complex revision 1.1.1.15
1 // The template and inlines for the -*- C++ -*- complex number classes. 2 3 // Copyright (C) 1997-2022 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 #if __cplusplus > 201703L 51 # define __cpp_lib_constexpr_complex 201711L 52 #endif 53 54 namespace std _GLIBCXX_VISIBILITY(default) 55 { 56 _GLIBCXX_BEGIN_NAMESPACE_VERSION 57 58 /** 59 * @defgroup complex_numbers Complex Numbers 60 * @ingroup numerics 61 * 62 * Classes and functions for complex numbers. 63 * @{ 64 */ 65 66 // Forward declarations. 67 template<typename _Tp> class complex; 68 template<> class complex<float>; 69 template<> class complex<double>; 70 template<> class complex<long double>; 71 72 /// Return magnitude of @a z. 73 template<typename _Tp> _Tp abs(const complex<_Tp>&); 74 /// Return phase angle of @a z. 75 template<typename _Tp> _Tp arg(const complex<_Tp>&); 76 /// Return @a z magnitude squared. 77 template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&); 78 79 /// Return complex conjugate of @a z. 80 template<typename _Tp> 81 _GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&); 82 /// Return complex with magnitude @a rho and angle @a theta. 83 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 84 85 // Transcendentals: 86 /// Return complex cosine of @a z. 87 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 88 /// Return complex hyperbolic cosine of @a z. 89 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 90 /// Return complex base e exponential of @a z. 91 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 92 /// Return complex natural logarithm of @a z. 93 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 94 /// Return complex base 10 logarithm of @a z. 95 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 96 /// Return @a x to the @a y'th power. 97 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 98 /// Return @a x to the @a y'th power. 99 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 100 /// Return @a x to the @a y'th power. 101 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 102 const complex<_Tp>&); 103 /// Return @a x to the @a y'th power. 104 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 105 /// Return complex sine of @a z. 106 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 107 /// Return complex hyperbolic sine of @a z. 108 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 109 /// Return complex square root of @a z. 110 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 111 /// Return complex tangent of @a z. 112 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 113 /// Return complex hyperbolic tangent of @a z. 114 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 115 116 117 // 26.2.2 Primary template class complex 118 /** 119 * Template to represent complex numbers. 120 * 121 * Specializations for float, double, and long double are part of the 122 * library. Results with any other type are not guaranteed. 123 * 124 * @param Tp Type of real and imaginary values. 125 */ 126 template<typename _Tp> 127 class complex 128 { 129 public: 130 /// Value typedef. 131 typedef _Tp value_type; 132 133 /// Default constructor. First parameter is x, second parameter is y. 134 /// Unspecified parameters default to 0. 135 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 136 : _M_real(__r), _M_imag(__i) { } 137 138 // Let the compiler synthesize the copy constructor 139 #if __cplusplus >= 201103L 140 constexpr complex(const complex&) = default; 141 #endif 142 143 /// Converting constructor. 144 template<typename _Up> 145 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 146 : _M_real(__z.real()), _M_imag(__z.imag()) { } 147 148 #if __cplusplus >= 201103L 149 // _GLIBCXX_RESOLVE_LIB_DEFECTS 150 // DR 387. std::complex over-encapsulated. 151 _GLIBCXX_ABI_TAG_CXX11 152 constexpr _Tp 153 real() const { return _M_real; } 154 155 _GLIBCXX_ABI_TAG_CXX11 156 constexpr _Tp 157 imag() const { return _M_imag; } 158 #else 159 /// Return real part of complex number. 160 _Tp& 161 real() { return _M_real; } 162 163 /// Return real part of complex number. 164 const _Tp& 165 real() const { return _M_real; } 166 167 /// Return imaginary part of complex number. 168 _Tp& 169 imag() { return _M_imag; } 170 171 /// Return imaginary part of complex number. 172 const _Tp& 173 imag() const { return _M_imag; } 174 #endif 175 176 // _GLIBCXX_RESOLVE_LIB_DEFECTS 177 // DR 387. std::complex over-encapsulated. 178 _GLIBCXX20_CONSTEXPR void 179 real(_Tp __val) { _M_real = __val; } 180 181 _GLIBCXX20_CONSTEXPR void 182 imag(_Tp __val) { _M_imag = __val; } 183 184 /// Assign a scalar to this complex number. 185 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&); 186 187 /// Add a scalar to this complex number. 188 // 26.2.5/1 189 _GLIBCXX20_CONSTEXPR complex<_Tp>& 190 operator+=(const _Tp& __t) 191 { 192 _M_real += __t; 193 return *this; 194 } 195 196 /// Subtract a scalar from this complex number. 197 // 26.2.5/3 198 _GLIBCXX20_CONSTEXPR complex<_Tp>& 199 operator-=(const _Tp& __t) 200 { 201 _M_real -= __t; 202 return *this; 203 } 204 205 /// Multiply this complex number by a scalar. 206 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&); 207 /// Divide this complex number by a scalar. 