complex revision 1.3
1 // The template and inlines for the -*- C++ -*- complex number classes. 2 3 // Copyright (C) 1997-2013 Free Software Foundation, Inc. 4 // 5 // This file is part of the GNU ISO C++ Library. This library is free 6 // software; you can redistribute it and/or modify it under the 7 // terms of the GNU General Public License as published by the 8 // Free Software Foundation; either version 3, or (at your option) 9 // any later version. 10 11 // This library is distributed in the hope that it will be useful, 12 // but WITHOUT ANY WARRANTY; without even the implied warranty of 13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 // GNU General Public License for more details. 15 16 // Under Section 7 of GPL version 3, you are granted additional 17 // permissions described in the GCC Runtime Library Exception, version 18 // 3.1, as published by the Free Software Foundation. 19 20 // You should have received a copy of the GNU General Public License and 21 // a copy of the GCC Runtime Library Exception along with this program; 22 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23 // <http://www.gnu.org/licenses/>. 24 25 /** @file include/complex 26 * This is a Standard C++ Library header. 27 */ 28 29 // 30 // ISO C++ 14882: 26.2 Complex Numbers 31 // Note: this is not a conforming implementation. 32 // Initially implemented by Ulrich Drepper <drepper (a] cygnus.com> 33 // Improved by Gabriel Dos Reis <dosreis (a] cmla.ens-cachan.fr> 34 // 35 36 #ifndef _GLIBCXX_COMPLEX 37 #define _GLIBCXX_COMPLEX 1 38 39 #pragma GCC system_header 40 41 #include <bits/c++config.h> 42 #include <bits/cpp_type_traits.h> 43 #include <ext/type_traits.h> 44 #include <cmath> 45 #include <sstream> 46 47 #if _GLIBCXX_USE_C99_COMPLEX 48 // This is disgusting; we can't include ccomplex because that requires c++11 49 // and we can't use the builtins because those point to the wrong 50 // ABI-wise cabs/cabsf so we manually declare those here and use 51 // them directly. 52 extern "C" float __c99_cabsf(_Complex float); 53 extern "C" double __c99_cabs(_Complex double); 54 extern "C" long double __c99_cabsl(_Complex long double); 55 #endif 56 57 // Get rid of a macro possibly defined in <complex.h> 58 #undef complex 59 60 namespace std _GLIBCXX_VISIBILITY(default) 61 { 62 _GLIBCXX_BEGIN_NAMESPACE_VERSION 63 64 /** 65 * @defgroup complex_numbers Complex Numbers 66 * @ingroup numerics 67 * 68 * Classes and functions for complex numbers. 69 * @{ 70 */ 71 72 // Forward declarations. 73 template<typename _Tp> class complex; 74 template<> class complex<float>; 75 template<> class complex<double>; 76 template<> class complex<long double>; 77 78 /// Return magnitude of @a z. 79 template<typename _Tp> _Tp abs(const complex<_Tp>&); 80 /// Return phase angle of @a z. 81 template<typename _Tp> _Tp arg(const complex<_Tp>&); 82 /// Return @a z magnitude squared. 83 template<typename _Tp> _Tp norm(const complex<_Tp>&); 84 85 /// Return complex conjugate of @a z. 86 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); 87 /// Return complex with magnitude @a rho and angle @a theta. 88 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 89 90 // Transcendentals: 91 /// Return complex cosine of @a z. 92 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 93 /// Return complex hyperbolic cosine of @a z. 94 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 95 /// Return complex base e exponential of @a z. 96 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 97 /// Return complex natural logarithm of @a z. 98 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 99 /// Return complex base 10 logarithm of @a z. 100 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 101 #if __cplusplus < 201103L 102 // DR 844. 103 /// Return @a x to the @a y'th power. 104 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 105 #endif 106 /// Return @a x to the @a y'th power. 107 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 108 /// Return @a x to the @a y'th power. 109 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 110 const complex<_Tp>&); 111 /// Return @a x to the @a y'th power. 112 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 113 /// Return complex sine of @a z. 114 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 115 /// Return complex hyperbolic sine of @a z. 116 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 117 /// Return complex square root of @a z. 118 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 119 /// Return complex tangent of @a z. 120 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 121 /// Return complex hyperbolic tangent of @a z. 122 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 123 124 125 // 26.2.2 Primary template class complex 126 /** 127 * Template to represent complex numbers. 128 * 129 * Specializations for float, double, and long double are part of the 130 * library. Results with any other type are not guaranteed. 131 * 132 * @param Tp Type of real and imaginary values. 133 */ 134 template<typename _Tp> 135 struct complex 136 { 137 /// Value typedef. 138 typedef _Tp value_type; 139 140 /// Default constructor. First parameter is x, second parameter is y. 141 /// Unspecified parameters default to 0. 142 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 143 : _M_real(__r), _M_imag(__i) { } 144 145 // Lets the compiler synthesize the copy constructor 146 // complex (const complex<_Tp>&); 147 /// Copy constructor. 