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@cygnus.com> 33// Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr> 34// 35 36#ifndef _GLIBCXX_COMPLEX 37#define _GLIBCXX_COMPLEX 1 38 39#pragma GCC system_header 40 41#include <bits/c++config.h> 42#include <bits/cpp_type_traits.h> 43#include <ext/type_traits.h> 44#include <cmath> 45#include <sstream> 46 47// Get rid of a macro possibly defined in <complex.h> 48#undef complex 49 50namespace std _GLIBCXX_VISIBILITY(default) 51{ 52_GLIBCXX_BEGIN_NAMESPACE_VERSION 53 54 /** 55 * @defgroup complex_numbers Complex Numbers 56 * @ingroup numerics 57 * 58 * Classes and functions for complex numbers. 59 * @{ 60 */ 61 62 // Forward declarations. 63 template<typename _Tp> class complex; 64 template<> class complex<float>; 65 template<> class complex<double>; 66 template<> class complex<long double>; 67 68 /// Return magnitude of @a z. 69 template<typename _Tp> _Tp abs(const complex<_Tp>&); 70 /// Return phase angle of @a z. 71 template<typename _Tp> _Tp arg(const complex<_Tp>&); 72 /// Return @a z magnitude squared. 73 template<typename _Tp> _Tp norm(const complex<_Tp>&); 74 75 /// Return complex conjugate of @a z. 76 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); 77 /// Return complex with magnitude @a rho and angle @a theta. 78 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 79 80 // Transcendentals: 81 /// Return complex cosine of @a z. 82 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 83 /// Return complex hyperbolic cosine of @a z. 84 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 85 /// Return complex base e exponential of @a z. 86 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 87 /// Return complex natural logarithm of @a z. 88 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 89 /// Return complex base 10 logarithm of @a z. 90 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 91#if __cplusplus < 201103L 92 // DR 844. 93 /// Return @a x to the @a y'th power. 94 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 95#endif 96 /// Return @a x to the @a y'th power. 97 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 98 /// Return @a x to the @a y'th power. 99 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 100 const complex<_Tp>&); 101 /// Return @a x to the @a y'th power. 102 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 103 /// Return complex sine of @a z. 104 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 105 /// Return complex hyperbolic sine of @a z. 106 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 107 /// Return complex square root of @a z. 108 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 109 /// Return complex tangent of @a z. 110 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 111 /// Return complex hyperbolic tangent of @a z. 112 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 113 114 115 // 26.2.2 Primary template class complex 116 /** 117 * Template to represent complex numbers. 118 * 119 * Specializations for float, double, and long double are part of the 120 * library. Results with any other type are not guaranteed. 121 * 122 * @param Tp Type of real and imaginary values. 123 */ 124 template<typename _Tp> 125 struct complex 126 { 127 /// Value typedef. 128 typedef _Tp value_type; 129 130 /// Default constructor. First parameter is x, second parameter is y. 131 /// Unspecified parameters default to 0. 132 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 133 : _M_real(__r), _M_imag(__i) { } 134 135 // Lets the compiler synthesize the copy constructor 136 // complex (const complex<_Tp>&); 137 /// Copy constructor. 