complex revision 1.1.1.5
1 // The template and inlines for the -*- C++ -*- complex number classes. 2 3 // Copyright (C) 1997-2016 Free Software Foundation, Inc. 4 // 5 // This file is part of the GNU ISO C++ Library. This library is free 6 // software; you can redistribute it and/or modify it under the 7 // terms of the GNU General Public License as published by the 8 // Free Software Foundation; either version 3, or (at your option) 9 // any later version. 10 11 // This library is distributed in the hope that it will be useful, 12 // but WITHOUT ANY WARRANTY; without even the implied warranty of 13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 // GNU General Public License for more details. 15 16 // Under Section 7 of GPL version 3, you are granted additional 17 // permissions described in the GCC Runtime Library Exception, version 18 // 3.1, as published by the Free Software Foundation. 19 20 // You should have received a copy of the GNU General Public License and 21 // a copy of the GCC Runtime Library Exception along with this program; 22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23 // <http://www.gnu.org/licenses/>. 24 25 /** @file include/complex 26 * This is a Standard C++ Library header. 27 */ 28 29 // 30 // ISO C++ 14882: 26.2 Complex Numbers 31 // Note: this is not a conforming implementation. 32 // Initially implemented by Ulrich Drepper <drepper (a] cygnus.com> 33 // Improved by Gabriel Dos Reis <dosreis (a] cmla.ens-cachan.fr> 34 // 35 36 #ifndef _GLIBCXX_COMPLEX 37 #define _GLIBCXX_COMPLEX 1 38 39 #pragma GCC system_header 40 41 #include <bits/c++config.h> 42 #include <bits/cpp_type_traits.h> 43 #include <ext/type_traits.h> 44 #include <cmath> 45 #include <sstream> 46 47 // Get rid of a macro possibly defined in <complex.h> 48 #undef complex 49 50 namespace std _GLIBCXX_VISIBILITY(default) 51 { 52 _GLIBCXX_BEGIN_NAMESPACE_VERSION 53 54 /** 55 * @defgroup complex_numbers Complex Numbers 56 * @ingroup numerics 57 * 58 * Classes and functions for complex numbers. 59 * @{ 60 */ 61 62 // Forward declarations. 63 template<typename _Tp> class complex; 64 template<> class complex<float>; 65 template<> class complex<double>; 66 template<> class complex<long double>; 67 68 /// Return magnitude of @a z. 69 template<typename _Tp> _Tp abs(const complex<_Tp>&); 70 /// Return phase angle of @a z. 71 template<typename _Tp> _Tp arg(const complex<_Tp>&); 72 /// Return @a z magnitude squared. 73 template<typename _Tp> _Tp norm(const complex<_Tp>&); 74 75 /// Return complex conjugate of @a z. 76 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); 77 /// Return complex with magnitude @a rho and angle @a theta. 78 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 79 80 // Transcendentals: 81 /// Return complex cosine of @a z. 82 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 83 /// Return complex hyperbolic cosine of @a z. 84 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 85 /// Return complex base e exponential of @a z. 86 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 87 /// Return complex natural logarithm of @a z. 88 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 89 /// Return complex base 10 logarithm of @a z. 90 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 91 /// Return @a x to the @a y'th power. 92 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 93 /// Return @a x to the @a y'th power. 94 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 95 /// Return @a x to the @a y'th power. 96 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 97 const complex<_Tp>&); 98 /// Return @a x to the @a y'th power. 99 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 100 /// Return complex sine of @a z. 101 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 102 /// Return complex hyperbolic sine of @a z. 103 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 104 /// Return complex square root of @a z. 105 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 106 /// Return complex tangent of @a z. 107 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 108 /// Return complex hyperbolic tangent of @a z. 109 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 110 111 112 // 26.2.2 Primary template class complex 113 /** 114 * Template to represent complex numbers. 115 * 116 * Specializations for float, double, and long double are part of the 117 * library. Results with any other type are not guaranteed. 118 * 119 * @param Tp Type of real and imaginary values. 120 */ 121 template<typename _Tp> 122 struct complex 123 { 124 /// Value typedef. 125 typedef _Tp value_type; 126 127 /// Default constructor. First parameter is x, second parameter is y. 128 /// Unspecified parameters default to 0. 129 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 130 : _M_real(__r), _M_imag(__i) { } 131 132 // Let the compiler synthesize the copy constructor 133 #if __cplusplus >= 201103L 134 constexpr complex(const complex&) = default; 135 #endif 136 137 /// Converting constructor. 138 template<typename _Up> 139 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 140 : _M_real(__z.real()), _M_imag(__z.imag()) { } 141 142 #if __cplusplus >= 201103L 143 // _GLIBCXX_RESOLVE_LIB_DEFECTS 144 // DR 387. std::complex over-encapsulated. 145 _GLIBCXX_ABI_TAG_CXX11 146 constexpr _Tp 147 real() const { return _M_real; } 148 149 _GLIBCXX_ABI_TAG_CXX11 150 constexpr _Tp 151 imag() const { return _M_imag; } 152 #else 153 /// Return real part of complex number. 154 _Tp& 155 real() { return _M_real; } 156 157 /// Return real part of complex number. 158 const _Tp& 159 real() const { return _M_real; } 160 161 /// Return imaginary part of complex number. 162 _Tp& 163 imag() { return _M_imag; } 164 165 /// Return imaginary part of complex number. 166 const _Tp& 167 imag() const { return _M_imag; } 168 #endif 169 170 // _GLIBCXX_RESOLVE_LIB_DEFECTS 171 // DR 387. std::complex over-encapsulated. 172 void 173 real(_Tp __val) { _M_real = __val; } 174 175 void 176 imag(_Tp __val) { _M_imag = __val; } 177 178 /// Assign a scalar to this complex number. 179 complex<_Tp>& operator=(const _Tp&); 180 181 /// Add a scalar to this complex number. 182 // 26.2.5/1 183 complex<_Tp>& 184 operator+=(const _Tp& __t) 185 { 186 _M_real += __t; 187 return *this; 188 } 189 190 /// Subtract a scalar from this complex number. 191 // 26.2.5/3 192 complex<_Tp>& 193 operator-=(const _Tp& __t) 194 { 195 _M_real -= __t; 196 return *this; 197 } 198 199 /// Multiply this complex number by a scalar. 200 complex<_Tp>& operator*=(const _Tp&); 201 /// Divide this complex number by a scalar. 