148 template<typename _Up> 149 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 150 : _M_real(__z.real()), _M_imag(__z.imag()) { } 151 152 #if __cplusplus >= 201103L 153 // _GLIBCXX_RESOLVE_LIB_DEFECTS 154 // DR 387. std::complex over-encapsulated. 155 _GLIBCXX_ABI_TAG_CXX11 156 constexpr _Tp 157 real() { return _M_real; } 158 159 _GLIBCXX_ABI_TAG_CXX11 160 constexpr _Tp 161 imag() { return _M_imag; } 162 #else 163 /// Return real part of complex number. 164 _Tp& 165 real() { return _M_real; } 166 167 /// Return real part of complex number. 168 const _Tp& 169 real() const { return _M_real; } 170 171 /// Return imaginary part of complex number. 172 _Tp& 173 imag() { return _M_imag; } 174 175 /// Return imaginary part of complex number. 176 const _Tp& 177 imag() const { return _M_imag; } 178 #endif 179 180 // _GLIBCXX_RESOLVE_LIB_DEFECTS 181 // DR 387. std::complex over-encapsulated. 182 void 183 real(_Tp __val) { _M_real = __val; } 184 185 void 186 imag(_Tp __val) { _M_imag = __val; } 187 188 /// Assign this complex number to scalar @a t. 189 complex<_Tp>& operator=(const _Tp&); 190 191 /// Add @a t to this complex number. 192 // 26.2.5/1 193 complex<_Tp>& 194 operator+=(const _Tp& __t) 195 { 196 _M_real += __t; 197 return *this; 198 } 199 200 /// Subtract @a t from this complex number. 201 // 26.2.5/3 202 complex<_Tp>& 203 operator-=(const _Tp& __t) 204 { 205 _M_real -= __t; 206 return *this; 207 } 208 209 /// Multiply this complex number by @a t. 210 complex<_Tp>& operator*=(const _Tp&); 211 /// Divide this complex number by @a t. 212 complex<_Tp>& operator/=(const _Tp&); 213 214 // Lets the compiler synthesize the 215 // copy and assignment operator 216 // complex<_Tp>& operator= (const complex<_Tp>&); 217 /// Assign this complex number to complex @a z. 218 template<typename _Up> 219 complex<_Tp>& operator=(const complex<_Up>&); 220 /// Add @a z to this complex number. 221 template<typename _Up> 222 complex<_Tp>& operator+=(const complex<_Up>&); 223 /// Subtract @a z from this complex number. 224 template<typename _Up> 225 complex<_Tp>& operator-=(const complex<_Up>&); 226 /// Multiply this complex number by @a z. 227 template<typename _Up> 228 complex<_Tp>& operator*=(const complex<_Up>&); 229 /// Divide this complex number by @a z. 230 template<typename _Up> 231 complex<_Tp>& operator/=(const complex<_Up>&); 232 233 _GLIBCXX_USE_CONSTEXPR complex __rep() const 234 { return *this; } 235 236 private: 237 _Tp _M_real; 238 _Tp _M_imag; 239 }; 240 241 template<typename _Tp> 242 complex<_Tp>& 243 complex<_Tp>::operator=(const _Tp& __t) 244 { 245 _M_real = __t; 246 _M_imag = _Tp(); 247 return *this; 248 } 249 250 // 26.2.5/5 251 template<typename _Tp> 252 complex<_Tp>& 253 complex<_Tp>::operator*=(const _Tp& __t) 254 { 255 _M_real *= __t; 256 _M_imag *= __t; 257 return *this; 258 } 259 260 // 26.2.5/7 261 template<typename _Tp> 262 complex<_Tp>& 263 complex<_Tp>::operator/=(const _Tp& __t) 264 { 265 _M_real /= __t; 266 _M_imag /= __t; 267 return *this; 268 } 269 270 template<typename _Tp> 271 template<typename _Up> 272 complex<_Tp>& 273 complex<_Tp>::operator=(const complex<_Up>& __z) 274 { 275 _M_real = __z.real(); 276 _M_imag = __z.imag(); 277 return *this; 278 } 279 280 // 26.2.5/9 281 template<typename _Tp> 282 template<typename _Up> 283 complex<_Tp>& 284 complex<_Tp>::operator+=(const complex<_Up>& __z) 285 { 286 _M_real += __z.real(); 287 _M_imag += __z.imag(); 288 return *this; 289 } 290 291 // 26.2.5/11 292 template<typename _Tp> 293 template<typename _Up> 294 complex<_Tp>& 295 complex<_Tp>::operator-=(const complex<_Up>& __z) 296 { 297 _M_real -= __z.real(); 298 _M_imag -= __z.imag(); 299 return *this; 300 } 301 302 // 26.2.5/13 303 // XXX: This is a grammar school implementation. 304 template<typename _Tp> 305 template<typename _Up> 306 complex<_Tp>& 307 complex<_Tp>::operator*=(const complex<_Up>& __z) 308 { 309 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 310 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 311 _M_real = __r; 312 return *this; 313 } 314 315 // 26.2.5/15 316 // XXX: This is a grammar school implementation. 317 template<typename _Tp> 318 template<typename _Up> 319 complex<_Tp>& 320 complex<_Tp>::operator/=(const complex<_Up>& __z) 321 { 322 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 323 const _Tp __n = std::norm(__z); 324 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 325 _M_real = __r / __n; 326 return *this; 327 } 328 329 // Operators: 330 //@{ 331 /// Return new complex value @a x plus @a y. 332 template<typename _Tp> 333 inline complex<_Tp> 334 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 335 { 336 complex<_Tp> __r = __x; 337 __r += __y; 338 return __r; 339 } 340 341 template<typename _Tp> 342 inline complex<_Tp> 343 operator+(const complex<_Tp>& __x, const _Tp& __y) 344 { 345 complex<_Tp> __r = __x; 346 __r += __y; 347 return __r; 348 } 349 350 template<typename _Tp> 351 inline complex<_Tp> 352 operator+(const _Tp& __x, const complex<_Tp>& __y) 353 { 354 complex<_Tp> __r = __y; 355 __r += __x; 356 return __r; 357 } 358 //@} 359 360 //@{ 361 /// Return new complex value @a x minus @a y. 362 template<typename _Tp> 363 inline complex<_Tp> 364 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 365 { 366 complex<_Tp> __r = __x; 367 __r -= __y; 368 return __r; 369 } 370 371 template<typename _Tp> 372 inline complex<_Tp> 373 operator-(const complex<_Tp>& __x, const _Tp& __y) 374 { 375 complex<_Tp> __r = __x; 