208 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&); 209 210 // Let the compiler synthesize the copy assignment operator 211 #if __cplusplus >= 201103L 212 _GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default; 213 #endif 214 215 /// Assign another complex number to this one. 216 template<typename _Up> 217 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&); 218 /// Add another complex number to this one. 219 template<typename _Up> 220 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&); 221 /// Subtract another complex number from this one. 222 template<typename _Up> 223 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&); 224 /// Multiply this complex number by another. 225 template<typename _Up> 226 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&); 227 /// Divide this complex number by another. 228 template<typename _Up> 229 _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&); 230 231 _GLIBCXX_CONSTEXPR complex __rep() const 232 { return *this; } 233 234 private: 235 _Tp _M_real; 236 _Tp _M_imag; 237 }; 238 239 template<typename _Tp> 240 _GLIBCXX20_CONSTEXPR complex<_Tp>& 241 complex<_Tp>::operator=(const _Tp& __t) 242 { 243 _M_real = __t; 244 _M_imag = _Tp(); 245 return *this; 246 } 247 248 // 26.2.5/5 249 template<typename _Tp> 250 _GLIBCXX20_CONSTEXPR complex<_Tp>& 251 complex<_Tp>::operator*=(const _Tp& __t) 252 { 253 _M_real *= __t; 254 _M_imag *= __t; 255 return *this; 256 } 257 258 // 26.2.5/7 259 template<typename _Tp> 260 _GLIBCXX20_CONSTEXPR complex<_Tp>& 261 complex<_Tp>::operator/=(const _Tp& __t) 262 { 263 _M_real /= __t; 264 _M_imag /= __t; 265 return *this; 266 } 267 268 template<typename _Tp> 269 template<typename _Up> 270 _GLIBCXX20_CONSTEXPR complex<_Tp>& 271 complex<_Tp>::operator=(const complex<_Up>& __z) 272 { 273 _M_real = __z.real(); 274 _M_imag = __z.imag(); 275 return *this; 276 } 277 278 // 26.2.5/9 279 template<typename _Tp> 280 template<typename _Up> 281 _GLIBCXX20_CONSTEXPR complex<_Tp>& 282 complex<_Tp>::operator+=(const complex<_Up>& __z) 283 { 284 _M_real += __z.real(); 285 _M_imag += __z.imag(); 286 return *this; 287 } 288 289 // 26.2.5/11 290 template<typename _Tp> 291 template<typename _Up> 292 _GLIBCXX20_CONSTEXPR complex<_Tp>& 293 complex<_Tp>::operator-=(const complex<_Up>& __z) 294 { 295 _M_real -= __z.real(); 296 _M_imag -= __z.imag(); 297 return *this; 298 } 299 300 // 26.2.5/13 301 // XXX: This is a grammar school implementation. 302 template<typename _Tp> 303 template<typename _Up> 304 _GLIBCXX20_CONSTEXPR complex<_Tp>& 305 complex<_Tp>::operator*=(const complex<_Up>& __z) 306 { 307 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 308 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 309 _M_real = __r; 310 return *this; 311 } 312 313 // 26.2.5/15 314 // XXX: This is a grammar school implementation. 315 template<typename _Tp> 316 template<typename _Up> 317 _GLIBCXX20_CONSTEXPR complex<_Tp>& 318 complex<_Tp>::operator/=(const complex<_Up>& __z) 319 { 320 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 321 const _Tp __n = std::norm(__z); 322 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 323 _M_real = __r / __n; 324 return *this; 325 } 326 327 // Operators: 328 ///@{ 329 /// Return new complex value @a x plus @a y. 330 template<typename _Tp> 331 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 332 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 333 { 334 complex<_Tp> __r = __x; 335 __r += __y; 336 return __r; 337 } 338 339 template<typename _Tp> 340 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 341 operator+(const complex<_Tp>& __x, const _Tp& __y) 342 { 343 complex<_Tp> __r = __x; 344 __r += __y; 345 return __r; 346 } 347 348 template<typename _Tp> 349 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 350 operator+(const _Tp& __x, const complex<_Tp>& __y) 351 { 352 complex<_Tp> __r = __y; 353 __r += __x; 354 return __r; 355 } 356 ///@} 357 358 ///@{ 359 /// Return new complex value @a x minus @a y. 360 template<typename _Tp> 361 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 362 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 363 { 364 complex<_Tp> __r = __x; 365 __r -= __y; 366 return __r; 367 } 368 369 template<typename _Tp> 370 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 371 operator-(const complex<_Tp>& __x, const _Tp& __y) 372 { 373 complex<_Tp> __r = __x; 374 __r -= __y; 375 return __r; 376 } 377 378 template<typename _Tp> 379 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 380 operator-(const _Tp& __x, const complex<_Tp>& __y) 381 { 382 complex<_Tp> __r = -__y; 383 __r += __x; 384 return __r; 385 } 386 ///@} 387 388 ///@{ 389 /// Return new complex value @a x times @a y. 390 template<typename _Tp> 391 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 392 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 393 { 394 complex<_Tp> __r = __x; 395 __r *= __y; 396 return __r; 397 } 398 399 template<typename _Tp> 400 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 401 operator*(const complex<_Tp>& __x, const _Tp& __y) 402 { 403 complex<_Tp> __r = __x; 404 __r *= __y; 405 return __r; 406 } 407 408 template<typename _Tp> 409 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 410 operator*(const _Tp& __x, const complex<_Tp>& __y) 411 { 412 complex<_Tp> __r = __y; 413 __r *= __x; 414 return __r; 415 } 416 ///@} 417 418 ///@{ 419 /// Return new complex value @a x divided by @a y. 420 template<typename _Tp> 421 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 422 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 423 { 424 complex<_Tp> __r = __x; 425 __r /= __y; 426 return __r; 427 } 428 429 template<typename _Tp> 430 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 431 operator/(const complex<_Tp>& __x, const _Tp& __y) 432 { 433 complex<_Tp> __r = __x; 434 __r /= __y; 435 return __r; 436 } 437 438 template<typename _Tp> 439 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 440 operator/(const _Tp& __x, const complex<_Tp>& __y) 441 { 442 complex<_Tp> __r = __x; 443 __r /= __y; 444 return __r; 445 } 446 ///@} 447 448 /// Return @a x. 449 template<typename _Tp> 450 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 451 operator+(const complex<_Tp>& __x) 452 { return __x; } 453 454 /// Return complex negation of @a x. 455 template<typename _Tp> 456 inline _GLIBCXX20_CONSTEXPR complex<_Tp> 457 operator-(const complex<_Tp>& __x) 458 { return complex<_Tp>(-__x.real(), -__x.imag()); } 459 460 ///@{ 461 /// Return true if @a x is equal to @a y. 462 template<typename _Tp> 463 inline _GLIBCXX_CONSTEXPR bool 464 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 465 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 466 467 template<typename _Tp> 468 inline _GLIBCXX_CONSTEXPR bool 469 operator==(const complex<_Tp>& __x, const _Tp& __y) 470 { return __x.real() == __y && __x.imag() == _Tp(); } 471 472 #if !(__cpp_impl_three_way_comparison >= 201907L) 473 template<typename _Tp> 474 inline _GLIBCXX_CONSTEXPR bool 475 operator==(const _Tp& __x, const complex<_Tp>& __y) 476 { return __x == __y.real() && _Tp() == __y.imag(); } 477 ///@} 478 479 ///@{ 480 /// Return false if @a x is equal to @a y. 481 template<typename _Tp> 482 inline _GLIBCXX_CONSTEXPR bool 483 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 484 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 485 486 template<typename _Tp> 487 inline _GLIBCXX_CONSTEXPR bool 488 operator!=(const complex<_Tp>& __x, const _Tp& __y) 489 { return __x.real() != __y || __x.imag() != _Tp(); } 490 491 template<typename _Tp> 492 inline _GLIBCXX_CONSTEXPR bool 493 operator!=(const _Tp& __x, const complex<_Tp>& __y) 494 { return __x != __y.real() || _Tp() != __y.imag(); } 495 #endif 496 ///@} 497 498 /// Extraction operator for complex values. 499 template<typename _Tp, typename _CharT, class _Traits> 500 basic_istream<_CharT, _Traits>& 501 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 502 { 503 bool __fail = true; 504 _CharT __ch; 505 if (__is >> __ch) 506 { 507 if (_Traits::eq(__ch, __is.widen('('))) 508 { 509 _Tp __u; 510 if (__is >> __u >> __ch) 511 { 512 const _CharT __rparen = __is.widen(')'); 513 if (_Traits::eq(__ch, __rparen)) 514 { 515 __x = __u; 516 __fail = false; 517 } 518 else if (_Traits::eq(__ch, __is.widen(','))) 519 { 520 _Tp __v; 521 if (__is >> __v >> __ch) 522 { 523 if (_Traits::eq(__ch, __rparen)) 524 { 525 __x = complex<_Tp>(__u, __v); 526 __fail = false; 527 } 528 else 529 __is.putback(__ch); 530 } 531 } 532 else 533 __is.putback(__ch); 534 } 535 } 536 else 537 { 538 __is.putback(__ch); 539 _Tp __u; 540 if (__is >> __u) 541 { 542 __x = __u; 543 __fail = false; 544 } 545 } 546 } 547 if (__fail) 548 __is.setstate(ios_base::failbit); 549 return __is; 550 } 551 552 /// Insertion operator for complex values. 553 template<typename _Tp, typename _CharT, class _Traits> 554 basic_ostream<_CharT, _Traits>& 555 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 556 { 557 basic_ostringstream<_CharT, _Traits> __s; 558 __s.flags(__os.flags()); 559 __s.imbue(__os.getloc()); 560 __s.precision(__os.precision()); 561 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 562 return __os << __s.str(); 563 } 564 565 // Values 566 #if __cplusplus >= 201103L 567 template<typename _Tp> 568 constexpr _Tp 569 real(const complex<_Tp>& __z) 570 { return __z.real(); } 571 572 template<typename _Tp> 573 constexpr _Tp 574 imag(const complex<_Tp>& __z) 575 { return __z.imag(); } 576 #else 577 template<typename _Tp> 578 inline _Tp& 579 real(complex<_Tp>& __z) 580 { return __z.real(); } 581 582 template<typename _Tp> 583 inline const _Tp& 584 real(const complex<_Tp>& __z) 585 { return __z.real(); } 586 587 template<typename _Tp> 588 inline _Tp& 589 imag(complex<_Tp>& __z) 590 { return __z.imag(); } 591 592 template<typename _Tp> 593 inline const _Tp& 594 imag(const complex<_Tp>& __z) 595 { return __z.imag(); } 596 #endif 597 598 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 599 template<typename _Tp> 600 inline _Tp 601 __complex_abs(const complex<_Tp>& __z) 602 { 603 _Tp __x = __z.real(); 604 _Tp __y = __z.imag(); 605 const _Tp __s = std::max(abs(__x), abs(__y)); 606 if (__s == _Tp()) // well ... 607 return __s; 608 __x /= __s; 609 __y /= __s; 610 return __s * sqrt(__x * __x + __y * __y); 611 } 612 613 #if _GLIBCXX_USE_C99_COMPLEX 614 inline float 615 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 616 617 inline double 618 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 619 620 inline long double 621 __complex_abs(const __complex__ long double& __z) 622 { return __builtin_cabsl(__z); } 623 624 template<typename _Tp> 625 inline _Tp 626 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 627 #else 628 template<typename _Tp> 629 inline _Tp 630 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 631 #endif 632 633 634 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 635 template<typename _Tp> 636 inline _Tp 637 __complex_arg(const complex<_Tp>& __z) 638 { return atan2(__z.imag(), __z.real()); } 639 640 #if _GLIBCXX_USE_C99_COMPLEX 641 inline float 642 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 643 644 inline double 645 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 646 647 inline long double 648 __complex_arg(const __complex__ long double& __z) 649 { return __builtin_cargl(__z); } 650 651 template<typename _Tp> 652 inline _Tp 653 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 654 #else 655 template<typename _Tp> 656 inline _Tp 657 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 658 #endif 659 660 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 661 // As defined, norm() is -not- a norm is the common mathematical 662 // sense used in numerics. The helper class _Norm_helper<> tries to 663 // distinguish between builtin floating point and the rest, so as 664 // to deliver an answer as close as possible to the real value. 