202 complex<_Tp>& operator/=(const _Tp&); 203 204 // Let the compiler synthesize the copy assignment operator 205 #if __cplusplus >= 201103L 206 complex& operator=(const complex&) = default; 207 #endif 208 209 /// Assign another complex number to this one. 210 template<typename _Up> 211 complex<_Tp>& operator=(const complex<_Up>&); 212 /// Add another complex number to this one. 213 template<typename _Up> 214 complex<_Tp>& operator+=(const complex<_Up>&); 215 /// Subtract another complex number from this one. 216 template<typename _Up> 217 complex<_Tp>& operator-=(const complex<_Up>&); 218 /// Multiply this complex number by another. 219 template<typename _Up> 220 complex<_Tp>& operator*=(const complex<_Up>&); 221 /// Divide this complex number by another. 222 template<typename _Up> 223 complex<_Tp>& operator/=(const complex<_Up>&); 224 225 _GLIBCXX_CONSTEXPR complex __rep() const 226 { return *this; } 227 228 private: 229 _Tp _M_real; 230 _Tp _M_imag; 231 }; 232 233 template<typename _Tp> 234 complex<_Tp>& 235 complex<_Tp>::operator=(const _Tp& __t) 236 { 237 _M_real = __t; 238 _M_imag = _Tp(); 239 return *this; 240 } 241 242 // 26.2.5/5 243 template<typename _Tp> 244 complex<_Tp>& 245 complex<_Tp>::operator*=(const _Tp& __t) 246 { 247 _M_real *= __t; 248 _M_imag *= __t; 249 return *this; 250 } 251 252 // 26.2.5/7 253 template<typename _Tp> 254 complex<_Tp>& 255 complex<_Tp>::operator/=(const _Tp& __t) 256 { 257 _M_real /= __t; 258 _M_imag /= __t; 259 return *this; 260 } 261 262 template<typename _Tp> 263 template<typename _Up> 264 complex<_Tp>& 265 complex<_Tp>::operator=(const complex<_Up>& __z) 266 { 267 _M_real = __z.real(); 268 _M_imag = __z.imag(); 269 return *this; 270 } 271 272 // 26.2.5/9 273 template<typename _Tp> 274 template<typename _Up> 275 complex<_Tp>& 276 complex<_Tp>::operator+=(const complex<_Up>& __z) 277 { 278 _M_real += __z.real(); 279 _M_imag += __z.imag(); 280 return *this; 281 } 282 283 // 26.2.5/11 284 template<typename _Tp> 285 template<typename _Up> 286 complex<_Tp>& 287 complex<_Tp>::operator-=(const complex<_Up>& __z) 288 { 289 _M_real -= __z.real(); 290 _M_imag -= __z.imag(); 291 return *this; 292 } 293 294 // 26.2.5/13 295 // XXX: This is a grammar school implementation. 296 template<typename _Tp> 297 template<typename _Up> 298 complex<_Tp>& 299 complex<_Tp>::operator*=(const complex<_Up>& __z) 300 { 301 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 302 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 303 _M_real = __r; 304 return *this; 305 } 306 307 // 26.2.5/15 308 // XXX: This is a grammar school implementation. 309 template<typename _Tp> 310 template<typename _Up> 311 complex<_Tp>& 312 complex<_Tp>::operator/=(const complex<_Up>& __z) 313 { 314 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 315 const _Tp __n = std::norm(__z); 316 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 317 _M_real = __r / __n; 318 return *this; 319 } 320 321 // Operators: 322 //@{ 323 /// Return new complex value @a x plus @a y. 324 template<typename _Tp> 325 inline complex<_Tp> 326 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 327 { 328 complex<_Tp> __r = __x; 329 __r += __y; 330 return __r; 331 } 332 333 template<typename _Tp> 334 inline complex<_Tp> 335 operator+(const complex<_Tp>& __x, const _Tp& __y) 336 { 337 complex<_Tp> __r = __x; 338 __r += __y; 339 return __r; 340 } 341 342 template<typename _Tp> 343 inline complex<_Tp> 344 operator+(const _Tp& __x, const complex<_Tp>& __y) 345 { 346 complex<_Tp> __r = __y; 347 __r += __x; 348 return __r; 349 } 350 //@} 351 352 //@{ 353 /// Return new complex value @a x minus @a y. 354 template<typename _Tp> 355 inline complex<_Tp> 356 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 357 { 358 complex<_Tp> __r = __x; 359 __r -= __y; 360 return __r; 361 } 362 363 template<typename _Tp> 364 inline complex<_Tp> 365 operator-(const complex<_Tp>& __x, const _Tp& __y) 366 { 367 complex<_Tp> __r = __x; 368 __r -= __y; 369 return __r; 370 } 371 372 template<typename _Tp> 373 inline complex<_Tp> 374 operator-(const _Tp& __x, const complex<_Tp>& __y) 375 { 376 complex<_Tp> __r(__x, -__y.imag()); 377 __r -= __y.real(); 378 return __r; 379 } 380 //@} 381 382 //@{ 383 /// Return new complex value @a x times @a y. 384 template<typename _Tp> 385 inline complex<_Tp> 386 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 387 { 388 complex<_Tp> __r = __x; 389 __r *= __y; 390 return __r; 391 } 392 393 template<typename _Tp> 394 inline complex<_Tp> 395 operator*(const complex<_Tp>& __x, const _Tp& __y) 396 { 397 complex<_Tp> __r = __x; 398 __r *= __y; 399 return __r; 400 } 401 402 template<typename _Tp> 403 inline complex<_Tp> 404 operator*(const _Tp& __x, const complex<_Tp>& __y) 405 { 406 complex<_Tp> __r = __y; 407 __r *= __x; 408 return __r; 409 } 410 //@} 411 412 //@{ 413 /// Return new complex value @a x divided by @a y. 414 template<typename _Tp> 415 inline complex<_Tp> 416 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 417 { 418 complex<_Tp> __r = __x; 419 __r /= __y; 420 return __r; 421 } 422 423 template<typename _Tp> 424 inline complex<_Tp> 425 operator/(const complex<_Tp>& __x, const _Tp& __y) 426 { 427 complex<_Tp> __r = __x; 428 __r /= __y; 429 return __r; 430 } 431 432 template<typename _Tp> 433 inline complex<_Tp> 434 operator/(const _Tp& __x, const complex<_Tp>& __y) 435 { 436 complex<_Tp> __r = __x; 437 __r /= __y; 438 return __r; 439 } 440 //@} 441 442 /// Return @a x. 443 template<typename _Tp> 444 inline complex<_Tp> 445 operator+(const complex<_Tp>& __x) 446 { return __x; } 447 448 /// Return complex negation of @a x. 449 template<typename _Tp> 450 inline complex<_Tp> 451 operator-(const complex<_Tp>& __x) 452 { return complex<_Tp>(-__x.real(), -__x.imag()); } 453 454 //@{ 455 /// Return true if @a x is equal to @a y. 456 template<typename _Tp> 457 inline _GLIBCXX_CONSTEXPR bool 458 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 459 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 460 461 template<typename _Tp> 462 inline _GLIBCXX_CONSTEXPR bool 463 operator==(const complex<_Tp>& __x, const _Tp& __y) 464 { return __x.real() == __y && __x.imag() == _Tp(); } 465 466 template<typename _Tp> 467 inline _GLIBCXX_CONSTEXPR bool 468 operator==(const _Tp& __x, const complex<_Tp>& __y) 469 { return __x == __y.real() && _Tp() == __y.imag(); } 470 //@} 471 472 //@{ 473 /// Return false if @a x is equal to @a y. 474 template<typename _Tp> 475 inline _GLIBCXX_CONSTEXPR bool 476 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 477 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 478 479 template<typename _Tp> 480 inline _GLIBCXX_CONSTEXPR bool 481 operator!=(const complex<_Tp>& __x, const _Tp& __y) 482 { return __x.real() != __y || __x.imag() != _Tp(); } 483 484 template<typename _Tp> 485 inline _GLIBCXX_CONSTEXPR bool 486 operator!=(const _Tp& __x, const complex<_Tp>& __y) 487 { return __x != __y.real() || _Tp() != __y.imag(); } 488 //@} 489 490 /// Extraction operator for complex values. 