376 __r -= __y; 377 return __r; 378 } 379 380 template<typename _Tp> 381 inline complex<_Tp> 382 operator-(const _Tp& __x, const complex<_Tp>& __y) 383 { 384 complex<_Tp> __r(__x, -__y.imag()); 385 __r -= __y.real(); 386 return __r; 387 } 388 //@} 389 390 //@{ 391 /// Return new complex value @a x times @a y. 392 template<typename _Tp> 393 inline complex<_Tp> 394 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 395 { 396 complex<_Tp> __r = __x; 397 __r *= __y; 398 return __r; 399 } 400 401 template<typename _Tp> 402 inline complex<_Tp> 403 operator*(const complex<_Tp>& __x, const _Tp& __y) 404 { 405 complex<_Tp> __r = __x; 406 __r *= __y; 407 return __r; 408 } 409 410 template<typename _Tp> 411 inline complex<_Tp> 412 operator*(const _Tp& __x, const complex<_Tp>& __y) 413 { 414 complex<_Tp> __r = __y; 415 __r *= __x; 416 return __r; 417 } 418 //@} 419 420 //@{ 421 /// Return new complex value @a x divided by @a y. 422 template<typename _Tp> 423 inline complex<_Tp> 424 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 425 { 426 complex<_Tp> __r = __x; 427 __r /= __y; 428 return __r; 429 } 430 431 template<typename _Tp> 432 inline complex<_Tp> 433 operator/(const complex<_Tp>& __x, const _Tp& __y) 434 { 435 complex<_Tp> __r = __x; 436 __r /= __y; 437 return __r; 438 } 439 440 template<typename _Tp> 441 inline complex<_Tp> 442 operator/(const _Tp& __x, const complex<_Tp>& __y) 443 { 444 complex<_Tp> __r = __x; 445 __r /= __y; 446 return __r; 447 } 448 //@} 449 450 /// Return @a x. 451 template<typename _Tp> 452 inline complex<_Tp> 453 operator+(const complex<_Tp>& __x) 454 { return __x; } 455 456 /// Return complex negation of @a x. 457 template<typename _Tp> 458 inline complex<_Tp> 459 operator-(const complex<_Tp>& __x) 460 { return complex<_Tp>(-__x.real(), -__x.imag()); } 461 462 //@{ 463 /// Return true if @a x is equal to @a y. 464 template<typename _Tp> 465 inline _GLIBCXX_CONSTEXPR bool 466 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 467 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 468 469 template<typename _Tp> 470 inline _GLIBCXX_CONSTEXPR bool 471 operator==(const complex<_Tp>& __x, const _Tp& __y) 472 { return __x.real() == __y && __x.imag() == _Tp(); } 473 474 template<typename _Tp> 475 inline _GLIBCXX_CONSTEXPR bool 476 operator==(const _Tp& __x, const complex<_Tp>& __y) 477 { return __x == __y.real() && _Tp() == __y.imag(); } 478 //@} 479 480 //@{ 481 /// Return false if @a x is equal to @a y. 482 template<typename _Tp> 483 inline _GLIBCXX_CONSTEXPR bool 484 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 485 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 486 487 template<typename _Tp> 488 inline _GLIBCXX_CONSTEXPR bool 489 operator!=(const complex<_Tp>& __x, const _Tp& __y) 490 { return __x.real() != __y || __x.imag() != _Tp(); } 491 492 template<typename _Tp> 493 inline _GLIBCXX_CONSTEXPR bool 494 operator!=(const _Tp& __x, const complex<_Tp>& __y) 495 { return __x != __y.real() || _Tp() != __y.imag(); } 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 _Tp __re_x, __im_x; 504 _CharT __ch; 505 __is >> __ch; 506 if (__ch == '(') 507 { 508 __is >> __re_x >> __ch; 509 if (__ch == ',') 510 { 511 __is >> __im_x >> __ch; 512 if (__ch == ')') 513 __x = complex<_Tp>(__re_x, __im_x); 514 else 515 __is.setstate(ios_base::failbit); 516 } 517 else if (__ch == ')') 518 __x = __re_x; 519 else 520 __is.setstate(ios_base::failbit); 521 } 522 else 523 { 524 __is.putback(__ch); 525 __is >> __re_x; 526 __x = __re_x; 527 } 528 return __is; 529 } 530 531 /// Insertion operator for complex values. 532 template<typename _Tp, typename _CharT, class _Traits> 533 basic_ostream<_CharT, _Traits>& 534 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 535 { 536 basic_ostringstream<_CharT, _Traits> __s; 537 __s.flags(__os.flags()); 538 __s.imbue(__os.getloc()); 539 __s.precision(__os.precision()); 540 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 541 return __os << __s.str(); 542 } 543 544 // Values 545 #if __cplusplus >= 201103L 546 template<typename _Tp> 547 constexpr _Tp 548 real(const complex<_Tp>& __z) 549 { return __z.real(); } 550 551 template<typename _Tp> 552 constexpr _Tp 553 imag(const complex<_Tp>& __z) 554 { return __z.imag(); } 555 #else 556 template<typename _Tp> 557 inline _Tp& 558 real(complex<_Tp>& __z) 559 { return __z.real(); } 560 561 template<typename _Tp> 562 inline const _Tp& 563 real(const complex<_Tp>& __z) 564 { return __z.real(); } 565 566 template<typename _Tp> 567 inline _Tp& 568 imag(complex<_Tp>& __z) 569 { return __z.imag(); } 570 571 template<typename _Tp> 572 inline const _Tp& 573 imag(const complex<_Tp>& __z) 574 { return __z.imag(); } 575 #endif 576 577 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 578 template<typename _Tp> 579 inline _Tp 580 __complex_abs(const complex<_Tp>& __z) 581 { 582 _Tp __x = __z.real(); 583 _Tp __y = __z.imag(); 584 const _Tp __s = std::max(abs(__x), abs(__y)); 585 if (__s == _Tp()) // well ... 