665 template<bool> 666 struct _Norm_helper 667 { 668 template<typename _Tp> 669 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) 670 { 671 const _Tp __x = __z.real(); 672 const _Tp __y = __z.imag(); 673 return __x * __x + __y * __y; 674 } 675 }; 676 677 template<> 678 struct _Norm_helper<true> 679 { 680 template<typename _Tp> 681 static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z) 682 { 683 //_Tp __res = std::abs(__z); 684 //return __res * __res; 685 const _Tp __x = __z.real(); 686 const _Tp __y = __z.imag(); 687 return __x * __x + __y * __y; 688 } 689 }; 690 691 template<typename _Tp> 692 inline _GLIBCXX20_CONSTEXPR _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 _GLIBCXX20_CONSTEXPR 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 class complex<float> 1084 { 1085 public: 1086 typedef float value_type; 1087 typedef __complex__ float _ComplexT; 1088 1089 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1090 1091 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1092 #if __cplusplus >= 201103L 1093 : _M_value{ __r, __i } { } 1094 #else 1095 { 1096 __real__ _M_value = __r; 1097 __imag__ _M_value = __i; 1098 } 1099 #endif 1100 1101 #if __cplusplus >= 201103L 1102 _GLIBCXX14_CONSTEXPR complex(const complex&) = default; 1103 #endif 1104 1105 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1106 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1107 1108 #if __cplusplus >= 201103L 1109 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1110 // DR 387. std::complex over-encapsulated. 1111 __attribute ((__abi_tag__ ("cxx11"))) 1112 constexpr float 1113 real() const { return __real__ _M_value; } 1114 1115 __attribute ((__abi_tag__ ("cxx11"))) 1116 constexpr float 1117 imag() const { return __imag__ _M_value; } 1118 #else 1119 float& 1120 real() { return __real__ _M_value; } 1121 1122 const float& 1123 real() const { return __real__ _M_value; } 1124 1125 float& 1126 imag() { return __imag__ _M_value; } 1127 1128 const float& 1129 imag() const { return __imag__ _M_value; } 1130 #endif 1131 1132 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1133 // DR 387. std::complex over-encapsulated. 1134 _GLIBCXX20_CONSTEXPR void 1135 real(float __val) { __real__ _M_value = __val; } 1136 1137 _GLIBCXX20_CONSTEXPR void 1138 imag(float __val) { __imag__ _M_value = __val; } 1139 1140 _GLIBCXX20_CONSTEXPR complex& 1141 operator=(float __f) 1142 { 1143 _M_value = __f; 1144 return *this; 1145 } 1146 1147 _GLIBCXX20_CONSTEXPR complex& 1148 operator+=(float __f) 1149 { 1150 _M_value += __f; 1151 return *this; 1152 } 1153 1154 _GLIBCXX20_CONSTEXPR complex& 1155 operator-=(float __f) 1156 { 1157 _M_value -= __f; 1158 return *this; 1159 } 1160 1161 _GLIBCXX20_CONSTEXPR complex& 1162 operator*=(float __f) 1163 { 1164 _M_value *= __f; 1165 return *this; 1166 } 1167 1168 _GLIBCXX20_CONSTEXPR complex& 1169 operator/=(float __f) 1170 { 1171 _M_value /= __f; 1172 return *this; 1173 } 1174 1175 // Let the compiler synthesize the copy and assignment 1176 // operator. It always does a pretty good job. 1177 #if __cplusplus >= 201103L 1178 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1179 #endif 1180 1181 template<typename _Tp> 1182 _GLIBCXX20_CONSTEXPR complex& 1183 operator=(const complex<_Tp>& __z) 1184 { 1185 __real__ _M_value = __z.real(); 1186 __imag__ _M_value = __z.imag(); 1187 return *this; 1188 } 1189 1190 template<typename _Tp> 1191 _GLIBCXX20_CONSTEXPR complex& 1192 operator+=(const complex<_Tp>& __z) 1193 { 1194 _M_value += __z.__rep(); 1195 return *this; 1196 } 1197 1198 template<class _Tp> 1199 _GLIBCXX20_CONSTEXPR complex& 1200 operator-=(const complex<_Tp>& __z) 1201 { 1202 _M_value -= __z.__rep(); 1203 return *this; 1204 } 1205 1206 template<class _Tp> 1207 _GLIBCXX20_CONSTEXPR complex& 1208 operator*=(const complex<_Tp>& __z) 1209 { 1210 const _ComplexT __t = __z.__rep(); 1211 _M_value *= __t; 1212 return *this; 1213 } 1214 1215 template<class _Tp> 1216 _GLIBCXX20_CONSTEXPR complex& 1217 operator/=(const complex<_Tp>& __z) 1218 { 1219 const _ComplexT __t = __z.__rep(); 1220 _M_value /= __t; 1221 return *this; 1222 } 1223 1224 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1225 1226 private: 1227 _ComplexT _M_value; 1228 }; 1229 1230 /// 26.2.3 complex specializations 1231 /// complex<double> specialization 1232 template<> 1233 class complex<double> 1234 { 1235 public: 1236 typedef double value_type; 1237 typedef __complex__ double _ComplexT; 1238 1239 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1240 1241 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1242 #if __cplusplus >= 201103L 1243 : _M_value{ __r, __i } { } 1244 #else 1245 { 1246 __real__ _M_value = __r; 1247 __imag__ _M_value = __i; 1248 } 1249 #endif 1250 1251 #if __cplusplus >= 201103L 1252 _GLIBCXX14_CONSTEXPR complex(const complex&) = default; 1253 #endif 1254 1255 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1256 : _M_value(__z.