491 template<typename _Tp, typename _CharT, class _Traits> 492 basic_istream<_CharT, _Traits>& 493 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 494 { 495 _Tp __re_x, __im_x; 496 _CharT __ch; 497 __is >> __ch; 498 if (__ch == '(') 499 { 500 __is >> __re_x >> __ch; 501 if (__ch == ',') 502 { 503 __is >> __im_x >> __ch; 504 if (__ch == ')') 505 __x = complex<_Tp>(__re_x, __im_x); 506 else 507 __is.setstate(ios_base::failbit); 508 } 509 else if (__ch == ')') 510 __x = __re_x; 511 else 512 __is.setstate(ios_base::failbit); 513 } 514 else 515 { 516 __is.putback(__ch); 517 __is >> __re_x; 518 __x = __re_x; 519 } 520 return __is; 521 } 522 523 /// Insertion operator for complex values. 524 template<typename _Tp, typename _CharT, class _Traits> 525 basic_ostream<_CharT, _Traits>& 526 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 527 { 528 basic_ostringstream<_CharT, _Traits> __s; 529 __s.flags(__os.flags()); 530 __s.imbue(__os.getloc()); 531 __s.precision(__os.precision()); 532 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 533 return __os << __s.str(); 534 } 535 536 // Values 537 #if __cplusplus >= 201103L 538 template<typename _Tp> 539 constexpr _Tp 540 real(const complex<_Tp>& __z) 541 { return __z.real(); } 542 543 template<typename _Tp> 544 constexpr _Tp 545 imag(const complex<_Tp>& __z) 546 { return __z.imag(); } 547 #else 548 template<typename _Tp> 549 inline _Tp& 550 real(complex<_Tp>& __z) 551 { return __z.real(); } 552 553 template<typename _Tp> 554 inline const _Tp& 555 real(const complex<_Tp>& __z) 556 { return __z.real(); } 557 558 template<typename _Tp> 559 inline _Tp& 560 imag(complex<_Tp>& __z) 561 { return __z.imag(); } 562 563 template<typename _Tp> 564 inline const _Tp& 565 imag(const complex<_Tp>& __z) 566 { return __z.imag(); } 567 #endif 568 569 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 570 template<typename _Tp> 571 inline _Tp 572 __complex_abs(const complex<_Tp>& __z) 573 { 574 _Tp __x = __z.real(); 575 _Tp __y = __z.imag(); 576 const _Tp __s = std::max(abs(__x), abs(__y)); 577 if (__s == _Tp()) // well ... 578 return __s; 579 __x /= __s; 580 __y /= __s; 581 return __s * sqrt(__x * __x + __y * __y); 582 } 583 584 #if _GLIBCXX_USE_C99_COMPLEX 585 inline float 586 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 587 588 inline double 589 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 590 591 inline long double 592 __complex_abs(const __complex__ long double& __z) 593 { return __builtin_cabsl(__z); } 594 595 template<typename _Tp> 596 inline _Tp 597 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 598 #else 599 template<typename _Tp> 600 inline _Tp 601 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 602 #endif 603 604 605 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 606 template<typename _Tp> 607 inline _Tp 608 __complex_arg(const complex<_Tp>& __z) 609 { return atan2(__z.imag(), __z.real()); } 610 611 #if _GLIBCXX_USE_C99_COMPLEX 612 inline float 613 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 614 615 inline double 616 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 617 618 inline long double 619 __complex_arg(const __complex__ long double& __z) 620 { return __builtin_cargl(__z); } 621 622 template<typename _Tp> 623 inline _Tp 624 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 625 #else 626 template<typename _Tp> 627 inline _Tp 628 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 629 #endif 630 631 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 632 // As defined, norm() is -not- a norm is the common mathematical 633 // sense used in numerics. The helper class _Norm_helper<> tries to 634 // distinguish between builtin floating point and the rest, so as 635 // to deliver an answer as close as possible to the real value. 636 template<bool> 637 struct _Norm_helper 638 { 639 template<typename _Tp> 640 static inline _Tp _S_do_it(const complex<_Tp>& __z) 641 { 642 const _Tp __x = __z.real(); 643 const _Tp __y = __z.imag(); 644 return __x * __x + __y * __y; 645 } 646 }; 647 648 template<> 649 struct _Norm_helper<true> 650 { 651 template<typename _Tp> 652 static inline _Tp _S_do_it(const complex<_Tp>& __z) 653 { 654 _Tp __res = std::abs(__z); 655 return __res * __res; 656 } 657 }; 658 659 template<typename _Tp> 660 inline _Tp 661 norm(const complex<_Tp>& __z) 662 { 663 return _Norm_helper<__is_floating<_Tp>::__value 664 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 665 } 666 667 template<typename _Tp> 668 inline complex<_Tp> 669 polar(const _Tp& __rho, const _Tp& __theta) 670 { 671 __glibcxx_assert( __rho >= 0 ); 672 return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); 673 } 674 675 template<typename _Tp> 676 inline complex<_Tp> 677 conj(const complex<_Tp>& __z) 678 { return complex<_Tp>(__z.real(), -__z.imag()); } 679 680 // Transcendentals 681 682 // 26.2.8/1 cos(__z): Returns the cosine of __z. 683 template<typename _Tp> 684 inline complex<_Tp> 685 __complex_cos(const complex<_Tp>& __z) 686 { 687 const _Tp __x = __z.real(); 688 const _Tp __y = __z.imag(); 689 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 690 } 691 692 #if _GLIBCXX_USE_C99_COMPLEX 693 inline __complex__ float 694 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 695 696 inline __complex__ double 697 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 698 699 inline __complex__ long double 700 __complex_cos(const __complex__ long double& __z) 701 { return __builtin_ccosl(__z); } 702 703 template<typename _Tp> 704 inline complex<_Tp> 705 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 706 #else 707 template<typename _Tp> 708 inline complex<_Tp> 709 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 710 #endif 711 712 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 713 template<typename _Tp> 714 inline complex<_Tp> 715 __complex_cosh(const complex<_Tp>& __z) 716 { 717 const _Tp __x = __z.real(); 718 const _Tp __y = __z.imag(); 719 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 720 } 721 722 #if _GLIBCXX_USE_C99_COMPLEX 723 inline __complex__ float 724 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 725 726 inline __complex__ double 727 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 728 729 inline __complex__ long double 730 __complex_cosh(const __complex__ long double& __z) 731 { return __builtin_ccoshl(__z); } 732 733 template<typename _Tp> 734 inline complex<_Tp> 735 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 736 #else 737 template<typename _Tp> 738 inline complex<_Tp> 739 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 740 #endif 741 742 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 743 template<typename _Tp> 744 inline complex<_Tp> 745 __complex_exp(const complex<_Tp>& __z) 746 { return std::polar<_Tp>(exp(__z.real()), __z.imag()); } 747 748 #if _GLIBCXX_USE_C99_COMPLEX 749 