586 return __s; 587 __x /= __s; 588 __y /= __s; 589 return __s * sqrt(__x * __x + __y * __y); 590 } 591 592 #if _GLIBCXX_USE_C99_COMPLEX 593 // XXX: We can't use __builtin_cabs* because they are broken 594 inline float 595 __complex_abs(__complex__ float __z) { return __c99_cabsf(__z); } 596 597 inline double 598 __complex_abs(__complex__ double __z) { return __c99_cabs(__z); } 599 600 inline long double 601 __complex_abs(const __complex__ long double& __z) 602 { return __c99_cabsl(__z); } 603 604 template<typename _Tp> 605 inline _Tp 606 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 607 #else 608 template<typename _Tp> 609 inline _Tp 610 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 611 #endif 612 613 614 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 615 template<typename _Tp> 616 inline _Tp 617 __complex_arg(const complex<_Tp>& __z) 618 { return atan2(__z.imag(), __z.real()); } 619 620 #if _GLIBCXX_USE_C99_COMPLEX 621 inline float 622 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 623 624 inline double 625 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 626 627 inline long double 628 __complex_arg(const __complex__ long double& __z) 629 { return __builtin_cargl(__z); } 630 631 template<typename _Tp> 632 inline _Tp 633 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 634 #else 635 template<typename _Tp> 636 inline _Tp 637 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 638 #endif 639 640 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 641 // As defined, norm() is -not- a norm is the common mathematical 642 // sens used in numerics. The helper class _Norm_helper<> tries to 643 // distinguish between builtin floating point and the rest, so as 644 // to deliver an answer as close as possible to the real value. 645 template<bool> 646 struct _Norm_helper 647 { 648 template<typename _Tp> 649 static inline _Tp _S_do_it(const complex<_Tp>& __z) 650 { 651 const _Tp __x = __z.real(); 652 const _Tp __y = __z.imag(); 653 return __x * __x + __y * __y; 654 } 655 }; 656 657 template<> 658 struct _Norm_helper<true> 659 { 660 template<typename _Tp> 661 static inline _Tp _S_do_it(const complex<_Tp>& __z) 662 { 663 _Tp __res = std::abs(__z); 664 return __res * __res; 665 } 666 }; 667 668 template<typename _Tp> 669 inline _Tp 670 norm(const complex<_Tp>& __z) 671 { 672 return _Norm_helper<__is_floating<_Tp>::__value 673 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 674 } 675 676 template<typename _Tp> 677 inline complex<_Tp> 678 polar(const _Tp& __rho, const _Tp& __theta) 679 { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } 680 681 template<typename _Tp> 682 inline complex<_Tp> 683 conj(const complex<_Tp>& __z) 684 { return complex<_Tp>(__z.real(), -__z.imag()); } 685 686 // Transcendentals 687 688 // 26.2.8/1 cos(__z): Returns the cosine of __z. 689 template<typename _Tp> 690 inline complex<_Tp> 691 __complex_cos(const complex<_Tp>& __z) 692 { 693 const _Tp __x = __z.real(); 694 const _Tp __y = __z.imag(); 695 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 696 } 697 698 #if _GLIBCXX_USE_C99_COMPLEX 699 inline __complex__ float 700 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 701 702 inline __complex__ double 703 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 704 705 inline __complex__ long double 706 __complex_cos(const __complex__ long double& __z) 707 { return __builtin_ccosl(__z); } 708 709 template<typename _Tp> 710 inline complex<_Tp> 711 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 712 #else 713 template<typename _Tp> 714 inline complex<_Tp> 715 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 716 #endif 717 718 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 719 template<typename _Tp> 720 inline complex<_Tp> 721 __complex_cosh(const complex<_Tp>& __z) 722 { 723 const _Tp __x = __z.real(); 724 const _Tp __y = __z.imag(); 725 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 726 } 727 728 #if _GLIBCXX_USE_C99_COMPLEX 729 inline __complex__ float 730 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 731 732 inline __complex__ double 733 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 734 735 inline __complex__ long double 736 __complex_cosh(const __complex__ long double& __z) 737 { return __builtin_ccoshl(__z); } 738 739 template<typename _Tp> 740 inline complex<_Tp> 741 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 742 #else 743 template<typename _Tp> 744 inline complex<_Tp> 745 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 746 #endif 747 748 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 749 template<typename _Tp> 750 inline complex<_Tp> 751 __complex_exp(const complex<_Tp>& __z) 752 { return std::polar(exp(__z.real()), __z.imag()); } 753 754 #if _GLIBCXX_USE_C99_COMPLEX 755 inline __complex__ float 756 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 757 758 inline __complex__ double 759 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 760 761 inline __complex__ long double 762 __complex_exp(const __complex__ long double& __z) 763 { return __builtin_cexpl(__z); } 764 765 template<typename _Tp> 766 inline complex<_Tp> 767 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 768 #else 769 template<typename _Tp> 770 inline complex<_Tp> 771 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 772 #endif 773 774 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 775 // The branch cut is along the negative axis. 776 template<typename _Tp> 777 inline complex<_Tp> 778 __complex_log(const complex<_Tp>& __z) 779 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 780 781 #if _GLIBCXX_USE_C99_COMPLEX 782 inline __complex__ float 783 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 784 785 inline __complex__ double 786 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 787 788 inline __complex__ long double 789 __complex_log(const __complex__ long double& __z) 790 { return __builtin_clogl(__z); } 