complex revision 1.6.4.2
1 // The template and inlines for the -*- C++ -*- complex number classes. 2 3 // Copyright (C) 1997-2018 Free Software Foundation, Inc. 4 // 5 // This file is part of the GNU ISO C++ Library. This library is free 6 // software; you can redistribute it and/or modify it under the 7 // terms of the GNU General Public License as published by the 8 // Free Software Foundation; either version 3, or (at your option) 9 // any later version. 10 11 // This library is distributed in the hope that it will be useful, 12 // but WITHOUT ANY WARRANTY; without even the implied warranty of 13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 // GNU General Public License for more details. 15 16 // Under Section 7 of GPL version 3, you are granted additional 17 // permissions described in the GCC Runtime Library Exception, version 18 // 3.1, as published by the Free Software Foundation. 19 20 // You should have received a copy of the GNU General Public License and 21 // a copy of the GCC Runtime Library Exception along with this program; 22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23 // <http://www.gnu.org/licenses/>. 24 25 /** @file include/complex 26 * This is a Standard C++ Library header. 27 */ 28 29 // 30 // ISO C++ 14882: 26.2 Complex Numbers 31 // Note: this is not a conforming implementation. 32 // Initially implemented by Ulrich Drepper <drepper (a] cygnus.com> 33 // Improved by Gabriel Dos Reis <dosreis (a] cmla.ens-cachan.fr> 34 // 35 36 #ifndef _GLIBCXX_COMPLEX 37 #define _GLIBCXX_COMPLEX 1 38 39 #pragma GCC system_header 40 41 #include <bits/c++config.h> 42 #include <bits/cpp_type_traits.h> 43 #include <ext/type_traits.h> 44 #include <cmath> 45 #include <sstream> 46 47 #if _GLIBCXX_USE_C99_COMPLEX 48 // This is disgusting; we can't include ccomplex because that requires c++11 49 // and we can't use the builtins because those point to the wrong 50 // ABI-wise cabs/cabsf so we manually declare those here and use 51 // them directly. 52 extern "C" float __c99_cabsf(_Complex float); 53 extern "C" double __c99_cabs(_Complex double); 54 extern "C" long double __c99_cabsl(_Complex long double); 55 #endif 56 57 // Get rid of a macro possibly defined in <complex.h> 58 #undef complex 59 60 namespace std _GLIBCXX_VISIBILITY(default) 61 { 62 _GLIBCXX_BEGIN_NAMESPACE_VERSION 63 64 /** 65 * @defgroup complex_numbers Complex Numbers 66 * @ingroup numerics 67 * 68 * Classes and functions for complex numbers. 69 * @{ 70 */ 71 72 // Forward declarations. 73 template<typename _Tp> class complex; 74 template<> class complex<float>; 75 template<> class complex<double>; 76 template<> class complex<long double>; 77 78 /// Return magnitude of @a z. 79 template<typename _Tp> _Tp abs(const complex<_Tp>&); 80 /// Return phase angle of @a z. 81 template<typename _Tp> _Tp arg(const complex<_Tp>&); 82 /// Return @a z magnitude squared. 83 template<typename _Tp> _Tp norm(const complex<_Tp>&); 84 85 /// Return complex conjugate of @a z. 86 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); 87 /// Return complex with magnitude @a rho and angle @a theta. 88 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 89 90 // Transcendentals: 91 /// Return complex cosine of @a z. 92 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 93 /// Return complex hyperbolic cosine of @a z. 94 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 95 /// Return complex base e exponential of @a z. 96 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 97 /// Return complex natural logarithm of @a z. 98 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 99 /// Return complex base 10 logarithm of @a z. 100 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 101 /// Return @a x to the @a y'th power. 102 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 103 /// Return @a x to the @a y'th power. 104 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 105 /// Return @a x to the @a y'th power. 106 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 107 const complex<_Tp>&); 108 /// Return @a x to the @a y'th power. 109 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 110 /// Return complex sine of @a z. 111 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 112 /// Return complex hyperbolic sine of @a z. 113 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 114 /// Return complex square root of @a z. 115 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 116 /// Return complex tangent of @a z. 117 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 118 /// Return complex hyperbolic tangent of @a z. 119 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 120 121 122 // 26.2.2 Primary template class complex 123 /** 124 * Template to represent complex numbers. 125 * 126 * Specializations for float, double, and long double are part of the 127 * library. Results with any other type are not guaranteed. 128 * 129 * @param Tp Type of real and imaginary values. 130 */ 131 template<typename _Tp> 132 struct complex 133 { 134 /// Value typedef. 135 typedef _Tp value_type; 136 137 /// Default constructor. First parameter is x, second parameter is y. 138 /// Unspecified parameters default to 0. 139 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 140 : _M_real(__r), _M_imag(__i) { } 141 142 // Let the compiler synthesize the copy constructor 143 #if __cplusplus >= 201103L 144 constexpr complex(const complex&) = default; 145 #endif 146 147 /// Converting constructor. 148 template<typename _Up> 149 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 150 : _M_real(__z.real()), _M_imag(__z.imag()) { } 151 152 #if __cplusplus >= 201103L 153 // _GLIBCXX_RESOLVE_LIB_DEFECTS 154 // DR 387. std::complex over-encapsulated. 155 _GLIBCXX_ABI_TAG_CXX11 156 constexpr _Tp 157 real() const { return _M_real; } 158 159 _GLIBCXX_ABI_TAG_CXX11 160 constexpr _Tp 161 imag() const { return _M_imag; } 162 #else 163 /// Return real part of complex number. 164 _Tp& 165 real() { return _M_real; } 166 167 /// Return real part of complex number. 168 const _Tp& 169 real() const { return _M_real; } 170 171 /// Return imaginary part of complex number. 172 _Tp& 173 imag() { return _M_imag; } 174 175 /// Return imaginary part of complex number. 176 const _Tp& 177 imag() const { return _M_imag; } 178 #endif 179 180 // _GLIBCXX_RESOLVE_LIB_DEFECTS 181 // DR 387. std::complex over-encapsulated. 182 void 183 real(_Tp __val) { _M_real = __val; } 184 185 void 186 imag(_Tp __val) { _M_imag = __val; } 187 188 /// Assign a scalar to this complex number. 189 complex<_Tp>& operator=(const _Tp&); 190 191 /// Add a scalar to this complex number. 192 // 26.2.5/1 193 complex<_Tp>& 194 operator+=(const _Tp& __t) 195 { 196 _M_real += __t; 197 return *this; 198 } 199 200 /// Subtract a scalar from this complex number. 201 // 26.2.5/3 202 complex<_Tp>& 203 operator-=(const _Tp& __t) 204 { 205 _M_real -= __t; 206 return *this; 207 } 208 209 /// Multiply this complex number by a scalar. 