inline __complex__ float 750 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 751 752 inline __complex__ double 753 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 754 755 inline __complex__ long double 756 __complex_exp(const __complex__ long double& __z) 757 { return __builtin_cexpl(__z); } 758 759 template<typename _Tp> 760 inline complex<_Tp> 761 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 762 #else 763 template<typename _Tp> 764 inline complex<_Tp> 765 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 766 #endif 767 768 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 769 // The branch cut is along the negative axis. 770 template<typename _Tp> 771 inline complex<_Tp> 772 __complex_log(const complex<_Tp>& __z) 773 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 774 775 #if _GLIBCXX_USE_C99_COMPLEX 776 inline __complex__ float 777 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 778 779 inline __complex__ double 780 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 781 782 inline __complex__ long double 783 __complex_log(const __complex__ long double& __z) 784 { return __builtin_clogl(__z); } 785 786 template<typename _Tp> 787 inline complex<_Tp> 788 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 789 #else 790 template<typename _Tp> 791 inline complex<_Tp> 792 log(const complex<_Tp>& __z) { return __complex_log(__z); } 793 #endif 794 795 template<typename _Tp> 796 inline complex<_Tp> 797 log10(const complex<_Tp>& __z) 798 { return std::log(__z) / log(_Tp(10.0)); } 799 800 // 26.2.8/10 sin(__z): Returns the sine of __z. 801 template<typename _Tp> 802 inline complex<_Tp> 803 __complex_sin(const complex<_Tp>& __z) 804 { 805 const _Tp __x = __z.real(); 806 const _Tp __y = __z.imag(); 807 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 808 } 809 810 #if _GLIBCXX_USE_C99_COMPLEX 811 inline __complex__ float 812 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 813 814 inline __complex__ double 815 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 816 817 inline __complex__ long double 818 __complex_sin(const __complex__ long double& __z) 819 { return __builtin_csinl(__z); } 820 821 template<typename _Tp> 822 inline complex<_Tp> 823 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 824 #else 825 template<typename _Tp> 826 inline complex<_Tp> 827 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 828 #endif 829 830 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 831 template<typename _Tp> 832 inline complex<_Tp> 833 __complex_sinh(const complex<_Tp>& __z) 834 { 835 const _Tp __x = __z.real(); 836 const _Tp __y = __z.imag(); 837 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 838 } 839 840 #if _GLIBCXX_USE_C99_COMPLEX 841 inline __complex__ float 842 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 843 844 inline __complex__ double 845 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 846 847 inline __complex__ long double 848 __complex_sinh(const __complex__ long double& __z) 849 { return __builtin_csinhl(__z); } 850 851 template<typename _Tp> 852 inline complex<_Tp> 853 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 854 #else 855 template<typename _Tp> 856 inline complex<_Tp> 857 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 858 #endif 859 860 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 861 // The branch cut is on the negative axis. 862 template<typename _Tp> 863 complex<_Tp> 864 __complex_sqrt(const complex<_Tp>& __z) 865 { 866 _Tp __x = __z.real(); 867 _Tp __y = __z.imag(); 868 869 if (__x == _Tp()) 870 { 871 _Tp __t = sqrt(abs(__y) / 2); 872 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 873 } 874 else 875 { 876 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 877 _Tp __u = __t / 2; 878 return __x > _Tp() 879 ? complex<_Tp>(__u, __y / __t) 880 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 881 } 882 } 883 884 #if _GLIBCXX_USE_C99_COMPLEX 885 inline __complex__ float 886 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 887 888 inline __complex__ double 889 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 890 891 inline __complex__ long double 892 __complex_sqrt(const __complex__ long double& __z) 893 { return __builtin_csqrtl(__z); } 894 895 template<typename _Tp> 896 inline complex<_Tp> 897 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 898 #else 899 template<typename _Tp> 900 inline complex<_Tp> 901 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 902 #endif 903 904 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 905 906 template<typename _Tp> 907 inline complex<_Tp> 908 __complex_tan(const complex<_Tp>& __z) 909 { return std::sin(__z) / std::cos(__z); } 910 911 #if _GLIBCXX_USE_C99_COMPLEX 912 inline __complex__ float 913 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 914 915 inline __complex__ double 916 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 917 918 inline __complex__ long double 919 __complex_tan(const __complex__ long double& __z) 920 { return __builtin_ctanl(__z); } 921 922 template<typename _Tp> 923 inline complex<_Tp> 924 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 925 #else 926 template<typename _Tp> 927 inline complex<_Tp> 928 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 929 #endif 930 931 932 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 933 934 template<typename _Tp> 935 inline complex<_Tp> 936 __complex_tanh(const complex<_Tp>& __z) 937 { return std::sinh(__z) / std::cosh(__z); } 938 939 #if _GLIBCXX_USE_C99_COMPLEX 940 inline __complex__ float 941 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 942 943 inline __complex__ double 944 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 945 946 inline __complex__ long double 947 __complex_tanh(const __complex__ long double& __z) 948 { return __builtin_ctanhl(__z); } 949 950 template<typename _Tp> 951 inline complex<_Tp> 952 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 953 #else 954 template<typename _Tp> 955 inline complex<_Tp> 956 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 957 #endif 958 959 960 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 961 // raised to the __y-th power. The branch 962 // cut is on the negative axis. 963 template<typename _Tp> 964 complex<_Tp> 965 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 966 { 967 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 968 969 while (__n >>= 1) 970 { 971 __x *= __x; 972 if (__n % 2) 973 __y *= __x; 974 } 975 976 return __y; 977 } 978 979 // In C++11 mode we used to implement the resolution of 980 // DR 844. complex pow return type is ambiguous. 981 // thus the following overload was disabled in that mode. However, doing 982 // that causes all sorts of issues, see, for example: 983 // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html 984 // and also PR57974. 