791 792 template<typename _Tp> 793 inline complex<_Tp> 794 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 795 #else 796 template<typename _Tp> 797 inline complex<_Tp> 798 log(const complex<_Tp>& __z) { return __complex_log(__z); } 799 #endif 800 801 template<typename _Tp> 802 inline complex<_Tp> 803 log10(const complex<_Tp>& __z) 804 { return std::log(__z) / log(_Tp(10.0)); } 805 806 // 26.2.8/10 sin(__z): Returns the sine of __z. 807 template<typename _Tp> 808 inline complex<_Tp> 809 __complex_sin(const complex<_Tp>& __z) 810 { 811 const _Tp __x = __z.real(); 812 const _Tp __y = __z.imag(); 813 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 814 } 815 816 #if _GLIBCXX_USE_C99_COMPLEX 817 inline __complex__ float 818 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 819 820 inline __complex__ double 821 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 822 823 inline __complex__ long double 824 __complex_sin(const __complex__ long double& __z) 825 { return __builtin_csinl(__z); } 826 827 template<typename _Tp> 828 inline complex<_Tp> 829 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 830 #else 831 template<typename _Tp> 832 inline complex<_Tp> 833 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 834 #endif 835 836 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 837 template<typename _Tp> 838 inline complex<_Tp> 839 __complex_sinh(const complex<_Tp>& __z) 840 { 841 const _Tp __x = __z.real(); 842 const _Tp __y = __z.imag(); 843 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 844 } 845 846 #if _GLIBCXX_USE_C99_COMPLEX 847 inline __complex__ float 848 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 849 850 inline __complex__ double 851 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 852 853 inline __complex__ long double 854 __complex_sinh(const __complex__ long double& __z) 855 { return __builtin_csinhl(__z); } 856 857 template<typename _Tp> 858 inline complex<_Tp> 859 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 860 #else 861 template<typename _Tp> 862 inline complex<_Tp> 863 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 864 #endif 865 866 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 867 // The branch cut is on the negative axis. 868 template<typename _Tp> 869 complex<_Tp> 870 __complex_sqrt(const complex<_Tp>& __z) 871 { 872 _Tp __x = __z.real(); 873 _Tp __y = __z.imag(); 874 875 if (__x == _Tp()) 876 { 877 _Tp __t = sqrt(abs(__y) / 2); 878 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 879 } 880 else 881 { 882 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 883 _Tp __u = __t / 2; 884 return __x > _Tp() 885 ? complex<_Tp>(__u, __y / __t) 886 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 887 } 888 } 889 890 #if _GLIBCXX_USE_C99_COMPLEX 891 inline __complex__ float 892 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 893 894 inline __complex__ double 895 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 896 897 inline __complex__ long double 898 __complex_sqrt(const __complex__ long double& __z) 899 { return __builtin_csqrtl(__z); } 900 901 template<typename _Tp> 902 inline complex<_Tp> 903 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 904 #else 905 template<typename _Tp> 906 inline complex<_Tp> 907 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 908 #endif 909 910 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 911 912 template<typename _Tp> 913 inline complex<_Tp> 914 __complex_tan(const complex<_Tp>& __z) 915 { return std::sin(__z) / std::cos(__z); } 916 917 #if _GLIBCXX_USE_C99_COMPLEX 918 inline __complex__ float 919 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 920 921 inline __complex__ double 922 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 923 924 inline __complex__ long double 925 __complex_tan(const __complex__ long double& __z) 926 { return __builtin_ctanl(__z); } 927 928 template<typename _Tp> 929 inline complex<_Tp> 930 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 931 #else 932 template<typename _Tp> 933 inline complex<_Tp> 934 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 935 #endif 936 937 938 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 939 940 template<typename _Tp> 941 inline complex<_Tp> 942 __complex_tanh(const complex<_Tp>& __z) 943 { return std::sinh(__z) / std::cosh(__z); } 944 945 #if _GLIBCXX_USE_C99_COMPLEX 946 inline __complex__ float 947 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 948 949 inline __complex__ double 950 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 951 952 inline __complex__ long double 953 __complex_tanh(const __complex__ long double& __z) 954 { return __builtin_ctanhl(__z); } 955 956 template<typename _Tp> 957 inline complex<_Tp> 958 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 959 #else 960 template<typename _Tp> 961 inline complex<_Tp> 962 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 963 #endif 964 965 966 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 967 // raised to the __y-th power. The branch 968 // cut is on the negative axis. 969 #if __cplusplus < 201103L 970 template<typename _Tp> 971 complex<_Tp> 972 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 973 { 974 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 975 976 while (__n >>= 1) 977 { 978 __x *= __x; 979 if (__n % 2) 980 __y *= __x; 981 } 982 983 return __y; 984 } 985 986 // _GLIBCXX_RESOLVE_LIB_DEFECTS 987 // DR 844. complex pow return type is ambiguous. 