210 complex<_Tp>& operator*=(const _Tp&); 211 /// Divide this complex number by a scalar. 212 complex<_Tp>& operator/=(const _Tp&); 213 214 // Let the compiler synthesize the copy assignment operator 215 #if __cplusplus >= 201103L 216 complex& operator=(const complex&) = default; 217 #endif 218 219 /// Assign another complex number to this one. 220 template<typename _Up> 221 complex<_Tp>& operator=(const complex<_Up>&); 222 /// Add another complex number to this one. 223 template<typename _Up> 224 complex<_Tp>& operator+=(const complex<_Up>&); 225 /// Subtract another complex number from this one. 226 template<typename _Up> 227 complex<_Tp>& operator-=(const complex<_Up>&); 228 /// Multiply this complex number by another. 229 template<typename _Up> 230 complex<_Tp>& operator*=(const complex<_Up>&); 231 /// Divide this complex number by another. 232 template<typename _Up> 233 complex<_Tp>& operator/=(const complex<_Up>&); 234 235 _GLIBCXX_CONSTEXPR complex __rep() const 236 { return *this; } 237 238 private: 239 _Tp _M_real; 240 _Tp _M_imag; 241 }; 242 243 template<typename _Tp> 244 complex<_Tp>& 245 complex<_Tp>::operator=(const _Tp& __t) 246 { 247 _M_real = __t; 248 _M_imag = _Tp(); 249 return *this; 250 } 251 252 // 26.2.5/5 253 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 // 26.2.5/7 263 template<typename _Tp> 264 complex<_Tp>& 265 complex<_Tp>::operator/=(const _Tp& __t) 266 { 267 _M_real /= __t; 268 _M_imag /= __t; 269 return *this; 270 } 271 272 template<typename _Tp> 273 template<typename _Up> 274 complex<_Tp>& 275 complex<_Tp>::operator=(const complex<_Up>& __z) 276 { 277 _M_real = __z.real(); 278 _M_imag = __z.imag(); 279 return *this; 280 } 281 282 // 26.2.5/9 283 template<typename _Tp> 284 template<typename _Up> 285 complex<_Tp>& 286 complex<_Tp>::operator+=(const complex<_Up>& __z) 287 { 288 _M_real += __z.real(); 289 _M_imag += __z.imag(); 290 return *this; 291 } 292 293 // 26.2.5/11 294 template<typename _Tp> 295 template<typename _Up> 296 complex<_Tp>& 297 complex<_Tp>::operator-=(const complex<_Up>& __z) 298 { 299 _M_real -= __z.real(); 300 _M_imag -= __z.imag(); 301 return *this; 302 } 303 304 // 26.2.5/13 305 // XXX: This is a grammar school implementation. 306 template<typename _Tp> 307 template<typename _Up> 308 complex<_Tp>& 309 complex<_Tp>::operator*=(const complex<_Up>& __z) 310 { 311 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 312 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 313 _M_real = __r; 314 return *this; 315 } 316 317 // 26.2.5/15 318 // XXX: This is a grammar school implementation. 319 template<typename _Tp> 320 template<typename _Up> 321 complex<_Tp>& 322 complex<_Tp>::operator/=(const complex<_Up>& __z) 323 { 324 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 325 const _Tp __n = std::norm(__z); 326 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 327 _M_real = __r / __n; 328 return *this; 329 } 330 331 // Operators: 332 //@{ 333 /// Return new complex value @a x plus @a y. 334 template<typename _Tp> 335 inline complex<_Tp> 336 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 337 { 338 complex<_Tp> __r = __x; 339 __r += __y; 340 return __r; 341 } 342 343 template<typename _Tp> 344 inline complex<_Tp> 345 operator+(const complex<_Tp>& __x, const _Tp& __y) 346 { 347 complex<_Tp> __r = __x; 348 __r += __y; 349 return __r; 350 } 351 352 template<typename _Tp> 353 inline complex<_Tp> 354 operator+(const _Tp& __x, const complex<_Tp>& __y) 355 { 356 complex<_Tp> __r = __y; 357 __r += __x; 358 return __r; 359 } 360 //@} 361 362 //@{ 363 /// Return new complex value @a x minus @a y. 364 template<typename _Tp> 365 inline complex<_Tp> 366 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 367 { 368 complex<_Tp> __r = __x; 369 __r -= __y; 370 return __r; 371 } 372 373 template<typename _Tp> 374 inline complex<_Tp> 375 operator-(const complex<_Tp>& __x, const _Tp& __y) 376 { 377 complex<_Tp> __r = __x; 378 __r -= __y; 379 return __r; 380 } 381 382 template<typename _Tp> 383 inline complex<_Tp> 384 operator-(const _Tp& __x, const complex<_Tp>& __y) 385 { 386 complex<_Tp> __r(__x, -__y.imag()); 387 __r -= __y.real(); 388 return __r; 389 } 390 //@} 391 392 //@{ 393 /// Return new complex value @a x times @a y. 394 template<typename _Tp> 395 inline complex<_Tp> 396 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 397 { 398 complex<_Tp> __r = __x; 399 __r *= __y; 400 return __r; 401 } 402 403 template<typename _Tp> 404 inline complex<_Tp> 405 operator*(const complex<_Tp>& __x, const _Tp& __y) 406 { 407 complex<_Tp> __r = __x; 408 __r *= __y; 409 return __r; 410 } 411 412 template<typename _Tp> 413 inline complex<_Tp> 414 operator*(const _Tp& __x, const complex<_Tp>& __y) 415 { 416 complex<_Tp> __r = __y; 417 __r *= __x; 418 return __r; 419 } 420 //@} 421 422 //@{ 423 /// Return new complex value @a x divided by @a y. 424 template<typename _Tp> 425 inline complex<_Tp> 426 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 427 { 428 complex<_Tp> __r = __x; 429 __r /= __y; 430 return __r; 431 } 432 433 template<typename _Tp> 434 inline complex<_Tp> 435 operator/(const complex<_Tp>& __x, const _Tp& __y) 436 { 437 complex<_Tp> __r = __x; 438 __r /= __y; 439 return __r; 440 } 441 442 template<typename _Tp> 443 inline complex<_Tp> 444 operator/(const _Tp& __x, const complex<_Tp>& __y) 445 { 446 complex<_Tp> __r = __x; 447 __r /= __y; 448 return __r; 449 } 450 //@} 451 452 /// Return @a x. 453 template<typename _Tp> 454 inline complex<_Tp> 455 operator+(const complex<_Tp>& __x) 456 { return __x; } 457 458 /// Return complex negation of @a x. 459 template<typename _Tp> 460 inline complex<_Tp> 461 operator-(const complex<_Tp>& __x) 462 { return complex<_Tp>(-__x.real(), -__x.imag()); } 463 464 //@{ 465 /// Return true if @a x is equal to @a y. 466 template<typename _Tp> 467 inline _GLIBCXX_CONSTEXPR bool 468 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 469 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 470 471 template<typename _Tp> 472 inline _GLIBCXX_CONSTEXPR bool 473 operator==(const complex<_Tp>& __x, const _Tp& __y) 474 { return __x.real() == __y && __x.imag() == _Tp(); } 475 476 template<typename _Tp> 477 inline _GLIBCXX_CONSTEXPR bool 478 operator==(const _Tp& __x, const complex<_Tp>& __y) 479 { return __x == __y.real() && _Tp() == __y.imag(); } 480 //@} 481 482 //@{ 483 /// Return false if @a x is equal to @a y. 484 template<typename _Tp> 485 inline _GLIBCXX_CONSTEXPR bool 486 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 487 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 488 489 template<typename _Tp> 490 inline _GLIBCXX_CONSTEXPR bool 491 operator!=(const complex<_Tp>& __x, const _Tp& __y) 492 { return __x.real() != __y || __x.imag() != _Tp(); } 493 494 template<typename _Tp> 495 inline _GLIBCXX_CONSTEXPR bool 496 operator!=(const _Tp& __x, const complex<_Tp>& __y) 497 { return __x != __y.real() || _Tp() != __y.imag(); } 498 //@} 499 500 /// Extraction operator for complex values. 