985 template<typename _Tp> 986 inline complex<_Tp> 987 pow(const complex<_Tp>& __z, int __n) 988 { 989 return __n < 0 990 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) 991 : std::__complex_pow_unsigned(__z, __n); 992 } 993 994 template<typename _Tp> 995 complex<_Tp> 996 pow(const complex<_Tp>& __x, const _Tp& __y) 997 { 998 #if ! _GLIBCXX_USE_C99_COMPLEX 999 if (__x == _Tp()) 1000 return _Tp(); 1001 #endif 1002 if (__x.imag() == _Tp() && __x.real() > _Tp()) 1003 return pow(__x.real(), __y); 1004 1005 complex<_Tp> __t = std::log(__x); 1006 return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag()); 1007 } 1008 1009 template<typename _Tp> 1010 inline complex<_Tp> 1011 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1012 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1013 1014 #if _GLIBCXX_USE_C99_COMPLEX 1015 inline __complex__ float 1016 __complex_pow(__complex__ float __x, __complex__ float __y) 1017 { return __builtin_cpowf(__x, __y); } 1018 1019 inline __complex__ double 1020 __complex_pow(__complex__ double __x, __complex__ double __y) 1021 { return __builtin_cpow(__x, __y); } 1022 1023 inline __complex__ long double 1024 __complex_pow(const __complex__ long double& __x, 1025 const __complex__ long double& __y) 1026 { return __builtin_cpowl(__x, __y); } 1027 1028 template<typename _Tp> 1029 inline complex<_Tp> 1030 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1031 { return __complex_pow(__x.__rep(), __y.__rep()); } 1032 #else 1033 template<typename _Tp> 1034 inline complex<_Tp> 1035 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1036 { return __complex_pow(__x, __y); } 1037 #endif 1038 1039 template<typename _Tp> 1040 inline complex<_Tp> 1041 pow(const _Tp& __x, const complex<_Tp>& __y) 1042 { 1043 return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()), 1044 __y.imag() * log(__x)) 1045 : std::pow(complex<_Tp>(__x), __y); 1046 } 1047 1048 /// 26.2.3 complex specializations 1049 /// complex<float> specialization 1050 template<> 1051 struct complex<float> 1052 { 1053 typedef float value_type; 1054 typedef __complex__ float _ComplexT; 1055 1056 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1057 1058 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1059 #if __cplusplus >= 201103L 1060 : _M_value{ __r, __i } { } 1061 #else 1062 { 1063 __real__ _M_value = __r; 1064 __imag__ _M_value = __i; 1065 } 1066 #endif 1067 1068 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1069 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1070 1071 #if __cplusplus >= 201103L 1072 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1073 // DR 387. std::complex over-encapsulated. 1074 __attribute ((__abi_tag__ ("cxx11"))) 1075 constexpr float 1076 real() const { return __real__ _M_value; } 1077 1078 __attribute ((__abi_tag__ ("cxx11"))) 1079 constexpr float 1080 imag() const { return __imag__ _M_value; } 1081 #else 1082 float& 1083 real() { return __real__ _M_value; } 1084 1085 const float& 1086 real() const { return __real__ _M_value; } 1087 1088 float& 1089 imag() { return __imag__ _M_value; } 1090 1091 const float& 1092 imag() const { return __imag__ _M_value; } 1093 #endif 1094 1095 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1096 // DR 387. std::complex over-encapsulated. 1097 void 1098 real(float __val) { __real__ _M_value = __val; } 1099 1100 void 1101 imag(float __val) { __imag__ _M_value = __val; } 1102 1103 complex& 1104 operator=(float __f) 1105 { 1106 _M_value = __f; 1107 return *this; 1108 } 1109 1110 complex& 1111 operator+=(float __f) 1112 { 1113 _M_value += __f; 1114 return *this; 1115 } 1116 1117 complex& 1118 operator-=(float __f) 1119 { 1120 _M_value -= __f; 1121 return *this; 1122 } 1123 1124 complex& 1125 operator*=(float __f) 1126 { 1127 _M_value *= __f; 1128 return *this; 1129 } 1130 1131 complex& 1132 operator/=(float __f) 1133 { 1134 _M_value /= __f; 1135 return *this; 1136 } 1137 1138 // Let the compiler synthesize the copy and assignment 1139 // operator. It always does a pretty good job. 1140 // complex& operator=(const complex&); 1141 1142 template<typename _Tp> 1143 complex& 1144 operator=(const complex<_Tp>& __z) 1145 { 1146 __real__ _M_value = __z.real(); 1147 __imag__ _M_value = __z.imag(); 1148 return *this; 1149 } 1150 1151 template<typename _Tp> 1152 complex& 1153 operator+=(const complex<_Tp>& __z) 1154 { 1155 __real__ _M_value += __z.real(); 1156 __imag__ _M_value += __z.imag(); 1157 return *this; 1158 } 1159 1160 template<class _Tp> 1161 complex& 1162 operator-=(const complex<_Tp>& __z) 1163 { 1164 __real__ _M_value -= __z.real(); 1165 __imag__ _M_value -= __z.imag(); 1166 return *this; 1167 } 1168 1169 template<class _Tp> 1170 complex& 1171 operator*=(const complex<_Tp>& __z) 1172 { 1173 _ComplexT __t; 1174 __real__ __t = __z.real(); 1175 __imag__ __t = __z.imag(); 1176 _M_value *= __t; 1177 return *this; 1178 } 1179 1180 template<class _Tp> 1181 complex& 1182 operator/=(const complex<_Tp>& __z) 1183 { 1184 _ComplexT __t; 1185 __real__ __t = __z.real(); 1186 __imag__ __t = __z.imag(); 1187 _M_value /= __t; 1188 return *this; 1189 } 1190 1191 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1192 1193 private: 1194 _ComplexT _M_value; 1195 }; 1196 1197 /// 26.2.3 complex specializations 1198 /// complex<double> specialization 1199 template<> 1200 struct complex<double> 1201 { 1202 typedef double value_type; 1203 typedef __complex__ double _ComplexT; 1204 1205 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1206 1207 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1208 #if __cplusplus >= 201103L 1209 : _M_value{ __r, __i } { } 1210 #else 1211 { 1212 __real__ _M_value = __r; 1213 __imag__ _M_value = __i; 1214 } 1215 #endif 1216 1217 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1218 : _M_value(__z.__rep()) { } 1219 1220 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1221 1222 #if __cplusplus >= 201103L 1223 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1224 // DR 387. std::complex over-encapsulated. 1225 __attribute ((__abi_tag__ ("cxx11"))) 1226 constexpr double 1227 real() const { return __real__ _M_value; } 1228 1229 __attribute ((__abi_tag__ ("cxx11"))) 1230 constexpr double 1231 imag() const { return __imag__ _M_value; } 1232 #else 1233 double& 1234 real() { return __real__ _M_value; } 1235 1236 const double& 1237 real() const { return __real__ _M_value; } 1238 1239 double& 1240 imag() { return __imag__ _M_value; } 1241 1242 const double& 1243 imag() const { return __imag__ _M_value; } 1244 #endif 1245 1246 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1247 // DR 387. std::complex over-encapsulated. 