138 template<typename _Up> 139 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 140 : _M_real(__z.real()), _M_imag(__z.imag()) { } 141 142#if __cplusplus >= 201103L 143 // _GLIBCXX_RESOLVE_LIB_DEFECTS 144 // DR 387. std::complex over-encapsulated. 145 __attribute ((__abi_tag__ ("cxx11"))) 146 constexpr _Tp 147 real() { return _M_real; } 148 149 __attribute ((__abi_tag__ ("cxx11"))) 150 constexpr _Tp 151 imag() { return _M_imag; } 152#else 153 /// Return real part of complex number. 154 _Tp& 155 real() { return _M_real; } 156 157 /// Return real part of complex number. 158 const _Tp& 159 real() const { return _M_real; } 160 161 /// Return imaginary part of complex number. 162 _Tp& 163 imag() { return _M_imag; } 164 165 /// Return imaginary part of complex number. 166 const _Tp& 167 imag() const { return _M_imag; } 168#endif 169 170 // _GLIBCXX_RESOLVE_LIB_DEFECTS 171 // DR 387. std::complex over-encapsulated. 172 void 173 real(_Tp __val) { _M_real = __val; } 174 175 void 176 imag(_Tp __val) { _M_imag = __val; } 177 178 /// Assign this complex number to scalar @a t. 179 complex<_Tp>& operator=(const _Tp&); 180 181 /// Add @a t to this complex number. 182 // 26.2.5/1 183 complex<_Tp>& 184 operator+=(const _Tp& __t) 185 { 186 _M_real += __t; 187 return *this; 188 } 189 190 /// Subtract @a t from this complex number. 191 // 26.2.5/3 192 complex<_Tp>& 193 operator-=(const _Tp& __t) 194 { 195 _M_real -= __t; 196 return *this; 197 } 198 199 /// Multiply this complex number by @a t. 200 complex<_Tp>& operator*=(const _Tp&); 201 /// Divide this complex number by @a t. 202 complex<_Tp>& operator/=(const _Tp&); 203 204 // Lets the compiler synthesize the 205 // copy and assignment operator 206 // complex<_Tp>& operator= (const complex<_Tp>&); 207 /// Assign this complex number to complex @a z. 208 template<typename _Up> 209 complex<_Tp>& operator=(const complex<_Up>&); 210 /// Add @a z to this complex number. 211 template<typename _Up> 212 complex<_Tp>& operator+=(const complex<_Up>&); 213 /// Subtract @a z from this complex number. 214 template<typename _Up> 215 complex<_Tp>& operator-=(const complex<_Up>&); 216 /// Multiply this complex number by @a z. 217 template<typename _Up> 218 complex<_Tp>& operator*=(const complex<_Up>&); 219 /// Divide this complex number by @a z. 220 template<typename _Up> 221 complex<_Tp>& operator/=(const complex<_Up>&); 222 223 _GLIBCXX_USE_CONSTEXPR complex __rep() const 224 { return *this; } 225 226 private: 227 _Tp _M_real; 228 _Tp _M_imag; 229 }; 230 231 template<typename _Tp> 232 complex<_Tp>& 233 complex<_Tp>::operator=(const _Tp& __t) 234 { 235 _M_real = __t; 236 _M_imag = _Tp(); 237 return *this; 238 } 239 240 // 26.2.5/5 241 template<typename _Tp> 242 complex<_Tp>& 243 complex<_Tp>::operator*=(const _Tp& __t) 244 { 245 _M_real *= __t; 246 _M_imag *= __t; 247 return *this; 248 } 249 250 // 26.2.5/7 251 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 template<typename _Tp> 261 template<typename _Up> 262 complex<_Tp>& 263 complex<_Tp>::operator=(const complex<_Up>& __z) 264 { 265 _M_real = __z.real(); 266 _M_imag = __z.imag(); 267 return *this; 268 } 269 270 // 26.2.5/9 271 template<typename _Tp> 272 template<typename _Up> 273 complex<_Tp>& 274 complex<_Tp>::operator+=(const complex<_Up>& __z) 275 { 276 _M_real += __z.real(); 277 _M_imag += __z.imag(); 278 return *this; 279 } 280 281 // 26.2.5/11 282 template<typename _Tp> 283 template<typename _Up> 284 complex<_Tp>& 285 complex<_Tp>::operator-=(const complex<_Up>& __z) 286 { 287 _M_real -= __z.real(); 288 _M_imag -= __z.imag(); 289 return *this; 290 } 291 292 // 26.2.5/13 293 // XXX: This is a grammar school implementation. 