501 template<typename _Tp, typename _CharT, class _Traits> 502 basic_istream<_CharT, _Traits>& 503 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 504 { 505 bool __fail = true; 506 _CharT __ch; 507 if (__is >> __ch) 508 { 509 if (_Traits::eq(__ch, __is.widen('('))) 510 { 511 _Tp __u; 512 if (__is >> __u >> __ch) 513 { 514 const _CharT __rparen = __is.widen(')'); 515 if (_Traits::eq(__ch, __rparen)) 516 { 517 __x = __u; 518 __fail = false; 519 } 520 else if (_Traits::eq(__ch, __is.widen(','))) 521 { 522 _Tp __v; 523 if (__is >> __v >> __ch) 524 { 525 if (_Traits::eq(__ch, __rparen)) 526 { 527 __x = complex<_Tp>(__u, __v); 528 __fail = false; 529 } 530 else 531 __is.putback(__ch); 532 } 533 } 534 else 535 __is.putback(__ch); 536 } 537 } 538 else 539 { 540 __is.putback(__ch); 541 _Tp __u; 542 if (__is >> __u) 543 { 544 __x = __u; 545 __fail = false; 546 } 547 } 548 } 549 if (__fail) 550 __is.setstate(ios_base::failbit); 551 return __is; 552 } 553 554 /// Insertion operator for complex values. 555 template<typename _Tp, typename _CharT, class _Traits> 556 basic_ostream<_CharT, _Traits>& 557 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 558 { 559 basic_ostringstream<_CharT, _Traits> __s; 560 __s.flags(__os.flags()); 561 __s.imbue(__os.getloc()); 562 __s.precision(__os.precision()); 563 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 564 return __os << __s.str(); 565 } 566 567 // Values 568 #if __cplusplus >= 201103L 569 template<typename _Tp> 570 constexpr _Tp 571 real(const complex<_Tp>& __z) 572 { return __z.real(); } 573 574 template<typename _Tp> 575 constexpr _Tp 576 imag(const complex<_Tp>& __z) 577 { return __z.imag(); } 578 #else 579 template<typename _Tp> 580 inline _Tp& 581 real(complex<_Tp>& __z) 582 { return __z.real(); } 583 584 template<typename _Tp> 585 inline const _Tp& 586 real(const complex<_Tp>& __z) 587 { return __z.real(); } 588 589 template<typename _Tp> 590 inline _Tp& 591 imag(complex<_Tp>& __z) 592 { return __z.imag(); } 593 594 template<typename _Tp> 595 inline const _Tp& 596 imag(const complex<_Tp>& __z) 597 { return __z.imag(); } 598 #endif 599 600 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 601 template<typename _Tp> 602 inline _Tp 603 __complex_abs(const complex<_Tp>& __z) 604 { 605 _Tp __x = __z.real(); 606 _Tp __y = __z.imag(); 607 const _Tp __s = std::max(abs(__x), abs(__y)); 608 if (__s == _Tp()) // well ... 609 return __s; 610 __x /= __s; 611 __y /= __s; 612 return __s * sqrt(__x * __x + __y * __y); 613 } 614 615 #if _GLIBCXX_USE_C99_COMPLEX 616 // XXX: We can't use __builtin_cabs* because they are broken 617 inline float 618 __complex_abs(__complex__ float __z) { return __c99_cabsf(__z); } 619 620 inline double 621 __complex_abs(__complex__ double __z) { return __c99_cabs(__z); } 622 623 inline long double 624 __complex_abs(const __complex__ long double& __z) 625 { return __c99_cabsl(__z); } 626 627 template<typename _Tp> 628 inline _Tp 629 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 630 #else 631 template<typename _Tp> 632 inline _Tp 633 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 634 #endif 635 636 637 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 638 template<typename _Tp> 639 inline _Tp 640 __complex_arg(const complex<_Tp>& __z) 641 { return atan2(__z.imag(), __z.real()); } 642 643 #if _GLIBCXX_USE_C99_COMPLEX 644 inline float 645 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 646 647 inline double 648 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 649 650 inline long double 651 __complex_arg(const __complex__ long double& __z) 652 { return __builtin_cargl(__z); } 653 654 template<typename _Tp> 655 inline _Tp 656 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 657 #else 658 template<typename _Tp> 659 inline _Tp 660 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 661 #endif 662 663 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 664 // As defined, norm() is -not- a norm is the common mathematical 665 // sense used in numerics. The helper class _Norm_helper<> tries to 666 // distinguish between builtin floating point and the rest, so as 667 // to deliver an answer as close as possible to the real value. 668 template<bool> 669 struct _Norm_helper 670 { 671 template<typename _Tp> 672 static inline _Tp _S_do_it(const complex<_Tp>& __z) 673 { 674 const _Tp __x = __z.real(); 675 const _Tp __y = __z.imag(); 676 return __x * __x + __y * __y; 677 } 678 }; 679 680 template<> 681 struct _Norm_helper<true> 682 { 683 template<typename _Tp> 684 static inline _Tp _S_do_it(const complex<_Tp>& __z) 685 { 686 _Tp __res = std::abs(__z); 687 return __res * __res; 688 } 689 }; 690 691 template<typename _Tp> 692 inline _Tp 693 norm(const complex<_Tp>& __z) 694 { 695 return _Norm_helper<__is_floating<_Tp>::__value 696 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 697 } 698 699 template<typename _Tp> 700 inline complex<_Tp> 701 polar(const _Tp& __rho, const _Tp& __theta) 702 { 703 __glibcxx_assert( __rho >= 0 ); 704 return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); 705 } 706 707 template<typename _Tp> 708 inline complex<_Tp> 709 conj(const complex<_Tp>& __z) 710 { return complex<_Tp>(__z.real(), -__z.imag()); } 711 712 // Transcendentals 713 714 // 26.2.8/1 cos(__z): Returns the cosine of __z. 715 template<typename _Tp> 716 inline complex<_Tp> 717 __complex_cos(const complex<_Tp>& __z) 718 { 719 const _Tp __x = __z.real(); 720 const _Tp __y = __z.imag(); 721 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 722 } 723 724 #if _GLIBCXX_USE_C99_COMPLEX 725 inline __complex__ float 726 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 727 728 inline __complex__ double 729 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 730 731 inline __complex__ long double 732 __complex_cos(const __complex__ long double& __z) 733 { return __builtin_ccosl(__z); } 734 735 template<typename _Tp> 736 inline complex<_Tp> 737 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 738 #else 739 template<typename _Tp> 740 inline complex<_Tp> 741 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 742 #endif 743 744 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 745 template<typename _Tp> 746 inline complex<_Tp> 747 __complex_cosh(const complex<_Tp>& __z) 748 { 749 const _Tp __x = __z.real(); 750 const _Tp __y = __z.imag(); 751 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 752 } 753 754 #if _GLIBCXX_USE_C99_COMPLEX 755 inline __complex__ float 756 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 757 758 inline __complex__ double 759 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 760 761 inline __complex__ long double 762 __complex_cosh(const __complex__ long double& __z) 763 { return __builtin_ccoshl(__z); } 764 765 template<typename _Tp> 766 inline complex<_Tp> 767 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 768 #else 769 template<typename _Tp> 770 