1248 void 1249 real(double __val) { __real__ _M_value = __val; } 1250 1251 void 1252 imag(double __val) { __imag__ _M_value = __val; } 1253 1254 complex& 1255 operator=(double __d) 1256 { 1257 _M_value = __d; 1258 return *this; 1259 } 1260 1261 complex& 1262 operator+=(double __d) 1263 { 1264 _M_value += __d; 1265 return *this; 1266 } 1267 1268 complex& 1269 operator-=(double __d) 1270 { 1271 _M_value -= __d; 1272 return *this; 1273 } 1274 1275 complex& 1276 operator*=(double __d) 1277 { 1278 _M_value *= __d; 1279 return *this; 1280 } 1281 1282 complex& 1283 operator/=(double __d) 1284 { 1285 _M_value /= __d; 1286 return *this; 1287 } 1288 1289 // The compiler will synthesize this, efficiently. 1290 // complex& operator=(const complex&); 1291 1292 template<typename _Tp> 1293 complex& 1294 operator=(const complex<_Tp>& __z) 1295 { 1296 __real__ _M_value = __z.real(); 1297 __imag__ _M_value = __z.imag(); 1298 return *this; 1299 } 1300 1301 template<typename _Tp> 1302 complex& 1303 operator+=(const complex<_Tp>& __z) 1304 { 1305 __real__ _M_value += __z.real(); 1306 __imag__ _M_value += __z.imag(); 1307 return *this; 1308 } 1309 1310 template<typename _Tp> 1311 complex& 1312 operator-=(const complex<_Tp>& __z) 1313 { 1314 __real__ _M_value -= __z.real(); 1315 __imag__ _M_value -= __z.imag(); 1316 return *this; 1317 } 1318 1319 template<typename _Tp> 1320 complex& 1321 operator*=(const complex<_Tp>& __z) 1322 { 1323 _ComplexT __t; 1324 __real__ __t = __z.real(); 1325 __imag__ __t = __z.imag(); 1326 _M_value *= __t; 1327 return *this; 1328 } 1329 1330 template<typename _Tp> 1331 complex& 1332 operator/=(const complex<_Tp>& __z) 1333 { 1334 _ComplexT __t; 1335 __real__ __t = __z.real(); 1336 __imag__ __t = __z.imag(); 1337 _M_value /= __t; 1338 return *this; 1339 } 1340 1341 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1342 1343 private: 1344 _ComplexT _M_value; 1345 }; 1346 1347 /// 26.2.3 complex specializations 1348 /// complex<long double> specialization 1349 template<> 1350 struct complex<long double> 1351 { 1352 typedef long double value_type; 1353 typedef __complex__ long double _ComplexT; 1354 1355 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1356 1357 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1358 long double __i = 0.0L) 1359 #if __cplusplus >= 201103L 1360 : _M_value{ __r, __i } { } 1361 #else 1362 { 1363 __real__ _M_value = __r; 1364 __imag__ _M_value = __i; 1365 } 1366 #endif 1367 1368 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1369 : _M_value(__z.__rep()) { } 1370 1371 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1372 : _M_value(__z.__rep()) { } 1373 1374 #if __cplusplus >= 201103L 1375 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1376 // DR 387. std::complex over-encapsulated. 1377 __attribute ((__abi_tag__ ("cxx11"))) 1378 constexpr long double 1379 real() const { return __real__ _M_value; } 1380 1381 __attribute ((__abi_tag__ ("cxx11"))) 1382 constexpr long double 1383 imag() const { return __imag__ _M_value; } 1384 #else 1385 long double& 1386 real() { return __real__ _M_value; } 1387 1388 const long double& 1389 real() const { return __real__ _M_value; } 1390 1391 long double& 1392 imag() { return __imag__ _M_value; } 1393 1394 const long double& 1395 imag() const { return __imag__ _M_value; } 1396 #endif 1397 1398 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1399 // DR 387. std::complex over-encapsulated. 1400 void 1401 real(long double __val) { __real__ _M_value = __val; } 1402 1403 void 1404 imag(long double __val) { __imag__ _M_value = __val; } 1405 1406 complex& 1407 operator=(long double __r) 1408 { 1409 _M_value = __r; 1410 return *this; 1411 } 1412 1413 complex& 1414 operator+=(long double __r) 1415 { 1416 _M_value += __r; 1417 return *this; 1418 } 1419 1420 complex& 1421 operator-=(long double __r) 1422 { 1423 _M_value -= __r; 1424 return *this; 1425 } 1426 1427 complex& 1428 operator*=(long double __r) 1429 { 1430 _M_value *= __r; 1431 return *this; 1432 } 1433 1434 complex& 1435 operator/=(long double __r) 1436 { 1437 _M_value /= __r; 1438 return *this; 1439 } 1440 1441 // The compiler knows how to do this efficiently 1442 // complex& operator=(const complex&); 1443 1444 template<typename _Tp> 1445 complex& 1446 operator=(const complex<_Tp>& __z) 1447 { 1448 __real__ _M_value = __z.real(); 1449 __imag__ _M_value = __z.imag(); 1450 return *this; 1451 } 1452 1453 template<typename _Tp> 1454 complex& 1455 operator+=(const complex<_Tp>& __z) 1456 { 1457 __real__ _M_value += __z.real(); 1458 __imag__ _M_value += __z.imag(); 1459 return *this; 1460 } 1461 1462 template<typename _Tp> 1463 complex& 1464 operator-=(const complex<_Tp>& __z) 1465 { 1466 __real__ _M_value -= __z.real(); 1467 __imag__ _M_value -= __z.imag(); 1468 return *this; 1469 } 1470 1471 template<typename _Tp> 1472 complex& 1473 operator*=(const complex<_Tp>& __z) 1474 { 1475 _ComplexT __t; 1476 __real__ __t = __z.real(); 1477 __imag__ __t = __z.imag(); 1478 _M_value *= __t; 1479 return *this; 1480 } 1481 1482 template<typename _Tp> 1483 complex& 1484 operator/=(const complex<_Tp>& __z) 1485 { 1486 _ComplexT __t; 1487 __real__ __t = __z.real(); 1488 __imag__ __t = __z.imag(); 1489 _M_value /= __t; 1490 return *this; 1491 } 1492 1493 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1494 1495 private: 1496 _ComplexT _M_value; 1497 }; 1498 1499 // These bits have to be at the end of this file, so that the 1500 // specializations have all been defined. 1501 inline _GLIBCXX_CONSTEXPR 1502 complex<float>::complex(const complex<double>& __z) 1503 : _M_value(__z.__rep()) { } 1504 1505 inline _GLIBCXX_CONSTEXPR 1506 complex<float>::complex(const complex<long double>& __z) 1507 : _M_value(__z.__rep()) { } 1508 1509 inline _GLIBCXX_CONSTEXPR 1510 complex<double>::complex(const complex<long double>& __z) 1511 : _M_value(__z.__rep()) { } 1512 1513 // Inhibit implicit instantiations for required instantiations, 1514 // which are defined via explicit instantiations elsewhere. 1515 // NB: This syntax is a GNU extension. 1516 #if _GLIBCXX_EXTERN_TEMPLATE 1517 extern template istream& operator>>(istream&, complex<float>&); 1518 extern template ostream& operator<<(ostream&, const complex<float>&); 1519 extern template istream& operator>>(istream&, complex<double>&); 1520 extern template ostream& operator<<(ostream&, const complex<double>&); 1521 extern template istream& operator>>(istream&, complex<long double>&); 1522 extern template ostream& operator<<(ostream&, const complex<long double>&); 1523 1524 #ifdef _GLIBCXX_USE_WCHAR_T 1525 extern template wistream& operator>>(wistream&, complex<float>&); 1526 extern template wostream& operator<<(wostream&, const complex<float>&); 1527 extern template wistream& operator>>(wistream&, complex<double>&); 1528 extern template wostream& operator<<(wostream&, const complex<double>&); 1529 extern template wistream& operator>>(wistream&, complex<long double>&); 1530 extern template wostream& operator<<(wostream&, const complex<long double>&); 1531 #endif 1532 #endif 1533 1534 // @} group complex_numbers 1535 1536 _GLIBCXX_END_NAMESPACE_VERSION 1537 } // namespace 1538 1539 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1540 { 1541 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1542 1543 // See ext/type_traits.h for the primary template. 