988 template<typename _Tp> 989 inline complex<_Tp> 990 pow(const complex<_Tp>& __z, int __n) 991 { 992 return __n < 0 993 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) 994 : std::__complex_pow_unsigned(__z, __n); 995 } 996 #endif 997 998 template<typename _Tp> 999 complex<_Tp> 1000 pow(const complex<_Tp>& __x, const _Tp& __y) 1001 { 1002 #ifndef _GLIBCXX_USE_C99_COMPLEX 1003 if (__x == _Tp()) 1004 return _Tp(); 1005 #endif 1006 if (__x.imag() == _Tp() && __x.real() > _Tp()) 1007 return pow(__x.real(), __y); 1008 1009 complex<_Tp> __t = std::log(__x); 1010 return std::polar(exp(__y * __t.real()), __y * __t.imag()); 1011 } 1012 1013 template<typename _Tp> 1014 inline complex<_Tp> 1015 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1016 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1017 1018 #if _GLIBCXX_USE_C99_COMPLEX 1019 inline __complex__ float 1020 __complex_pow(__complex__ float __x, __complex__ float __y) 1021 { return __builtin_cpowf(__x, __y); } 1022 1023 inline __complex__ double 1024 __complex_pow(__complex__ double __x, __complex__ double __y) 1025 { return __builtin_cpow(__x, __y); } 1026 1027 inline __complex__ long double 1028 __complex_pow(const __complex__ long double& __x, 1029 const __complex__ long double& __y) 1030 { return __builtin_cpowl(__x, __y); } 1031 1032 template<typename _Tp> 1033 inline complex<_Tp> 1034 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1035 { return __complex_pow(__x.__rep(), __y.__rep()); } 1036 #else 1037 template<typename _Tp> 1038 inline complex<_Tp> 1039 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1040 { return __complex_pow(__x, __y); } 1041 #endif 1042 1043 template<typename _Tp> 1044 inline complex<_Tp> 1045 pow(const _Tp& __x, const complex<_Tp>& __y) 1046 { 1047 return __x > _Tp() ? std::polar(pow(__x, __y.real()), 1048 __y.imag() * log(__x)) 1049 : std::pow(complex<_Tp>(__x), __y); 1050 } 1051 1052 /// 26.2.3 complex specializations 1053 /// complex<float> specialization 1054 template<> 1055 struct complex<float> 1056 { 1057 typedef float value_type; 1058 typedef __complex__ float _ComplexT; 1059 1060 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1061 1062 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1063 #if __cplusplus >= 201103L 1064 : _M_value{ __r, __i } { } 1065 #else 1066 { 1067 __real__ _M_value = __r; 1068 __imag__ _M_value = __i; 1069 } 1070 #endif 1071 1072 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1073 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1074 1075 #if __cplusplus >= 201103L 1076 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1077 // DR 387. std::complex over-encapsulated. 1078 __attribute ((__abi_tag__ ("cxx11"))) 1079 constexpr float 1080 real() { return __real__ _M_value; } 1081 1082 __attribute ((__abi_tag__ ("cxx11"))) 1083 constexpr float 1084 imag() { return __imag__ _M_value; } 1085 #else 1086 float& 1087 real() { return __real__ _M_value; } 1088 1089 const float& 1090 real() const { return __real__ _M_value; } 1091 1092 float& 1093 imag() { return __imag__ _M_value; } 1094 1095 const float& 1096 imag() const { return __imag__ _M_value; } 1097 #endif 1098 1099 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1100 // DR 387. std::complex over-encapsulated. 1101 void 1102 real(float __val) { __real__ _M_value = __val; } 1103 1104 void 1105 imag(float __val) { __imag__ _M_value = __val; } 1106 1107 complex& 1108 operator=(float __f) 1109 { 1110 _M_value = __f; 1111 return *this; 1112 } 1113 1114 complex& 1115 operator+=(float __f) 1116 { 1117 _M_value += __f; 1118 return *this; 1119 } 1120 1121 complex& 1122 operator-=(float __f) 1123 { 1124 _M_value -= __f; 1125 return *this; 1126 } 1127 1128 complex& 1129 operator*=(float __f) 1130 { 1131 _M_value *= __f; 1132 return *this; 1133 } 1134 1135 complex& 1136 operator/=(float __f) 1137 { 1138 _M_value /= __f; 1139 return *this; 1140 } 1141 1142 // Let the compiler synthesize the copy and assignment 1143 // operator. It always does a pretty good job. 1144 // complex& operator=(const complex&); 1145 1146 template<typename _Tp> 1147 complex& 1148 operator=(const complex<_Tp>& __z) 1149 { 1150 __real__ _M_value = __z.real(); 1151 __imag__ _M_value = __z.imag(); 1152 return *this; 1153 } 1154 1155 template<typename _Tp> 1156 complex& 1157 operator+=(const complex<_Tp>& __z) 1158 { 1159 __real__ _M_value += __z.real(); 1160 __imag__ _M_value += __z.imag(); 1161 return *this; 1162 } 1163 1164 template<class _Tp> 1165 complex& 1166 operator-=(const complex<_Tp>& __z) 1167 { 1168 __real__ _M_value -= __z.real(); 1169 __imag__ _M_value -= __z.imag(); 1170 return *this; 1171 } 1172 1173 template<class _Tp> 1174 complex& 1175 operator*=(const complex<_Tp>& __z) 1176 { 1177 _ComplexT __t; 1178 __real__ __t = __z.real(); 1179 __imag__ __t = __z.imag(); 1180 _M_value *= __t; 1181 return *this; 1182 } 1183 1184 template<class _Tp> 1185 complex& 1186 operator/=(const complex<_Tp>& __z) 1187 { 1188 _ComplexT __t; 1189 __real__ __t = __z.real(); 1190 __imag__ __t = __z.imag(); 1191 _M_value /= __t; 1192 return *this; 1193 } 1194 1195 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1196 1197 private: 1198 _ComplexT _M_value; 1199 }; 1200 1201 /// 26.2.3 complex specializations 1202 /// complex<double> specialization 1203 template<> 1204 struct complex<double> 1205 { 1206 typedef double value_type; 1207 typedef __complex__ double _ComplexT; 1208 1209 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1210 1211 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1212 #if __cplusplus >= 201103L 1213 : _M_value{ __r, __i } { } 1214 #else 1215 { 1216 __real__ _M_value = __r; 1217 __imag__ _M_value = __i; 1218 } 1219 #endif 1220 1221 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1222 : _M_value(__z.