inline complex<_Tp> 771 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 772 #endif 773 774 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 775 template<typename _Tp> 776 inline complex<_Tp> 777 __complex_exp(const complex<_Tp>& __z) 778 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); } 779 780 #if _GLIBCXX_USE_C99_COMPLEX 781 inline __complex__ float 782 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 783 784 inline __complex__ double 785 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 786 787 inline __complex__ long double 788 __complex_exp(const __complex__ long double& __z) 789 { return __builtin_cexpl(__z); } 790 791 template<typename _Tp> 792 inline complex<_Tp> 793 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 794 #else 795 template<typename _Tp> 796 inline complex<_Tp> 797 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 798 #endif 799 800 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 801 // The branch cut is along the negative axis. 802 template<typename _Tp> 803 inline complex<_Tp> 804 __complex_log(const complex<_Tp>& __z) 805 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 806 807 #if _GLIBCXX_USE_C99_COMPLEX 808 inline __complex__ float 809 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 810 811 inline __complex__ double 812 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 813 814 inline __complex__ long double 815 __complex_log(const __complex__ long double& __z) 816 { return __builtin_clogl(__z); } 817 818 template<typename _Tp> 819 inline complex<_Tp> 820 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 821 #else 822 template<typename _Tp> 823 inline complex<_Tp> 824 log(const complex<_Tp>& __z) { return __complex_log(__z); } 825 #endif 826 827 template<typename _Tp> 828 inline complex<_Tp> 829 log10(const complex<_Tp>& __z) 830 { return std::log(__z) / log(_Tp(10.0)); } 831 832 // 26.2.8/10 sin(__z): Returns the sine of __z. 833 template<typename _Tp> 834 inline complex<_Tp> 835 __complex_sin(const complex<_Tp>& __z) 836 { 837 const _Tp __x = __z.real(); 838 const _Tp __y = __z.imag(); 839 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 840 } 841 842 #if _GLIBCXX_USE_C99_COMPLEX 843 inline __complex__ float 844 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 845 846 inline __complex__ double 847 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 848 849 inline __complex__ long double 850 __complex_sin(const __complex__ long double& __z) 851 { return __builtin_csinl(__z); } 852 853 template<typename _Tp> 854 inline complex<_Tp> 855 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 856 #else 857 template<typename _Tp> 858 inline complex<_Tp> 859 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 860 #endif 861 862 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 863 template<typename _Tp> 864 inline complex<_Tp> 865 __complex_sinh(const complex<_Tp>& __z) 866 { 867 const _Tp __x = __z.real(); 868 const _Tp __y = __z.imag(); 869 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 870 } 871 872 #if _GLIBCXX_USE_C99_COMPLEX 873 inline __complex__ float 874 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 875 876 inline __complex__ double 877 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 878 879 inline __complex__ long double 880 __complex_sinh(const __complex__ long double& __z) 881 { return __builtin_csinhl(__z); } 882 883 template<typename _Tp> 884 inline complex<_Tp> 885 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 886 #else 887 template<typename _Tp> 888 inline complex<_Tp> 889 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 890 #endif 891 892 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 893 // The branch cut is on the negative axis. 894 template<typename _Tp> 895 complex<_Tp> 896 __complex_sqrt(const complex<_Tp>& __z) 897 { 898 _Tp __x = __z.real(); 899 _Tp __y = __z.imag(); 900 901 if (__x == _Tp()) 902 { 903 _Tp __t = sqrt(abs(__y) / 2); 904 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 905 } 906 else 907 { 908 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 909 _Tp __u = __t / 2; 910 return __x > _Tp() 911 ? complex<_Tp>(__u, __y / __t) 912 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 913 } 914 } 915 916 #if _GLIBCXX_USE_C99_COMPLEX 917 inline __complex__ float 918 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 919 920 inline __complex__ double 921 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 922 923 inline __complex__ long double 924 __complex_sqrt(const __complex__ long double& __z) 925 { return __builtin_csqrtl(__z); } 926 927 template<typename _Tp> 928 inline complex<_Tp> 929 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 930 #else 931 template<typename _Tp> 932 inline complex<_Tp> 933 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 934 #endif 935 936 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 937 938 template<typename _Tp> 939 inline complex<_Tp> 940 __complex_tan(const complex<_Tp>& __z) 941 { return std::sin(__z) / std::cos(__z); } 942 943 #if _GLIBCXX_USE_C99_COMPLEX 944 inline __complex__ float 945 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 946 947 inline __complex__ double 948 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 949 950 inline __complex__ long double 951 __complex_tan(const __complex__ long double& __z) 952 { return __builtin_ctanl(__z); } 953 954 template<typename _Tp> 955 inline complex<_Tp> 956 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 957 #else 958 template<typename _Tp> 959 inline complex<_Tp> 960 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 961 #endif 962 963 964 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 965 966 template<typename _Tp> 967 inline complex<_Tp> 968 __complex_tanh(const complex<_Tp>& __z) 969 { return std::sinh(__z) / std::cosh(__z); } 970 971 #if _GLIBCXX_USE_C99_COMPLEX 972 inline __complex__ float 973 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 974 975 inline __complex__ double 976 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 977 978 inline __complex__ long double 979 __complex_tanh(const __complex__ long double& __z) 980 { return __builtin_ctanhl(__z); } 981 982 template<typename _Tp> 983 inline complex<_Tp> 984 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 985 #else 986 template<typename _Tp> 987 inline complex<_Tp> 988 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 989 #endif 990 991 992 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 993 // raised to the __y-th power. The branch 994 // cut is on the negative axis. 995 template<typename _Tp> 996 complex<_Tp> 997 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 998 { 999 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 1000 1001 while (__n >>= 1) 1002 { 1003 __x *= __x; 1004 if (__n % 2) 1005 __y *= __x; 1006 } 1007 1008 return __y; 1009 } 1010 1011 // In C++11 mode we used to implement the resolution of 1012 // DR 844. complex pow return type is ambiguous. 