__rep()) { } 1257 1258 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1259 1260 #if __cplusplus >= 201103L 1261 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1262 // DR 387. std::complex over-encapsulated. 1263 __attribute ((__abi_tag__ ("cxx11"))) 1264 constexpr double 1265 real() const { return __real__ _M_value; } 1266 1267 __attribute ((__abi_tag__ ("cxx11"))) 1268 constexpr double 1269 imag() const { return __imag__ _M_value; } 1270 #else 1271 double& 1272 real() { return __real__ _M_value; } 1273 1274 const double& 1275 real() const { return __real__ _M_value; } 1276 1277 double& 1278 imag() { return __imag__ _M_value; } 1279 1280 const double& 1281 imag() const { return __imag__ _M_value; } 1282 #endif 1283 1284 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1285 // DR 387. std::complex over-encapsulated. 1286 _GLIBCXX20_CONSTEXPR void 1287 real(double __val) { __real__ _M_value = __val; } 1288 1289 _GLIBCXX20_CONSTEXPR void 1290 imag(double __val) { __imag__ _M_value = __val; } 1291 1292 _GLIBCXX20_CONSTEXPR complex& 1293 operator=(double __d) 1294 { 1295 _M_value = __d; 1296 return *this; 1297 } 1298 1299 _GLIBCXX20_CONSTEXPR complex& 1300 operator+=(double __d) 1301 { 1302 _M_value += __d; 1303 return *this; 1304 } 1305 1306 _GLIBCXX20_CONSTEXPR complex& 1307 operator-=(double __d) 1308 { 1309 _M_value -= __d; 1310 return *this; 1311 } 1312 1313 _GLIBCXX20_CONSTEXPR complex& 1314 operator*=(double __d) 1315 { 1316 _M_value *= __d; 1317 return *this; 1318 } 1319 1320 _GLIBCXX20_CONSTEXPR complex& 1321 operator/=(double __d) 1322 { 1323 _M_value /= __d; 1324 return *this; 1325 } 1326 1327 // The compiler will synthesize this, efficiently. 1328 #if __cplusplus >= 201103L 1329 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1330 #endif 1331 1332 template<typename _Tp> 1333 _GLIBCXX20_CONSTEXPR complex& 1334 operator=(const complex<_Tp>& __z) 1335 { 1336 _M_value = __z.__rep(); 1337 return *this; 1338 } 1339 1340 template<typename _Tp> 1341 _GLIBCXX20_CONSTEXPR complex& 1342 operator+=(const complex<_Tp>& __z) 1343 { 1344 _M_value += __z.__rep(); 1345 return *this; 1346 } 1347 1348 template<typename _Tp> 1349 _GLIBCXX20_CONSTEXPR complex& 1350 operator-=(const complex<_Tp>& __z) 1351 { 1352 _M_value -= __z.__rep(); 1353 return *this; 1354 } 1355 1356 template<typename _Tp> 1357 _GLIBCXX20_CONSTEXPR complex& 1358 operator*=(const complex<_Tp>& __z) 1359 { 1360 const _ComplexT __t = __z.__rep(); 1361 _M_value *= __t; 1362 return *this; 1363 } 1364 1365 template<typename _Tp> 1366 _GLIBCXX20_CONSTEXPR complex& 1367 operator/=(const complex<_Tp>& __z) 1368 { 1369 const _ComplexT __t = __z.__rep(); 1370 _M_value /= __t; 1371 return *this; 1372 } 1373 1374 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1375 1376 private: 1377 _ComplexT _M_value; 1378 }; 1379 1380 /// 26.2.3 complex specializations 1381 /// complex<long double> specialization 1382 template<> 1383 class complex<long double> 1384 { 1385 public: 1386 typedef long double value_type; 1387 typedef __complex__ long double _ComplexT; 1388 1389 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1390 1391 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1392 long double __i = 0.0L) 1393 #if __cplusplus >= 201103L 1394 : _M_value{ __r, __i } { } 1395 #else 1396 { 1397 __real__ _M_value = __r; 1398 __imag__ _M_value = __i; 1399 } 1400 #endif 1401 1402 #if __cplusplus >= 201103L 1403 _GLIBCXX14_CONSTEXPR complex(const complex&) = default; 1404 #endif 1405 1406 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1407 : _M_value(__z.__rep()) { } 1408 1409 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1410 : _M_value(__z.__rep()) { } 1411 1412 #if __cplusplus >= 201103L 1413 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1414 // DR 387. std::complex over-encapsulated. 1415 __attribute ((__abi_tag__ ("cxx11"))) 1416 constexpr long double 1417 real() const { return __real__ _M_value; } 1418 1419 __attribute ((__abi_tag__ ("cxx11"))) 1420 constexpr long double 1421 imag() const { return __imag__ _M_value; } 1422 #else 1423 long double& 1424 real() { return __real__ _M_value; } 1425 1426 const long double& 1427 real() const { return __real__ _M_value; } 1428 1429 long double& 1430 imag() { return __imag__ _M_value; } 1431 1432 const long double& 1433 imag() const { return __imag__ _M_value; } 1434 #endif 1435 1436 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1437 // DR 387. std::complex over-encapsulated. 1438 _GLIBCXX20_CONSTEXPR void 1439 real(long double __val) { __real__ _M_value = __val; } 1440 1441 _GLIBCXX20_CONSTEXPR void 1442 imag(long double __val) { __imag__ _M_value = __val; } 1443 1444 _GLIBCXX20_CONSTEXPR complex& 1445 operator=(long double __r) 1446 { 1447 _M_value = __r; 1448 return *this; 1449 } 1450 1451 _GLIBCXX20_CONSTEXPR complex& 1452 operator+=(long double __r) 1453 { 1454 _M_value += __r; 1455 return *this; 1456 } 1457 1458 _GLIBCXX20_CONSTEXPR complex& 1459 operator-=(long double __r) 1460 { 1461 _M_value -= __r; 1462 return *this; 1463 } 1464 1465 _GLIBCXX20_CONSTEXPR complex& 1466 operator*=(long double __r) 1467 { 1468 _M_value *= __r; 1469 return *this; 1470 } 1471 1472 _GLIBCXX20_CONSTEXPR complex& 1473 operator/=(long double __r) 1474 { 1475 _M_value /= __r; 1476 return *this; 1477 } 1478 1479 // The compiler knows how to do this efficiently 1480 #if __cplusplus >= 201103L 1481 _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default; 1482 #endif 1483 1484 template<typename _Tp> 1485 _GLIBCXX20_CONSTEXPR complex& 1486 operator=(const complex<_Tp>& __z) 1487 { 1488 _M_value = __z.