__rep()) { } 1223 1224 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1225 1226 #if __cplusplus >= 201103L 1227 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1228 // DR 387. std::complex over-encapsulated. 1229 __attribute ((__abi_tag__ ("cxx11"))) 1230 constexpr double 1231 real() { return __real__ _M_value; } 1232 1233 __attribute ((__abi_tag__ ("cxx11"))) 1234 constexpr double 1235 imag() { return __imag__ _M_value; } 1236 #else 1237 double& 1238 real() { return __real__ _M_value; } 1239 1240 const double& 1241 real() const { return __real__ _M_value; } 1242 1243 double& 1244 imag() { return __imag__ _M_value; } 1245 1246 const double& 1247 imag() const { return __imag__ _M_value; } 1248 #endif 1249 1250 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1251 // DR 387. std::complex over-encapsulated. 1252 void 1253 real(double __val) { __real__ _M_value = __val; } 1254 1255 void 1256 imag(double __val) { __imag__ _M_value = __val; } 1257 1258 complex& 1259 operator=(double __d) 1260 { 1261 _M_value = __d; 1262 return *this; 1263 } 1264 1265 complex& 1266 operator+=(double __d) 1267 { 1268 _M_value += __d; 1269 return *this; 1270 } 1271 1272 complex& 1273 operator-=(double __d) 1274 { 1275 _M_value -= __d; 1276 return *this; 1277 } 1278 1279 complex& 1280 operator*=(double __d) 1281 { 1282 _M_value *= __d; 1283 return *this; 1284 } 1285 1286 complex& 1287 operator/=(double __d) 1288 { 1289 _M_value /= __d; 1290 return *this; 1291 } 1292 1293 // The compiler will synthesize this, efficiently. 1294 // complex& operator=(const complex&); 1295 1296 template<typename _Tp> 1297 complex& 1298 operator=(const complex<_Tp>& __z) 1299 { 1300 __real__ _M_value = __z.real(); 1301 __imag__ _M_value = __z.imag(); 1302 return *this; 1303 } 1304 1305 template<typename _Tp> 1306 complex& 1307 operator+=(const complex<_Tp>& __z) 1308 { 1309 __real__ _M_value += __z.real(); 1310 __imag__ _M_value += __z.imag(); 1311 return *this; 1312 } 1313 1314 template<typename _Tp> 1315 complex& 1316 operator-=(const complex<_Tp>& __z) 1317 { 1318 __real__ _M_value -= __z.real(); 1319 __imag__ _M_value -= __z.imag(); 1320 return *this; 1321 } 1322 1323 template<typename _Tp> 1324 complex& 1325 operator*=(const complex<_Tp>& __z) 1326 { 1327 _ComplexT __t; 1328 __real__ __t = __z.real(); 1329 __imag__ __t = __z.imag(); 1330 _M_value *= __t; 1331 return *this; 1332 } 1333 1334 template<typename _Tp> 1335 complex& 1336 operator/=(const complex<_Tp>& __z) 1337 { 1338 _ComplexT __t; 1339 __real__ __t = __z.real(); 1340 __imag__ __t = __z.imag(); 1341 _M_value /= __t; 1342 return *this; 1343 } 1344 1345 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1346 1347 private: 1348 _ComplexT _M_value; 1349 }; 1350 1351 /// 26.2.3 complex specializations 1352 /// complex<long double> specialization 1353 template<> 1354 struct complex<long double> 1355 { 1356 typedef long double value_type; 1357 typedef __complex__ long double _ComplexT; 1358 1359 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1360 1361 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1362 long double __i = 0.0L) 1363 #if __cplusplus >= 201103L 1364 : _M_value{ __r, __i } { } 1365 #else 1366 { 1367 __real__ _M_value = __r; 1368 __imag__ _M_value = __i; 1369 } 1370 #endif 1371 1372 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1373 : _M_value(__z.__rep()) { } 1374 1375 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1376 : _M_value(__z.__rep()) { } 1377 1378 #if __cplusplus >= 201103L 1379 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1380 // DR 387. std::complex over-encapsulated. 1381 __attribute ((__abi_tag__ ("cxx11"))) 1382 constexpr long double 1383 real() { return __real__ _M_value; } 1384 1385 __attribute ((__abi_tag__ ("cxx11"))) 1386 constexpr long double 1387 imag() { return __imag__ _M_value; } 1388 #else 1389 long double& 1390 real() { return __real__ _M_value; } 1391 1392 const long double& 1393 real() const { return __real__ _M_value; } 1394 1395 long double& 1396 imag() { return __imag__ _M_value; } 1397 1398 const long double& 1399 imag() const { return __imag__ _M_value; } 1400 #endif 1401 1402 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1403 // DR 387. std::complex over-encapsulated. 1404 void 1405 real(long double __val) { __real__ _M_value = __val; } 1406 1407 void 1408 imag(long double __val) { __imag__ _M_value = __val; } 1409 1410 complex& 1411 operator=(long double __r) 1412 { 1413 _M_value = __r; 1414 return *this; 1415 } 1416 1417 complex& 1418 operator+=(long double __r) 1419 { 1420 _M_value += __r; 1421 return *this; 1422 } 1423 1424 complex& 1425 operator-=(long double __r) 1426 { 1427 _M_value -= __r; 1428 return *this; 1429 } 1430 1431 complex& 1432 operator*=(long double __r) 1433 { 1434 _M_value *= __r; 1435 return *this; 1436 } 1437 1438 complex& 1439 operator/=(long double __r) 1440 { 1441 _M_value /= __r; 1442 return *this; 1443 } 1444 1445 // The compiler knows how to do this efficiently 1446 // complex& operator=(const complex&); 1447 1448 template<typename _Tp> 1449 complex& 1450 operator=(const complex<_Tp>& __z) 