 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1783 } 1784 1785#if _GLIBCXX_USE_C99_COMPLEX_TR1 1786 inline __complex__ float 1787 __complex_atanh(__complex__ float __z) 1788 { return __builtin_catanhf(__z); } 1789 1790 inline __complex__ double 1791 __complex_atanh(__complex__ double __z) 1792 { return __builtin_catanh(__z); } 1793 1794 inline __complex__ long double 1795 __complex_atanh(const __complex__ long double& __z) 1796 { return __builtin_catanhl(__z); } 1797 1798 template<typename _Tp> 1799 inline std::complex<_Tp> 1800 atanh(const std::complex<_Tp>& __z) 1801 { return __complex_atanh(__z.__rep()); } 1802#else 1803 /// atanh(__z) [8.1.7]. 1804 // Effects: Behaves the same as C99 function catanh, defined 1805 // in subclause 7.3.6.3. 1806 template<typename _Tp> 1807 inline std::complex<_Tp> 1808 atanh(const std::complex<_Tp>& __z) 1809 { return __complex_atanh(__z); } 1810#endif 1811 1812 template<typename _Tp> 1813 inline _Tp 1814 /// fabs(__z) [8.1.8]. 1815 // Effects: Behaves the same as C99 function cabs, defined 1816 // in subclause 7.3.8.1. 1817 fabs(const std::complex<_Tp>& __z) 1818 { return std::abs(__z); } 1819 1820 /// Additional overloads [8.1.9]. 1821 template<typename _Tp> 1822 inline typename __gnu_cxx::__promote<_Tp>::__type 1823 arg(_Tp __x) 1824 { 1825 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1826#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1827 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1828 : __type(); 1829#else 1830 return std::arg(std::complex<__type>(__x)); 1831#endif 1832 } 1833 1834 template<typename _Tp> 1835 inline typename __gnu_cxx::__promote<_Tp>::__type 1836 imag(_Tp) 1837 { return _Tp(); } 1838 1839 template<typename _Tp> 1840 inline typename __gnu_cxx::__promote<_Tp>::__type 1841 norm(_Tp __x) 1842 { 1843 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1844 return __type(__x) * __type(__x); 1845 } 1846 1847 template<typename _Tp> 1848 inline typename __gnu_cxx::__promote<_Tp>::__type 1849 real(_Tp __x) 1850 { return __x; } 1851 1852 template<typename _Tp, typename _Up> 1853 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1854 pow(const std::complex<_Tp>& __x, const _Up& __y) 1855 { 1856 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1857 return std::pow(std::complex<__type>(__x), __type(__y)); 1858 } 1859 1860 template<typename _Tp, typename _Up> 1861 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1862 pow(const _Tp& __x, const std::complex<_Up>& __y) 1863 { 1864 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1865 return std::pow(__type(__x), std::complex<__type>(__y)); 1866 } 1867 1868 template<typename _Tp, typename _Up> 1869 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1870 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1871 { 1872 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1873 return std::pow(std::complex<__type>(__x), 1874 std::complex<__type>(__y)); 1875 } 1876 1877 // Forward declarations. 1878 // DR 781. 1879 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); 1880 1881 template<typename _Tp> 1882 std::complex<_Tp> 1883 __complex_proj(const std::complex<_Tp>& __z) 1884 { 1885 const _Tp __den = (__z.real() * __z.real() 1886 + __z.imag() * __z.imag() + _Tp(1.0)); 1887 1888 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, 1889 (_Tp(2.0) * __z.imag()) / __den); 1890 } 1891 1892#if _GLIBCXX_USE_C99_COMPLEX 1893 inline __complex__ float 1894 __complex_proj(__complex__ float __z) 1895 { return __builtin_cprojf(__z); } 1896 1897 inline __complex__ double 1898 __complex_proj(__complex__ double __z) 1899 { return __builtin_cproj(__z); } 1900 1901 inline __complex__ long double 1902 __complex_proj(const __complex__ long double& __z) 1903 { return __builtin_cprojl(__z); } 1904 1905 template<typename _Tp> 1906 inline std::complex<_Tp> 1907 proj(const std::complex<_Tp>& __z) 1908 { return __complex_proj(__z.__rep()); } 1909#else 1910 template<typename _Tp> 1911 inline std::complex<_Tp> 1912 proj(const std::complex<_Tp>& __z) 1913 { return __complex_proj(__z); } 1914#endif 1915 1916 // DR 1137. 1917 template<typename _Tp> 1918 inline typename __gnu_cxx::__promote<_Tp>::__type 1919 proj(_Tp __x) 1920 { return __x; } 1921 1922 template<typename _Tp> 1923 inline typename __gnu_cxx::__promote<_Tp>::__type 1924 conj(_Tp __x) 1925 { return __x; } 1926 1927#if __cplusplus > 201103L 1928 1929inline namespace literals { 1930inline namespace complex_literals { 1931 1932#define __cpp_lib_complex_udls 201309 1933 1934 constexpr std::complex<float> 1935 operator""if(long double __num) 1936 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1937 1938 constexpr std::complex<float> 1939 operator""if(unsigned long long __num) 1940 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1941 1942 constexpr std::complex<double> 1943 operator""i(long double __num) 1944 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1945 1946 constexpr std::complex<double> 1947 operator""i(unsigned long long __num) 1948 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1949 1950 constexpr std::complex<long double> 1951 operator""il(long double __num) 1952 { return std::complex<long double>{0.0L, __num}; } 1953 1954 constexpr std::complex<long double> 1955 operator""il(unsigned long long __num) 1956 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } 1957 1958} // inline namespace complex_literals 1959} // inline namespace literals 1960 1961#endif // C++14 1962 1963_GLIBCXX_END_NAMESPACE_VERSION 1964} // namespace 1965 1966#endif // C++11 1967 1968#endif /* _GLIBCXX_COMPLEX */ 1969