__rep(); 1489 return *this; 1490 } 1491 1492 template<typename _Tp> 1493 _GLIBCXX20_CONSTEXPR complex& 1494 operator+=(const complex<_Tp>& __z) 1495 { 1496 _M_value += __z.__rep(); 1497 return *this; 1498 } 1499 1500 template<typename _Tp> 1501 _GLIBCXX20_CONSTEXPR complex& 1502 operator-=(const complex<_Tp>& __z) 1503 { 1504 _M_value -= __z.__rep(); 1505 return *this; 1506 } 1507 1508 template<typename _Tp> 1509 _GLIBCXX20_CONSTEXPR complex& 1510 operator*=(const complex<_Tp>& __z) 1511 { 1512 const _ComplexT __t = __z.__rep(); 1513 _M_value *= __t; 1514 return *this; 1515 } 1516 1517 template<typename _Tp> 1518 _GLIBCXX20_CONSTEXPR complex& 1519 operator/=(const complex<_Tp>& __z) 1520 { 1521 const _ComplexT __t = __z.__rep(); 1522 _M_value /= __t; 1523 return *this; 1524 } 1525 1526 _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1527 1528 private: 1529 _ComplexT _M_value; 1530 }; 1531 1532 // These bits have to be at the end of this file, so that the 1533 // specializations have all been defined. 1534 inline _GLIBCXX_CONSTEXPR 1535 complex<float>::complex(const complex<double>& __z) 1536 : _M_value(__z.__rep()) { } 1537 1538 inline _GLIBCXX_CONSTEXPR 1539 complex<float>::complex(const complex<long double>& __z) 1540 : _M_value(__z.__rep()) { } 1541 1542 inline _GLIBCXX_CONSTEXPR 1543 complex<double>::complex(const complex<long double>& __z) 1544 : _M_value(__z.__rep()) { } 1545 1546 // Inhibit implicit instantiations for required instantiations, 1547 // which are defined via explicit instantiations elsewhere. 1548 // NB: This syntax is a GNU extension. 1549 #if _GLIBCXX_EXTERN_TEMPLATE 1550 extern template istream& operator>>(istream&, complex<float>&); 1551 extern template ostream& operator<<(ostream&, const complex<float>&); 1552 extern template istream& operator>>(istream&, complex<double>&); 1553 extern template ostream& operator<<(ostream&, const complex<double>&); 1554 extern template istream& operator>>(istream&, complex<long double>&); 1555 extern template ostream& operator<<(ostream&, const complex<long double>&); 1556 1557 #ifdef _GLIBCXX_USE_WCHAR_T 1558 extern template wistream& operator>>(wistream&, complex<float>&); 1559 extern template wostream& operator<<(wostream&, const complex<float>&); 1560 extern template wistream& operator>>(wistream&, complex<double>&); 1561 extern template wostream& operator<<(wostream&, const complex<double>&); 1562 extern template wistream& operator>>(wistream&, complex<long double>&); 1563 extern template wostream& operator<<(wostream&, const complex<long double>&); 1564 #endif 1565 #endif 1566 1567 /// @} group complex_numbers 1568 1569 _GLIBCXX_END_NAMESPACE_VERSION 1570 } // namespace 1571 1572 #if __cplusplus >= 201103L 1573 1574 namespace std _GLIBCXX_VISIBILITY(default) 1575 { 1576 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1577 1578 // Forward declarations. 1579 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1580 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1581 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1582 1583 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1584 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1585 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1586 // DR 595. 1587 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1588 1589 template<typename _Tp> 1590 inline std::complex<_Tp> 1591 __complex_acos(const std::complex<_Tp>& __z) 1592 { 1593 const std::complex<_Tp> __t = std::asin(__z); 1594 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1595 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1596 } 1597 1598 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1599 inline __complex__ float 1600 __complex_acos(__complex__ float __z) 1601 { return __builtin_cacosf(__z); } 1602 1603 inline __complex__ double 1604 __complex_acos(__complex__ double __z) 1605 { return __builtin_cacos(__z); } 1606 1607 inline __complex__ long double 1608 __complex_acos(const __complex__ long double& __z) 1609 { return __builtin_cacosl(__z); } 1610 1611 template<typename _Tp> 1612 inline std::complex<_Tp> 1613 acos(const std::complex<_Tp>& __z) 1614 { return __complex_acos(__z.__rep()); } 1615 #else 1616 /// acos(__z) [8.1.2]. 1617 // Effects: Behaves the same as C99 function cacos, defined 1618 // in subclause 7.3.5.1. 1619 template<typename _Tp> 1620 inline std::complex<_Tp> 1621 acos(const std::complex<_Tp>& __z) 1622 { return __complex_acos(__z); } 1623 #endif 1624 1625 template<typename _Tp> 1626 inline std::complex<_Tp> 1627 __complex_asin(const std::complex<_Tp>& __z) 1628 { 1629 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1630 __t = std::asinh(__t); 1631 return std::complex<_Tp>(__t.imag(), -__t.real()); 1632 } 1633 1634 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1635 inline __complex__ float 1636 __complex_asin(__complex__ float __z) 1637 { return __builtin_casinf(__z); } 1638 1639 inline __complex__ double 1640 __complex_asin(__complex__ double __z) 1641 { return __builtin_casin(__z); } 1642 1643 inline __complex__ long double 1644 __complex_asin(const __complex__ long double& __z) 1645 { return __builtin_casinl(__z); } 1646 1647 template<typename _Tp> 1648 inline std::complex<_Tp> 1649 asin(const std::complex<_Tp>& __z) 1650 { return __complex_asin(__z.__rep()); } 1651 #else 1652 /// asin(__z) [8.1.3]. 