1013 // thus the following overload was disabled in that mode. However, doing 1014 // that causes all sorts of issues, see, for example: 1015 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html 1016 // and also PR57974. 1017 template<typename _Tp> 1018 inline complex<_Tp> 1019 pow(const complex<_Tp>& __z, int __n) 1020 { 1021 return __n < 0 1022 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) 1023 : std::__complex_pow_unsigned(__z, __n); 1024 } 1025 1026 template<typename _Tp> 1027 complex<_Tp> 1028 pow(const complex<_Tp>& __x, const _Tp& __y) 1029 { 1030 #if ! _GLIBCXX_USE_C99_COMPLEX 1031 if (__x == _Tp()) 1032 return _Tp(); 1033 #endif 1034 if (__x.imag() == _Tp() && __x.real() > _Tp()) 1035 return pow(__x.real(), __y); 1036 1037 complex<_Tp> __t = std::log(__x); 1038 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag()); 1039 } 1040 1041 template<typename _Tp> 1042 inline complex<_Tp> 1043 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1044 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1045 1046 #if _GLIBCXX_USE_C99_COMPLEX 1047 inline __complex__ float 1048 __complex_pow(__complex__ float __x, __complex__ float __y) 1049 { return __builtin_cpowf(__x, __y); } 1050 1051 inline __complex__ double 1052 __complex_pow(__complex__ double __x, __complex__ double __y) 1053 { return __builtin_cpow(__x, __y); } 1054 1055 inline __complex__ long double 1056 __complex_pow(const __complex__ long double& __x, 1057 const __complex__ long double& __y) 1058 { return __builtin_cpowl(__x, __y); } 1059 1060 template<typename _Tp> 1061 inline complex<_Tp> 1062 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1063 { return __complex_pow(__x.__rep(), __y.__rep()); } 1064 #else 1065 template<typename _Tp> 1066 inline complex<_Tp> 1067 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1068 { return __complex_pow(__x, __y); } 1069 #endif 1070 1071 template<typename _Tp> 1072 inline complex<_Tp> 1073 pow(const _Tp& __x, const complex<_Tp>& __y) 1074 { 1075 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()), 1076 __y.imag() * log(__x)) 1077 : std::pow(complex<_Tp>(__x), __y); 1078 } 1079 1080 /// 26.2.3 complex specializations 1081 /// complex<float> specialization 1082 template<> 1083 struct complex<float> 1084 { 1085 typedef float value_type; 1086 typedef __complex__ float _ComplexT; 1087 1088 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1089 1090 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1091 #if __cplusplus >= 201103L 1092 : _M_value{ __r, __i } { } 1093 #else 1094 { 1095 __real__ _M_value = __r; 1096 __imag__ _M_value = __i; 1097 } 1098 #endif 1099 1100 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1101 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1102 1103 #if __cplusplus >= 201103L 1104 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1105 // DR 387. std::complex over-encapsulated. 1106 __attribute ((__abi_tag__ ("cxx11"))) 1107 constexpr float 1108 real() const { return __real__ _M_value; } 1109 1110 __attribute ((__abi_tag__ ("cxx11"))) 1111 constexpr float 1112 imag() const { return __imag__ _M_value; } 1113 #else 1114 float& 1115 real() { return __real__ _M_value; } 1116 1117 const float& 1118 real() const { return __real__ _M_value; } 1119 1120 float& 1121 imag() { return __imag__ _M_value; } 1122 1123 const float& 1124 imag() const { return __imag__ _M_value; } 1125 #endif 1126 1127 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1128 // DR 387. std::complex over-encapsulated. 1129 void 1130 real(float __val) { __real__ _M_value = __val; } 1131 1132 void 1133 imag(float __val) { __imag__ _M_value = __val; } 1134 1135 complex& 1136 operator=(float __f) 1137 { 1138 _M_value = __f; 1139 return *this; 1140 } 1141 1142 complex& 1143 operator+=(float __f) 1144 { 1145 _M_value += __f; 1146 return *this; 1147 } 1148 1149 complex& 1150 operator-=(float __f) 1151 { 1152 _M_value -= __f; 1153 return *this; 1154 } 1155 1156 complex& 1157 operator*=(float __f) 1158 { 1159 _M_value *= __f; 1160 return *this; 1161 } 1162 1163 complex& 1164 operator/=(float __f) 1165 { 1166 _M_value /= __f; 1167 return *this; 1168 } 1169 1170 // Let the compiler synthesize the copy and assignment 1171 // operator. It always does a pretty good job. 1172 // complex& operator=(const complex&); 1173 1174 template<typename _Tp> 1175 complex& 1176 operator=(const complex<_Tp>& __z) 1177 { 1178 __real__ _M_value = __z.real(); 1179 __imag__ _M_value = __z.imag(); 1180 return *this; 1181 } 1182 1183 template<typename _Tp> 1184 complex& 1185 operator+=(const complex<_Tp>& __z) 1186 { 1187 __real__ _M_value += __z.real(); 1188 __imag__ _M_value += __z.imag(); 1189 return *this; 1190 } 1191 1192 template<class _Tp> 1193 complex& 1194 operator-=(const complex<_Tp>& __z) 1195 { 1196 __real__ _M_value -= __z.real(); 1197 __imag__ _M_value -= __z.imag(); 1198 return *this; 1199 } 1200 1201 template<class _Tp> 1202 complex& 1203 operator*=(const complex<_Tp>& __z) 1204 { 1205 _ComplexT __t; 1206 __real__ __t = __z.real(); 1207 __imag__ __t = __z.imag(); 1208 _M_value *= __t; 1209 return *this; 1210 } 1211 1212 template<class _Tp> 1213 complex& 1214 operator/=(const complex<_Tp>& __z) 1215 { 1216 _ComplexT __t; 1217 __real__ __t = __z.real(); 1218 __imag__ __t = __z.imag(); 1219 _M_value /= __t; 1220 return *this; 1221 } 1222 1223 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1224 1225 private: 1226 _ComplexT _M_value; 1227 }; 1228 1229 /// 26.2.3 complex specializations 1230 /// complex<double> specialization 1231 template<> 1232 struct complex<double> 1233 { 1234 typedef double value_type; 1235 typedef __complex__ double _ComplexT; 1236 1237 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1238 1239 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1240 #if __cplusplus >= 201103L 1241 : _M_value{ __r, __i } { } 1242 #else 1243 { 1244 __real__ _M_value = __r; 1245 __imag__ _M_value = __i; 1246 } 1247 #endif 1248 1249 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1250 : _M_value(__z.__rep()) { } 1251 1252 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1253 1254 #if __cplusplus >= 201103L 1255 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1256 // DR 387. std::complex over-encapsulated. 1257 __attribute ((__abi_tag__ ("cxx11"))) 1258 constexpr double 1259 real() const { return __real__ _M_value; } 1260 1261 __attribute ((__abi_tag__ ("cxx11"))) 1262 constexpr double 1263 imag() const { return __imag__ _M_value; } 1264 #else 1265 double& 1266 real() { return __real__ _M_value; } 1267 1268 const double& 1269 real() const { return __real__ _M_value; } 1270 1271 double& 1272 imag() { return __imag__ _M_value; } 1273 1274 const double& 1275 imag() const { return __imag__ _M_value; } 1276 #endif 1277 1278 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1279 // DR 387. std::complex over-encapsulated. 