1544 template<typename _Tp, typename _Up> 1545 struct __promote_2<std::complex<_Tp>, _Up> 1546 { 1547 public: 1548 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1549 }; 1550 1551 template<typename _Tp, typename _Up> 1552 struct __promote_2<_Tp, std::complex<_Up> > 1553 { 1554 public: 1555 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1556 }; 1557 1558 template<typename _Tp, typename _Up> 1559 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1560 { 1561 public: 1562 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1563 }; 1564 1565 _GLIBCXX_END_NAMESPACE_VERSION 1566 } // namespace 1567 1568 #if __cplusplus >= 201103L 1569 1570 namespace std _GLIBCXX_VISIBILITY(default) 1571 { 1572 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1573 1574 // Forward declarations. 1575 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1576 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1577 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1578 1579 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1580 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1581 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1582 // DR 595. 1583 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1584 1585 template<typename _Tp> 1586 inline std::complex<_Tp> 1587 __complex_acos(const std::complex<_Tp>& __z) 1588 { 1589 const std::complex<_Tp> __t = std::asin(__z); 1590 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1591 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1592 } 1593 1594 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1595 inline __complex__ float 1596 __complex_acos(__complex__ float __z) 1597 { return __builtin_cacosf(__z); } 1598 1599 inline __complex__ double 1600 __complex_acos(__complex__ double __z) 1601 { return __builtin_cacos(__z); } 1602 1603 inline __complex__ long double 1604 __complex_acos(const __complex__ long double& __z) 1605 { return __builtin_cacosl(__z); } 1606 1607 template<typename _Tp> 1608 inline std::complex<_Tp> 1609 acos(const std::complex<_Tp>& __z) 1610 { return __complex_acos(__z.__rep()); } 1611 #else 1612 /// acos(__z) [8.1.2]. 1613 // Effects: Behaves the same as C99 function cacos, defined 1614 // in subclause 7.3.5.1. 1615 template<typename _Tp> 1616 inline std::complex<_Tp> 1617 acos(const std::complex<_Tp>& __z) 1618 { return __complex_acos(__z); } 1619 #endif 1620 1621 template<typename _Tp> 1622 inline std::complex<_Tp> 1623 __complex_asin(const std::complex<_Tp>& __z) 1624 { 1625 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1626 __t = std::asinh(__t); 1627 return std::complex<_Tp>(__t.imag(), -__t.real()); 1628 } 1629 1630 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1631 inline __complex__ float 1632 __complex_asin(__complex__ float __z) 1633 { return __builtin_casinf(__z); } 1634 1635 inline __complex__ double 1636 __complex_asin(__complex__ double __z) 1637 { return __builtin_casin(__z); } 1638 1639 inline __complex__ long double 1640 __complex_asin(const __complex__ long double& __z) 1641 { return __builtin_casinl(__z); } 1642 1643 template<typename _Tp> 1644 inline std::complex<_Tp> 1645 asin(const std::complex<_Tp>& __z) 1646 { return __complex_asin(__z.__rep()); } 1647 #else 1648 /// asin(__z) [8.1.3]. 1649 // Effects: Behaves the same as C99 function casin, defined 1650 // in subclause 7.3.5.2. 1651 template<typename _Tp> 1652 inline std::complex<_Tp> 1653 asin(const std::complex<_Tp>& __z) 1654 { return __complex_asin(__z); } 1655 #endif 1656 1657 template<typename _Tp> 1658 std::complex<_Tp> 1659 __complex_atan(const std::complex<_Tp>& __z) 1660 { 1661 const _Tp __r2 = __z.real() * __z.real(); 1662 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1663 1664 _Tp __num = __z.imag() + _Tp(1.0); 1665 _Tp __den = __z.imag() - _Tp(1.0); 1666 1667 __num = __r2 + __num * __num; 1668 __den = __r2 + __den * __den; 1669 1670 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1671 _Tp(0.25) * log(__num / __den)); 1672 } 1673 1674 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1675 inline __complex__ float 1676 __complex_atan(__complex__ float __z) 1677 { return __builtin_catanf(__z); } 1678 1679 inline __complex__ double 1680 __complex_atan(__complex__ double __z) 1681 { return __builtin_catan(__z); } 1682 1683 inline __complex__ long double 1684 __complex_atan(const __complex__ long double& __z) 1685 { return __builtin_catanl(__z); } 1686 1687 template<typename _Tp> 1688 inline std::complex<_Tp> 1689 atan(const std::complex<_Tp>& __z) 1690 { return __complex_atan(__z.__rep()); } 1691 #else 1692 /// atan(__z) [8.1.4]. 1693 // Effects: Behaves the same as C99 function catan, defined 1694 // in subclause 7.3.5.3. 1695 template<typename _Tp> 1696 inline std::complex<_Tp> 1697 atan(const std::complex<_Tp>& __z) 1698 { return __complex_atan(__z); } 1699 #endif 1700 1701 template<typename _Tp> 1702 std::complex<_Tp> 1703 __complex_acosh(const std::complex<_Tp>& __z) 1704 { 1705 // Kahan's formula. 1706 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1707 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1708 } 1709 1710 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1711 inline __complex__ float 1712 __complex_acosh(__complex__ float __z) 1713 { return __builtin_cacoshf(__z); } 1714 1715 inline __complex__ double 1716 __complex_acosh(__complex__ double __z) 1717 { return __builtin_cacosh(__z); } 1718 1719 inline __complex__ long double 1720 __complex_acosh(const __complex__ long double& __z) 1721 { return __builtin_cacoshl(__z); } 1722 1723 template<typename _Tp> 1724 inline std::complex<_Tp> 1725 acosh(const std::complex<_Tp>& __z) 1726 { return __complex_acosh(__z.__rep()); } 1727 #else 1728 /// acosh(__z) [8.1.5]. 1729 // Effects: Behaves the same as C99 function cacosh, defined 1730 // in subclause 7.3.6.1. 1731 template<typename _Tp> 1732 inline std::complex<_Tp> 1733 acosh(const std::complex<_Tp>& __z) 1734 { return __complex_acosh(__z); } 1735 #endif 1736 1737 template<typename _Tp> 1738 std::complex<_Tp> 1739 __complex_asinh(const std::complex<_Tp>& __z) 1740 { 1741 std::complex<_Tp> __t((__z.real() - __z.imag()) 1742 * (__z.real() + __z.imag()) + _Tp(1.0), 1743 _Tp(2.0) * __z.real() * __z.imag()); 1744 __t = std::sqrt(__t); 1745 1746 return std::log(__t + __z); 1747 } 1748 1749 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1750 inline __complex__ float 1751 __complex_asinh(__complex__ float __z) 1752 { return __builtin_casinhf(__z); } 1753 1754 inline __complex__ double 1755 __complex_asinh(__complex__ double __z) 1756 { return __builtin_casinh(__z); } 1757 1758 inline __complex__ long double 1759 __complex_asinh(const __complex__ long double& __z) 1760 { return __builtin_casinhl(__z); } 1761 1762 template<typename _Tp> 1763 inline std::complex<_Tp> 1764 asinh(const std::complex<_Tp>& __z) 1765 { return __complex_asinh(__z.