1653 // Effects: Behaves the same as C99 function casin, defined 1654 // in subclause 7.3.5.2. 1655 template<typename _Tp> 1656 inline std::complex<_Tp> 1657 asin(const std::complex<_Tp>& __z) 1658 { return __complex_asin(__z); } 1659 #endif 1660 1661 template<typename _Tp> 1662 std::complex<_Tp> 1663 __complex_atan(const std::complex<_Tp>& __z) 1664 { 1665 const _Tp __r2 = __z.real() * __z.real(); 1666 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1667 1668 _Tp __num = __z.imag() + _Tp(1.0); 1669 _Tp __den = __z.imag() - _Tp(1.0); 1670 1671 __num = __r2 + __num * __num; 1672 __den = __r2 + __den * __den; 1673 1674 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1675 _Tp(0.25) * log(__num / __den)); 1676 } 1677 1678 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1679 inline __complex__ float 1680 __complex_atan(__complex__ float __z) 1681 { return __builtin_catanf(__z); } 1682 1683 inline __complex__ double 1684 __complex_atan(__complex__ double __z) 1685 { return __builtin_catan(__z); } 1686 1687 inline __complex__ long double 1688 __complex_atan(const __complex__ long double& __z) 1689 { return __builtin_catanl(__z); } 1690 1691 template<typename _Tp> 1692 inline std::complex<_Tp> 1693 atan(const std::complex<_Tp>& __z) 1694 { return __complex_atan(__z.__rep()); } 1695 #else 1696 /// atan(__z) [8.1.4]. 1697 // Effects: Behaves the same as C99 function catan, defined 1698 // in subclause 7.3.5.3. 1699 template<typename _Tp> 1700 inline std::complex<_Tp> 1701 atan(const std::complex<_Tp>& __z) 1702 { return __complex_atan(__z); } 1703 #endif 1704 1705 template<typename _Tp> 1706 std::complex<_Tp> 1707 __complex_acosh(const std::complex<_Tp>& __z) 1708 { 1709 // Kahan's formula. 1710 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1711 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1712 } 1713 1714 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1715 inline __complex__ float 1716 __complex_acosh(__complex__ float __z) 1717 { return __builtin_cacoshf(__z); } 1718 1719 inline __complex__ double 1720 __complex_acosh(__complex__ double __z) 1721 { return __builtin_cacosh(__z); } 1722 1723 inline __complex__ long double 1724 __complex_acosh(const __complex__ long double& __z) 1725 { return __builtin_cacoshl(__z); } 1726 1727 template<typename _Tp> 1728 inline std::complex<_Tp> 1729 acosh(const std::complex<_Tp>& __z) 1730 { return __complex_acosh(__z.__rep()); } 1731 #else 1732 /// acosh(__z) [8.1.5]. 1733 // Effects: Behaves the same as C99 function cacosh, defined 1734 // in subclause 7.3.6.1. 1735 template<typename _Tp> 1736 inline std::complex<_Tp> 1737 acosh(const std::complex<_Tp>& __z) 1738 { return __complex_acosh(__z); } 1739 #endif 1740 1741 template<typename _Tp> 1742 std::complex<_Tp> 1743 __complex_asinh(const std::complex<_Tp>& __z) 1744 { 1745 std::complex<_Tp> __t((__z.real() - __z.imag()) 1746 * (__z.real() + __z.imag()) + _Tp(1.0), 1747 _Tp(2.0) * __z.real() * __z.imag()); 1748 __t = std::sqrt(__t); 1749 1750 return std::log(__t + __z); 1751 } 1752 1753 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1754 inline __complex__ float 1755 __complex_asinh(__complex__ float __z) 1756 { return __builtin_casinhf(__z); } 1757 1758 inline __complex__ double 1759 __complex_asinh(__complex__ double __z) 1760 { return __builtin_casinh(__z); } 1761 1762 inline __complex__ long double 1763 __complex_asinh(const __complex__ long double& __z) 1764 { return __builtin_casinhl(__z); } 1765 1766 template<typename _Tp> 1767 inline std::complex<_Tp> 1768 asinh(const std::complex<_Tp>& __z) 1769 { return __complex_asinh(__z.__rep()); } 1770 #else 1771 /// asinh(__z) [8.1.6]. 1772 // Effects: Behaves the same as C99 function casin, defined 1773 // in subclause 7.3.6.2. 1774 template<typename _Tp> 1775 inline std::complex<_Tp> 1776 asinh(const std::complex<_Tp>& __z) 1777 { return __complex_asinh(__z); } 1778 #endif 1779 1780 template<typename _Tp> 1781 std::complex<_Tp> 1782 __complex_atanh(const std::complex<_Tp>& __z) 1783 { 1784 const _Tp __i2 = __z.imag() * __z.imag(); 1785 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1786 1787 _Tp __num = _Tp(1.0) + __z.real(); 1788 _Tp __den = _Tp(1.0) - __z.real(); 1789 1790 __num = __i2 + __num * __num; 1791 __den = __i2 + __den * __den; 1792 1793 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1794 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1795 } 1796 1797 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1798 inline __complex__ float 1799 __complex_atanh(__complex__ float __z) 1800 { return __builtin_catanhf(__z); } 1801 1802 inline __complex__ double 1803 __complex_atanh(__complex__ double __z) 1804 { return __builtin_catanh(__z); } 1805 1806 inline __complex__ long double 1807 __complex_atanh(const __complex__ long double& __z) 1808 { return __builtin_catanhl(__z); } 1809 1810 template<typename _Tp> 1811 inline std::complex<_Tp> 1812 atanh(const std::complex<_Tp>& __z) 1813 { return __complex_atanh(__z.__rep()); } 1814 #else 1815 /// atanh(__z) [8.1.7]. 1816 // Effects: Behaves the same as C99 function catanh, defined 1817 // in subclause 7.3.6.3. 1818 template<typename _Tp> 1819 inline std::complex<_Tp> 1820 atanh(const std::complex<_Tp>& __z) 1821 { return __complex_atanh(__z); } 1822 #endif 1823 1824 template<typename _Tp> 1825 inline _Tp 1826 /// fabs(__z) [8.1.8]. 1827 // Effects: Behaves the same as C99 function cabs, defined 1828 // in subclause 7.3.8.1. 1829 fabs(const std::complex<_Tp>& __z) 1830 { return std::abs(__z); } 1831 1832 /// Additional overloads [8.1.9]. 