1280 void 1281 real(double __val) { __real__ _M_value = __val; } 1282 1283 void 1284 imag(double __val) { __imag__ _M_value = __val; } 1285 1286 complex& 1287 operator=(double __d) 1288 { 1289 _M_value = __d; 1290 return *this; 1291 } 1292 1293 complex& 1294 operator+=(double __d) 1295 { 1296 _M_value += __d; 1297 return *this; 1298 } 1299 1300 complex& 1301 operator-=(double __d) 1302 { 1303 _M_value -= __d; 1304 return *this; 1305 } 1306 1307 complex& 1308 operator*=(double __d) 1309 { 1310 _M_value *= __d; 1311 return *this; 1312 } 1313 1314 complex& 1315 operator/=(double __d) 1316 { 1317 _M_value /= __d; 1318 return *this; 1319 } 1320 1321 // The compiler will synthesize this, efficiently. 1322 // complex& operator=(const complex&); 1323 1324 template<typename _Tp> 1325 complex& 1326 operator=(const complex<_Tp>& __z) 1327 { 1328 __real__ _M_value = __z.real(); 1329 __imag__ _M_value = __z.imag(); 1330 return *this; 1331 } 1332 1333 template<typename _Tp> 1334 complex& 1335 operator+=(const complex<_Tp>& __z) 1336 { 1337 __real__ _M_value += __z.real(); 1338 __imag__ _M_value += __z.imag(); 1339 return *this; 1340 } 1341 1342 template<typename _Tp> 1343 complex& 1344 operator-=(const complex<_Tp>& __z) 1345 { 1346 __real__ _M_value -= __z.real(); 1347 __imag__ _M_value -= __z.imag(); 1348 return *this; 1349 } 1350 1351 template<typename _Tp> 1352 complex& 1353 operator*=(const complex<_Tp>& __z) 1354 { 1355 _ComplexT __t; 1356 __real__ __t = __z.real(); 1357 __imag__ __t = __z.imag(); 1358 _M_value *= __t; 1359 return *this; 1360 } 1361 1362 template<typename _Tp> 1363 complex& 1364 operator/=(const complex<_Tp>& __z) 1365 { 1366 _ComplexT __t; 1367 __real__ __t = __z.real(); 1368 __imag__ __t = __z.imag(); 1369 _M_value /= __t; 1370 return *this; 1371 } 1372 1373 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1374 1375 private: 1376 _ComplexT _M_value; 1377 }; 1378 1379 /// 26.2.3 complex specializations 1380 /// complex<long double> specialization 1381 template<> 1382 struct complex<long double> 1383 { 1384 typedef long double value_type; 1385 typedef __complex__ long double _ComplexT; 1386 1387 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1388 1389 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1390 long double __i = 0.0L) 1391 #if __cplusplus >= 201103L 1392 : _M_value{ __r, __i } { } 1393 #else 1394 { 1395 __real__ _M_value = __r; 1396 __imag__ _M_value = __i; 1397 } 1398 #endif 1399 1400 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1401 : _M_value(__z.__rep()) { } 1402 1403 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1404 : _M_value(__z.__rep()) { } 1405 1406 #if __cplusplus >= 201103L 1407 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1408 // DR 387. std::complex over-encapsulated. 1409 __attribute ((__abi_tag__ ("cxx11"))) 1410 constexpr long double 1411 real() const { return __real__ _M_value; } 1412 1413 __attribute ((__abi_tag__ ("cxx11"))) 1414 constexpr long double 1415 imag() const { return __imag__ _M_value; } 1416 #else 1417 long double& 1418 real() { return __real__ _M_value; } 1419 1420 const long double& 1421 real() const { return __real__ _M_value; } 1422 1423 long double& 1424 imag() { return __imag__ _M_value; } 1425 1426 const long double& 1427 imag() const { return __imag__ _M_value; } 1428 #endif 1429 1430 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1431 // DR 387. std::complex over-encapsulated. 1432 void 1433 real(long double __val) { __real__ _M_value = __val; } 1434 1435 void 1436 imag(long double __val) { __imag__ _M_value = __val; } 1437 1438 complex& 1439 operator=(long double __r) 1440 { 1441 _M_value = __r; 1442 return *this; 1443 } 1444 1445 complex& 1446 operator+=(long double __r) 1447 { 1448 _M_value += __r; 1449 return *this; 1450 } 1451 1452 complex& 1453 operator-=(long double __r) 1454 { 1455 _M_value -= __r; 1456 return *this; 1457 } 1458 1459 complex& 1460 operator*=(long double __r) 1461 { 1462 _M_value *= __r; 1463 return *this; 1464 } 1465 1466 complex& 1467 operator/=(long double __r) 1468 { 1469 _M_value /= __r; 1470 return *this; 1471 } 1472 1473 // The compiler knows how to do this efficiently 1474 // complex& operator=(const complex&); 1475 1476 template<typename _Tp> 1477 complex& 1478 operator=(const complex<_Tp>& __z) 1479 { 1480 __real__ _M_value = __z.real(); 1481 __imag__ _M_value = __z.imag(); 1482 return *this; 1483 } 1484 1485 template<typename _Tp> 1486 complex& 1487 operator+=(const complex<_Tp>& __z) 1488 { 1489 __real__ _M_value += __z.real(); 1490 __imag__ _M_value += __z.imag(); 1491 return *this; 1492 } 1493 1494 template<typename _Tp> 1495 complex& 1496 operator-=(const complex<_Tp>& __z) 1497 { 1498 __real__ _M_value -= __z.real(); 1499 __imag__ _M_value -= __z.imag(); 1500 return *this; 1501 } 1502 1503 template<typename _Tp> 1504 complex& 1505 operator*=(const complex<_Tp>& __z) 1506 { 1507 _ComplexT __t; 1508 __real__ __t = __z.real(); 1509 __imag__ __t = __z.imag(); 1510 _M_value *= __t; 1511 return *this; 1512 } 1513 1514 template<typename _Tp> 1515 complex& 1516 operator/=(const complex<_Tp>& __z) 1517 { 1518 _ComplexT __t; 1519 __real__ __t = __z.real(); 1520 __imag__ __t = __z.imag(); 1521 _M_value /= __t; 1522 return *this; 1523 } 1524 1525 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1526 1527 private: 1528 _ComplexT _M_value; 1529 }; 1530 1531 // These bits have to be at the end of this file, so that the 1532 // specializations have all been defined. 1533 inline _GLIBCXX_CONSTEXPR 1534 complex<float>::complex(const complex<double>& __z) 1535 : _M_value(__z.__rep()) { } 1536 1537 inline _GLIBCXX_CONSTEXPR 1538 complex<float>::complex(const complex<long double>& __z) 1539 : _M_value(__z.__rep()) { } 1540 1541 inline _GLIBCXX_CONSTEXPR 1542 complex<double>::complex(const complex<long double>& __z) 1543 : _M_value(__z.__rep()) { } 1544 1545 // Inhibit implicit instantiations for required instantiations, 1546 // which are defined via explicit instantiations elsewhere. 1547 // NB: This syntax is a GNU extension. 1548 #if _GLIBCXX_EXTERN_TEMPLATE 1549 extern template istream& operator>>(istream&, complex<float>&); 1550 extern template ostream& operator<<(ostream&, const complex<float>&); 1551 extern template istream& operator>>(istream&, complex<double>&); 1552 extern template ostream& operator<<(ostream&, const complex<double>&); 1553 extern template istream& operator>>(istream&, complex<long double>&); 1554 extern template ostream& operator<<(ostream&, const complex<long double>&); 1555 1556 #ifdef _GLIBCXX_USE_WCHAR_T 1557 extern template wistream& operator>>(wistream&, complex<float>&); 1558 extern template wostream& operator<<(wostream&, const complex<float>&); 1559 extern template wistream& operator>>(wistream&, complex<double>&); 1560 extern template wostream& operator<<(wostream&, const complex<double>&); 1561 extern template wistream& operator>>(wistream&, complex<long double>&); 1562 extern template wostream& operator<<(wostream&, const complex<long double>&); 1563 #endif 1564 #endif 1565 1566 // @} group complex_numbers 1567 1568 _GLIBCXX_END_NAMESPACE_VERSION 1569 } // namespace 1570 1571 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1572 { 1573 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1574 1575 // See ext/type_traits.h for the primary template. 