1451 { 1452 __real__ _M_value = __z.real(); 1453 __imag__ _M_value = __z.imag(); 1454 return *this; 1455 } 1456 1457 template<typename _Tp> 1458 complex& 1459 operator+=(const complex<_Tp>& __z) 1460 { 1461 __real__ _M_value += __z.real(); 1462 __imag__ _M_value += __z.imag(); 1463 return *this; 1464 } 1465 1466 template<typename _Tp> 1467 complex& 1468 operator-=(const complex<_Tp>& __z) 1469 { 1470 __real__ _M_value -= __z.real(); 1471 __imag__ _M_value -= __z.imag(); 1472 return *this; 1473 } 1474 1475 template<typename _Tp> 1476 complex& 1477 operator*=(const complex<_Tp>& __z) 1478 { 1479 _ComplexT __t; 1480 __real__ __t = __z.real(); 1481 __imag__ __t = __z.imag(); 1482 _M_value *= __t; 1483 return *this; 1484 } 1485 1486 template<typename _Tp> 1487 complex& 1488 operator/=(const complex<_Tp>& __z) 1489 { 1490 _ComplexT __t; 1491 __real__ __t = __z.real(); 1492 __imag__ __t = __z.imag(); 1493 _M_value /= __t; 1494 return *this; 1495 } 1496 1497 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1498 1499 private: 1500 _ComplexT _M_value; 1501 }; 1502 1503 // These bits have to be at the end of this file, so that the 1504 // specializations have all been defined. 1505 inline _GLIBCXX_CONSTEXPR 1506 complex<float>::complex(const complex<double>& __z) 1507 : _M_value(__z.__rep()) { } 1508 1509 inline _GLIBCXX_CONSTEXPR 1510 complex<float>::complex(const complex<long double>& __z) 1511 : _M_value(__z.__rep()) { } 1512 1513 inline _GLIBCXX_CONSTEXPR 1514 complex<double>::complex(const complex<long double>& __z) 1515 : _M_value(__z.__rep()) { } 1516 1517 // Inhibit implicit instantiations for required instantiations, 1518 // which are defined via explicit instantiations elsewhere. 1519 // NB: This syntax is a GNU extension. 1520 #if _GLIBCXX_EXTERN_TEMPLATE 1521 extern template istream& operator>>(istream&, complex<float>&); 1522 extern template ostream& operator<<(ostream&, const complex<float>&); 1523 extern template istream& operator>>(istream&, complex<double>&); 1524 extern template ostream& operator<<(ostream&, const complex<double>&); 1525 extern template istream& operator>>(istream&, complex<long double>&); 1526 extern template ostream& operator<<(ostream&, const complex<long double>&); 1527 1528 #ifdef _GLIBCXX_USE_WCHAR_T 1529 extern template wistream& operator>>(wistream&, complex<float>&); 1530 extern template wostream& operator<<(wostream&, const complex<float>&); 1531 extern template wistream& operator>>(wistream&, complex<double>&); 1532 extern template wostream& operator<<(wostream&, const complex<double>&); 1533 extern template wistream& operator>>(wistream&, complex<long double>&); 1534 extern template wostream& operator<<(wostream&, const complex<long double>&); 1535 #endif 1536 #endif 1537 1538 // @} group complex_numbers 1539 1540 _GLIBCXX_END_NAMESPACE_VERSION 1541 } // namespace 1542 1543 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1544 { 1545 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1546 1547 // See ext/type_traits.h for the primary template. 1548 template<typename _Tp, typename _Up> 1549 struct __promote_2<std::complex<_Tp>, _Up> 1550 { 1551 public: 1552 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1553 }; 1554 1555 template<typename _Tp, typename _Up> 1556 struct __promote_2<_Tp, std::complex<_Up> > 1557 { 1558 public: 1559 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1560 }; 1561 1562 template<typename _Tp, typename _Up> 1563 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1564 { 1565 public: 1566 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1567 }; 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 (_GLIBCXX_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 inline typename __gnu_cxx::__promote<_Tp>::__type 1848 imag(_Tp) 1849 { return _Tp(); } 1850 1851 template<typename _Tp> 1852 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 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> std::complex<_Tp> proj(const std::complex<_Tp>&); 1892 1893 template<typename _Tp> 1894 std::complex<_Tp> 1895 __complex_proj(const std::complex<_Tp>& __z) 1896 { 1897 const _Tp __den = (__z.real() * __z.real() 1898 + __z.imag() * __z.imag() + _Tp(1.0)); 1899 1900 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, 1901 (_Tp(2.0) * __z.imag()) / __den); 1902 } 1903 1904 #if _GLIBCXX_USE_C99_COMPLEX 1905 inline __complex__ float 1906 __complex_proj(__complex__ float __z) 1907 { return __builtin_cprojf(__z); } 1908 1909 inline __complex__ double 1910 __complex_proj(__complex__ double __z) 1911 { return __builtin_cproj(__z); } 1912 1913 inline __complex__ long double 1914 __complex_proj(const __complex__ long double& __z) 1915 { return __builtin_cprojl(__z); } 1916 1917 template<typename _Tp> 1918 inline std::complex<_Tp> 1919 proj(const std::complex<_Tp>& __z) 1920 { return __complex_proj(__z.__rep()); } 1921 #else 1922 template<typename _Tp> 1923 inline std::complex<_Tp> 1924 proj(const std::complex<_Tp>& __z) 1925 { return __complex_proj(__z); } 1926 #endif 1927 1928 // DR 1137. 1929 template<typename _Tp> 1930 inline typename __gnu_cxx::__promote<_Tp>::__type 1931 proj(_Tp __x) 1932 { return __x; } 1933 1934 template<typename _Tp> 1935 inline typename __gnu_cxx::__promote<_Tp>::__type 1936 conj(_Tp __x) 1937 { return __x; } 1938 1939 _GLIBCXX_END_NAMESPACE_VERSION 1940 } // namespace 1941 1942 #endif // C++11 1943 1944 #endif /* _GLIBCXX_COMPLEX */ 1945
Indexes created Fri Mar 06 19:51:54 UTC 2026