1833 template<typename _Tp> 1834 inline typename __gnu_cxx::__promote<_Tp>::__type 1835 arg(_Tp __x) 1836 { 1837 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1838 #if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1839 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1840 : __type(); 1841 #else 1842 return std::arg(std::complex<__type>(__x)); 1843 #endif 1844 } 1845 1846 template<typename _Tp> 1847 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1848 imag(_Tp) 1849 { return _Tp(); } 1850 1851 template<typename _Tp> 1852 _GLIBCXX20_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1853 norm(_Tp __x) 1854 { 1855 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1856 return __type(__x) * __type(__x); 1857 } 1858 1859 template<typename _Tp> 1860 _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type 1861 real(_Tp __x) 1862 { return __x; } 1863 1864 template<typename _Tp, typename _Up> 1865 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1866 pow(const std::complex<_Tp>& __x, const _Up& __y) 1867 { 1868 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1869 return std::pow(std::complex<__type>(__x), __type(__y)); 1870 } 1871 1872 template<typename _Tp, typename _Up> 1873 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1874 pow(const _Tp& __x, const std::complex<_Up>& __y) 1875 { 1876 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1877 return std::pow(__type(__x), std::complex<__type>(__y)); 1878 } 1879 1880 template<typename _Tp, typename _Up> 1881 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1882 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1883 { 1884 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1885 return std::pow(std::complex<__type>(__x), 1886 std::complex<__type>(__y)); 1887 } 1888 1889 // Forward declarations. 1890 // DR 781. 1891 template<typename _Tp> 1892 std::complex<_Tp> proj(const std::complex<_Tp>&); 1893 1894 // Generic implementation of std::proj, does not work for infinities. 1895 template<typename _Tp> 1896 inline std::complex<_Tp> 1897 __complex_proj(const std::complex<_Tp>& __z) 1898 { return __z; } 1899 1900 #if _GLIBCXX_USE_C99_COMPLEX 1901 inline complex<float> 1902 __complex_proj(const complex<float>& __z) 1903 { return __builtin_cprojf(__z.__rep()); } 1904 1905 inline complex<double> 1906 __complex_proj(const complex<double>& __z) 1907 { return __builtin_cproj(__z.__rep()); } 1908 1909 inline complex<long double> 1910 __complex_proj(const complex<long double>& __z) 1911 { return __builtin_cprojl(__z.__rep()); } 1912 #elif defined _GLIBCXX_USE_C99_MATH_TR1 1913 inline complex<float> 1914 __complex_proj(const complex<float>& __z) 1915 { 1916 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1917 return complex<float>(__builtin_inff(), 1918 __builtin_copysignf(0.0f, __z.imag())); 1919 return __z; 1920 } 1921 1922 inline complex<double> 1923 __complex_proj(const complex<double>& __z) 1924 { 1925 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1926 return complex<double>(__builtin_inf(), 1927 __builtin_copysign(0.0, __z.imag())); 1928 return __z; 1929 } 1930 1931 inline complex<long double> 1932 __complex_proj(const complex<long double>& __z) 1933 { 1934 if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag())) 1935 return complex<long double>(__builtin_infl(), 1936 __builtin_copysignl(0.0l, __z.imag())); 1937 return __z; 1938 } 1939 #endif 1940 1941 template<typename _Tp> 1942 inline std::complex<_Tp> 1943 proj(const std::complex<_Tp>& __z) 1944 { return __complex_proj(__z); } 1945 1946 // Overload for scalars 1947 template<typename _Tp> 1948 inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 1949 proj(_Tp __x) 1950 { 1951 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1952 return std::proj(std::complex<__type>(__x)); 1953 } 1954 1955 template<typename _Tp> 1956 inline _GLIBCXX20_CONSTEXPR 1957 std::complex<typename __gnu_cxx::__promote<_Tp>::__type> 1958 conj(_Tp __x) 1959 { 1960 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1961 return std::complex<__type>(__x, -__type()); 1962 } 1963 1964 #if __cplusplus > 201103L 1965 1966 inline namespace literals { 1967 inline namespace complex_literals { 1968 #pragma GCC diagnostic push 1969 #pragma GCC diagnostic ignored "-Wliteral-suffix" 1970 #define __cpp_lib_complex_udls 201309L 1971 1972 constexpr std::complex<float> 1973 operator""if(long double __num) 1974 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1975 1976 constexpr std::complex<float> 1977 operator""if(unsigned long long __num) 1978 { return std::complex<float>{0.0F, static_cast<float>(__num)}; } 1979 1980 constexpr std::complex<double> 1981 operator""i(long double __num) 1982 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1983 1984 constexpr std::complex<double> 1985 operator""i(unsigned long long __num) 1986 { return std::complex<double>{0.0, static_cast<double>(__num)}; } 1987 1988 constexpr std::complex<long double> 1989 operator""il(long double __num) 1990 { return std::complex<long double>{0.0L, __num}; } 1991 1992 constexpr std::complex<long double> 1993 operator""il(unsigned long long __num) 1994 { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } 1995 1996 #pragma GCC diagnostic pop 1997 } // inline namespace complex_literals 1998 } // inline namespace literals 1999 2000 #endif // C++14 2001 2002 _GLIBCXX_END_NAMESPACE_VERSION 2003 } // namespace 2004 2005 #endif // C++11 2006 2007 #endif /* _GLIBCXX_COMPLEX */ 2008
Indexes created Thu Sep 10 00:26:39 UTC 2026