1576 template<typename _Tp, typename _Up> 1577 struct __promote_2<std::complex<_Tp>, _Up> 1578 { 1579 public: 1580 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1581 }; 1582 1583 template<typename _Tp, typename _Up> 1584 struct __promote_2<_Tp, std::complex<_Up> > 1585 { 1586 public: 1587 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1588 }; 1589 1590 template<typename _Tp, typename _Up> 1591 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1592 { 1593 public: 1594 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1595 }; 1596 1597 _GLIBCXX_END_NAMESPACE_VERSION 1598 } // namespace 1599 1600 #if __cplusplus >= 201103L 1601 1602 namespace std _GLIBCXX_VISIBILITY(default) 1603 { 1604 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1605 1606 // Forward declarations. 1607 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1608 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1609 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1610 1611 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1612 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1613 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1614 // DR 595. 1615 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1616 1617 template<typename _Tp> 1618 inline std::complex<_Tp> 1619 __complex_acos(const std::complex<_Tp>& __z) 1620 { 1621 const std::complex<_Tp> __t = std::asin(__z); 1622 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1623 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1624 } 1625 1626 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1627 inline __complex__ float 1628 __complex_acos(__complex__ float __z) 1629 { return __builtin_cacosf(__z); } 1630 1631 inline __complex__ double 1632 __complex_acos(__complex__ double __z) 1633 { return __builtin_cacos(__z); } 1634 1635 inline __complex__ long double 1636 __complex_acos(const __complex__ long double& __z) 1637 { return __builtin_cacosl(__z); } 1638 1639 template<typename _Tp> 1640 inline std::complex<_Tp> 1641 acos(const std::complex<_Tp>& __z) 1642 { return __complex_acos(__z.__rep()); } 1643 #else 1644 /// acos(__z) [8.1.2]. 1645 // Effects: Behaves the same as C99 function cacos, defined 1646 // in subclause 7.3.5.1. 1647 template<typename _Tp> 1648 inline std::complex<_Tp> 1649 acos(const std::complex<_Tp>& __z) 1650 { return __complex_acos(__z); } 1651 #endif 1652 1653 template<typename _Tp> 1654 inline std::complex<_Tp> 1655 __complex_asin(const std::complex<_Tp>& __z) 1656 { 1657 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1658 __t = std::asinh(__t); 1659 return std::complex<_Tp>(__t.imag(), -__t.real()); 1660 } 1661 1662 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1663 inline __complex__ float 1664 __complex_asin(__complex__ float __z) 1665 { return __builtin_casinf(__z); } 1666 1667 inline __complex__ double 1668 __complex_asin(__complex__ double __z) 1669 { return __builtin_casin(__z); } 1670 1671 inline __complex__ long double 1672 __complex_asin(const __complex__ long double& __z) 1673 { return __builtin_casinl(__z); } 1674 1675 template<typename _Tp> 1676 inline std::complex<_Tp> 1677 asin(const std::complex<_Tp>& __z) 1678 { return __complex_asin(__z.__rep()); } 1679 #else 1680 /// asin(__z) [8.1.3]. 1681 // Effects: Behaves the same as C99 function casin, defined 1682 // in subclause 7.3.5.2. 1683 template<typename _Tp> 1684 inline std::complex<_Tp> 1685 asin(const std::complex<_Tp>& __z) 1686 { return __complex_asin(__z); } 1687 #endif 1688 1689 template<typename _Tp> 1690 std::complex<_Tp> 1691 __complex_atan(const std::complex<_Tp>& __z) 1692 { 1693 const _Tp __r2 = __z.real() * __z.real(); 1694 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1695 1696 _Tp __num = __z.imag() + _Tp(1.0); 1697 _Tp __den = __z.imag() - _Tp(1.0); 1698 1699 __num = __r2 + __num * __num; 1700 __den = __r2 + __den * __den; 1701 1702 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1703 _Tp(0.25) * log(__num / __den)); 1704 } 1705 1706 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1707 inline __complex__ float 1708 __complex_atan(__complex__ float __z) 1709 { return __builtin_catanf(__z); } 1710 1711 inline __complex__ double 1712 __complex_atan(__complex__ double __z) 1713 { return __builtin_catan(__z); } 1714 1715 inline __complex__ long double 1716 __complex_atan(const __complex__ long double& __z) 1717 { return __builtin_catanl(__z); } 1718 1719 template<typename _Tp> 1720 inline std::complex<_Tp> 1721 atan(const std::complex<_Tp>& __z) 1722 { return __complex_atan(__z.__rep()); } 1723 #else 1724 /// atan(__z) [8.1.4]. 1725 // Effects: Behaves the same as C99 function catan, defined 1726 // in subclause 7.3.5.3. 1727 template<typename _Tp> 1728 inline std::complex<_Tp> 1729 atan(const std::complex<_Tp>& __z) 1730 { return __complex_atan(__z); } 1731 #endif 1732 1733 template<typename _Tp> 1734 std::complex<_Tp> 1735 __complex_acosh(const std::complex<_Tp>& __z) 1736 { 1737 // Kahan's formula. 1738 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1739 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1740 } 1741 1742 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1743 inline __complex__ float 1744 __complex_acosh(__complex__ float __z) 1745 { return __builtin_cacoshf(__z); } 1746 1747 inline __complex__ double 1748 __complex_acosh(__complex__ double __z) 1749 { return __builtin_cacosh(__z); } 1750 1751 inline __complex__ long double 1752 __complex_acosh(const __complex__ long double& __z) 1753 { return __builtin_cacoshl(__z); } 1754 1755 template<typename _Tp> 1756 inline std::complex<_Tp> 1757 acosh(const std::complex<_Tp>& __z) 1758 { return __complex_acosh(__z.__rep()); } 1759 #else 1760 /// acosh(__z) [8.1.5]. 1761 // Effects: Behaves the same as C99 function cacosh, defined 1762 // in subclause 7.3.6.1. 1763 template<typename _Tp> 1764 inline std::complex<_Tp> 1765 acosh(const std::complex<_Tp>& __z) 1766 { return __complex_acosh(__z); } 1767 #endif 1768 1769 template<typename _Tp> 1770 std::complex<_Tp> 1771 __complex_asinh(const std::complex<_Tp>& __z) 1772 { 1773 std::complex<_Tp> __t((__z.real() - __z.imag()) 1774 * (__z.real() + __z.imag()) + _Tp(1.0), 1775 _Tp(2.0) * __z.real() * __z.imag()); 1776 __t = std::sqrt(__t); 1777 1778 return std::log(__t + __z); 1779 } 1780 1781 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1782 inline __complex__ float 1783 __complex_asinh(__complex__ float __z) 1784 { return __builtin_casinhf(__z); } 1785 1786 inline __complex__ double 1787 __complex_asinh(__complex__ double __z) 1788 { return __builtin_casinh(__z); } 1789 1790 inline __complex__ long double 1791 __complex_asinh(const __complex__ long double& __z) 1792 { return __builtin_casinhl(__z); } 1793 1794 template<typename _Tp> 1795 inline std::complex<_Tp> 1796 asinh(const std::complex<_Tp>& __z) 1797 { return __complex_asinh(__z.