__rep()); } 1766 #else 1767 /// asinh(__z) [8.1.6]. 1768 // Effects: Behaves the same as C99 function casin, defined 1769 // in subclause 7.3.6.2. 1770 template<typename _Tp> 1771 inline std::complex<_Tp> 1772 asinh(const std::complex<_Tp>& __z) 1773 { return __complex_asinh(__z); } 1774 #endif 1775 1776 template<typename _Tp> 1777 std::complex<_Tp> 1778 __complex_atanh(const std::complex<_Tp>& __z) 1779 { 1780 const _Tp __i2 = __z.imag() * __z.imag(); 1781 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1782 1783 _Tp __num = _Tp(1.0) + __z.real(); 1784 _Tp __den = _Tp(1.0) - __z.real(); 1785 1786 __num = __i2 + __num * __num; 1787 __den = __i2 + __den * __den; 1788 1789 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1790 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1791 } 1792 1793 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1794 inline __complex__ float 1795 __complex_atanh(__complex__ float __z) 1796 { return __builtin_catanhf(__z); } 1797 1798 inline __complex__ double 1799 __complex_atanh(__complex__ double __z) 1800 { return __builtin_catanh(__z); } 1801 1802 inline __complex__ long double 1803 __complex_atanh(const __complex__ long double& __z) 1804 { return __builtin_catanhl(__z); } 1805 1806 template<typename _Tp> 1807 inline std::complex<_Tp> 1808 atanh(const std::complex<_Tp>& __z) 1809 { return __complex_atanh(__z.__rep()); } 1810 #else 1811 /// atanh(__z) [8.1.7]. 1812 // Effects: Behaves the same as C99 function catanh, defined 1813 // in subclause 7.3.6.3. 1814 template<typename _Tp> 1815 inline std::complex<_Tp> 1816 atanh(const std::complex<_Tp>& __z) 1817 { return __complex_atanh(__z); } 1818 #endif 1819 1820 template<typename _Tp> 1821 inline _Tp 1822 /// fabs(__z) [8.1.8]. 1823 // Effects: Behaves the same as C99 function cabs, defined 1824 // in subclause 7.3.8.1. 1825 fabs(const std::complex<_Tp>& __z) 1826 { return std::abs(__z); } 1827 1828 /// Additional overloads [8.1.9]. 1829 template<typename _Tp> 1830 inline typename __gnu_cxx::__promote<_Tp>::__type 1831 arg(_Tp __x) 1832 { 1833 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1834 #if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1835 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1836 : __type(); 1837 #else 1838 return std::arg(std::complex<__type>(__x)); 1839 #endif 1840 } 1841 1842 template<typename _Tp> 1843 inline typename __gnu_cxx::__promote<_Tp>::__type 1844 imag(_Tp) 1845 { return _Tp(); } 1846 1847 template<typename _Tp> 1848 inline typename __gnu_cxx::__promote<_Tp>::__type 1849 norm(_Tp __x) 1850 { 1851 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1852 return __type(__x) * __type(__x); 1853 } 1854 1855 template<typename _Tp> 1856 inline typename __gnu_cxx::__promote<_Tp>::__type 1857 real(_Tp __x) 1858 { return __x; } 1859 1860 template<typename _Tp, typename _Up> 1861 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1862 pow(const std::complex<_Tp>& __x, const _Up& __y) 1863 { 1864 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1865 return std::pow(std::complex<__type>(__x), __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 _Tp& __x, const std::complex<_Up>& __y) 1871 { 1872 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1873 return std::pow(__type(__x), std::complex<__type>(__y)); 1874 } 1875 1876 template<typename _Tp, typename _Up> 1877 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1878 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1879 { 1880 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1881 return std::pow(std::complex<__type>(__x), 1882 std::complex<__type>(__y)); 1883 } 1884 1885 // Forward declarations. 1886 // DR 781. 1887 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); 1888 1889 template<typename _Tp> 1890 std::complex<_Tp> 1891 __complex_proj(const std::complex<_Tp>& __z) 1892 { 1893 const _Tp __den = (__z.real() * __z.real() 1894 + __z.imag() * __z.imag() + _Tp(1.0)); 1895 1896 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, 1897 (_Tp(2.0) * __z.imag()) / __den); 1898 } 1899 1900 #if _GLIBCXX_USE_C99_COMPLEX 1901 inline __complex__ float 1902 __complex_proj(__complex__ float __z) 1903 { return __builtin_cprojf(__z); } 1904 1905 inline __complex__ double 1906 __complex_proj(__complex__ double __z) 1907 { return __builtin_cproj(__z); } 1908 1909 inline __complex__ long double 1910 __complex_proj(const __complex__ long double& __z) 1911 { return __builtin_cprojl(__z); } 1912 1913 template<typename _Tp> 1914 inline std::complex<_Tp> 1915 proj(const std::complex<_Tp>& __z) 1916 { return __complex_proj(__z.__rep()); } 1917 #else 1918 template<typename _Tp> 1919 inline std::complex<_Tp> 1920 proj(const std::complex<_Tp>& __z) 1921 { return __complex_proj(__z); } 1922 #endif 1923 1924 // DR 1137. 1925 template<typename _Tp> 1926 inline typename __gnu_cxx::__promote<_Tp>::__type 1927 proj(_Tp __x) 1928 { return __x; } 1929 1930 template<typename _Tp> 1931 inline typename __gnu_cxx::__promote<_Tp>::__type 1932 conj(_Tp __x) 1933 { return __x; } 1934 1935 _GLIBCXX_END_NAMESPACE_VERSION 1936 1937 #if __cplusplus > 201103L 1938 1939 inline namespace literals { 1940 inline namespace complex_literals { 1941 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1942 1943 #define __cpp_lib_complex_udls 201309 1944 1945 constexpr std::complex<float> 1946 operator""if(long double __num) 1947 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1948 1949 constexpr std::complex<float> 1950 operator""if(unsigned long long __num) 1951 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1952 1953 constexpr std::complex<double> 1954 operator""i(long double __num) 1955 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1956 1957 constexpr std::complex<double> 1958 operator""i(unsigned long long __num) 1959 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1960 1961 constexpr std::complex<long double> 1962 operator""il(long double __num) 1963 { return std::complex<long double>{0.0L, __num}; } 1964 1965 constexpr std::complex<long double> 1966 operator""il(unsigned long long __num) 1967 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } 1968 1969 _GLIBCXX_END_NAMESPACE_VERSION 1970 } // inline namespace complex_literals 1971 } // inline namespace literals 1972 1973 #endif // C++14 1974 1975 } // namespace 1976 1977 #endif // C++11 1978 1979 #endif /* _GLIBCXX_COMPLEX */ 1980
Indexes created Fri Mar 06 19:51:54 UTC 2026