__rep()); } 1798 #else 1799 /// asinh(__z) [8.1.6]. 1800 // Effects: Behaves the same as C99 function casin, defined 1801 // in subclause 7.3.6.2. 1802 template<typename _Tp> 1803 inline std::complex<_Tp> 1804 asinh(const std::complex<_Tp>& __z) 1805 { return __complex_asinh(__z); } 1806 #endif 1807 1808 template<typename _Tp> 1809 std::complex<_Tp> 1810 __complex_atanh(const std::complex<_Tp>& __z) 1811 { 1812 const _Tp __i2 = __z.imag() * __z.imag(); 1813 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1814 1815 _Tp __num = _Tp(1.0) + __z.real(); 1816 _Tp __den = _Tp(1.0) - __z.real(); 1817 1818 __num = __i2 + __num * __num; 1819 __den = __i2 + __den * __den; 1820 1821 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1822 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1823 } 1824 1825 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1826 inline __complex__ float 1827 __complex_atanh(__complex__ float __z) 1828 { return __builtin_catanhf(__z); } 1829 1830 inline __complex__ double 1831 __complex_atanh(__complex__ double __z) 1832 { return __builtin_catanh(__z); } 1833 1834 inline __complex__ long double 1835 __complex_atanh(const __complex__ long double& __z) 1836 { return __builtin_catanhl(__z); } 1837 1838 template<typename _Tp> 1839 inline std::complex<_Tp> 1840 atanh(const std::complex<_Tp>& __z) 1841 { return __complex_atanh(__z.__rep()); } 1842 #else 1843 /// atanh(__z) [8.1.7]. 1844 // Effects: Behaves the same as C99 function catanh, defined 1845 // in subclause 7.3.6.3. 1846 template<typename _Tp> 1847 inline std::complex<_Tp> 1848 atanh(const std::complex<_Tp>& __z) 1849 { return __complex_atanh(__z); } 1850 #endif 1851 1852 template<typename _Tp> 1853 inline _Tp 1854 /// fabs(__z) [8.1.8]. 1855 // Effects: Behaves the same as C99 function cabs, defined 1856 // in subclause 7.3.8.1. 1857 fabs(const std::complex<_Tp>& __z) 1858 { return std::abs(__z); } 1859 1860 /// Additional overloads [8.1.9]. 1861 template<typename _Tp> 1862 inline typename __gnu_cxx::__promote<_Tp>::__type 1863 arg(_Tp __x) 1864 { 1865 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1866 #if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1867 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1868 : __type(); 1869 #else 1870 return std::arg(std::complex<__type>(__x)); 1871 #endif 1872 } 1873 1874 template<typename _Tp> 1875 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1876 imag(_Tp) 1877 { return _Tp(); } 1878 1879 template<typename _Tp> 1880 inline typename __gnu_cxx::__promote<_Tp>::__type 1881 norm(_Tp __x) 1882 { 1883 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1884 return __type(__x) * __type(__x); 1885 } 1886 1887 template<typename _Tp> 1888 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1889 real(_Tp __x) 1890 { return __x; } 1891 1892 template<typename _Tp, typename _Up> 1893 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1894 pow(const std::complex<_Tp>& __x, const _Up& __y) 1895 { 1896 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1897 return std::pow(std::complex<__type>(__x), __type(__y)); 1898 } 1899 1900 template<typename _Tp, typename _Up> 1901 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1902 pow(const _Tp& __x, const std::complex<_Up>& __y) 1903 { 1904 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1905 return std::pow(__type(__x), std::complex<__type>(__y)); 1906 } 1907 1908 template<typename _Tp, typename _Up> 1909 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1910 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1911 { 1912 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1913 return std::pow(std::complex<__type>(__x), 1914 std::complex<__type>(__y)); 1915 } 1916 1917 // Forward declarations. 1918 // DR 781. 1919 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); 1920 1921 template<typename _Tp> 1922 std::complex<_Tp> 1923 __complex_proj(const std::complex<_Tp>& __z) 1924 { 1925 const _Tp __den = (__z.real() * __z.real() 1926 + __z.imag() * __z.imag() + _Tp(1.0)); 1927 1928 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, 1929 (_Tp(2.0) * __z.imag()) / __den); 1930 } 1931 1932 #if _GLIBCXX_USE_C99_COMPLEX 1933 inline __complex__ float 1934 __complex_proj(__complex__ float __z) 1935 { return __builtin_cprojf(__z); } 1936 1937 inline __complex__ double 1938 __complex_proj(__complex__ double __z) 1939 { return __builtin_cproj(__z); } 1940 1941 inline __complex__ long double 1942 __complex_proj(const __complex__ long double& __z) 1943 { return __builtin_cprojl(__z); } 1944 1945 template<typename _Tp> 1946 inline std::complex<_Tp> 1947 proj(const std::complex<_Tp>& __z) 1948 { return __complex_proj(__z.__rep()); } 1949 #else 1950 template<typename _Tp> 1951 inline std::complex<_Tp> 1952 proj(const std::complex<_Tp>& __z) 1953 { return __complex_proj(__z); } 1954 #endif 1955 1956 template<typename _Tp> 1957 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 1958 proj(_Tp __x) 1959 { 1960 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1961 return std::proj(std::complex<__type>(__x)); 1962 } 1963 1964 template<typename _Tp> 1965 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 1966 conj(_Tp __x) 1967 { 1968 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1969 return std::complex<__type>(__x, -__type()); 1970 } 1971 1972 #if __cplusplus > 201103L 1973 1974 inline namespace literals { 1975 inline namespace complex_literals { 1976 #pragma GCC diagnostic push 1977 #pragma GCC diagnostic ignored "-Wliteral-suffix" 1978 #define __cpp_lib_complex_udls 201309 1979 1980 constexpr std::complex<float> 1981 operator""if(long double __num) 1982 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1983 1984 constexpr std::complex<float> 1985 operator""if(unsigned long long __num) 1986 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1987 1988 constexpr std::complex<double> 1989 operator""i(long double __num) 1990 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1991 1992 constexpr std::complex<double> 1993 operator""i(unsigned long long __num) 1994 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1995 1996 constexpr std::complex<long double> 1997 operator""il(long double __num) 1998 { return std::complex<long double>{0.0L, __num}; } 1999 2000 constexpr std::complex<long double> 2001 operator""il(unsigned long long __num) 2002 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } 2003 2004 #pragma GCC diagnostic pop 2005 } // inline namespace complex_literals 2006 } // inline namespace literals 2007 2008 #endif // C++14 2009 2010 _GLIBCXX_END_NAMESPACE_VERSION 2011 } // namespace 2012 2013 #endif // C++11 2014 2015 #endif /* _GLIBCXX_COMPLEX */ 2016
Indexes created Tue Sep 08 00:25:21 UTC 2026