294 template<typename _Tp> 295 template<typename _Up> 296 complex<_Tp>& 297 complex<_Tp>::operator*=(const complex<_Up>& __z) 298 { 299 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 300 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 301 _M_real = __r; 302 return *this; 303 } 304 305 // 26.2.5/15 306 // XXX: This is a grammar school implementation. 307 template<typename _Tp> 308 template<typename _Up> 309 complex<_Tp>& 310 complex<_Tp>::operator/=(const complex<_Up>& __z) 311 { 312 const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); 313 const _Tp __n = std::norm(__z); 314 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 315 _M_real = __r / __n; 316 return *this; 317 } 318 319 // Operators: 320 //@{ 321 /// Return new complex value @a x plus @a y. 322 template<typename _Tp> 323 inline complex<_Tp> 324 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 325 { 326 complex<_Tp> __r = __x; 327 __r += __y; 328 return __r; 329 } 330 331 template<typename _Tp> 332 inline complex<_Tp> 333 operator+(const complex<_Tp>& __x, const _Tp& __y) 334 { 335 complex<_Tp> __r = __x; 336 __r += __y; 337 return __r; 338 } 339 340 template<typename _Tp> 341 inline complex<_Tp> 342 operator+(const _Tp& __x, const complex<_Tp>& __y) 343 { 344 complex<_Tp> __r = __y; 345 __r += __x; 346 return __r; 347 } 348 //@} 349 350 //@{ 351 /// Return new complex value @a x minus @a y. 352 template<typename _Tp> 353 inline complex<_Tp> 354 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 355 { 356 complex<_Tp> __r = __x; 357 __r -= __y; 358 return __r; 359 } 360 361 template<typename _Tp> 362 inline complex<_Tp> 363 operator-(const complex<_Tp>& __x, const _Tp& __y) 364 { 365 complex<_Tp> __r = __x; 366 __r -= __y; 367 return __r; 368 } 369 370 template<typename _Tp> 371 inline complex<_Tp> 372 operator-(const _Tp& __x, const complex<_Tp>& __y) 373 { 374 complex<_Tp> __r(__x, -__y.imag()); 375 __r -= __y.real(); 376 return __r; 377 } 378 //@} 379 380 //@{ 381 /// Return new complex value @a x times @a y. 382 template<typename _Tp> 383 inline complex<_Tp> 384 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 385 { 386 complex<_Tp> __r = __x; 387 __r *= __y; 388 return __r; 389 } 390 391 template<typename _Tp> 392 inline complex<_Tp> 393 operator*(const complex<_Tp>& __x, const _Tp& __y) 394 { 395 complex<_Tp> __r = __x; 396 __r *= __y; 397 return __r; 398 } 399 400 template<typename _Tp> 401 inline complex<_Tp> 402 operator*(const _Tp& __x, const complex<_Tp>& __y) 403 { 404 complex<_Tp> __r = __y; 405 __r *= __x; 406 return __r; 407 } 408 //@} 409 410 //@{ 411 /// Return new complex value @a x divided by @a y. 412 template<typename _Tp> 413 inline complex<_Tp> 414 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 415 { 416 complex<_Tp> __r = __x; 417 __r /= __y; 418 return __r; 419 } 420 421 template<typename _Tp> 422 inline complex<_Tp> 423 operator/(const complex<_Tp>& __x, const _Tp& __y) 424 { 425 complex<_Tp> __r = __x; 426 __r /= __y; 427 return __r; 428 } 429 430 template<typename _Tp> 431 inline complex<_Tp> 432 operator/(const _Tp& __x, const complex<_Tp>& __y) 433 { 434 complex<_Tp> __r = __x; 435 __r /= __y; 436 return __r; 437 } 438 //@} 439 440 /// Return @a x. 441 template<typename _Tp> 442 inline complex<_Tp> 443 operator+(const complex<_Tp>& __x) 444 { return __x; } 445 446 /// Return complex negation of @a x. 447 template<typename _Tp> 448 inline complex<_Tp> 449 operator-(const complex<_Tp>& __x) 450 { return complex<_Tp>(-__x.real(), -__x.imag()); } 451 452 //@{ 453 /// Return true if @a x is equal to @a y. 454 template<typename _Tp> 455 inline _GLIBCXX_CONSTEXPR bool 456 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 457 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 458 459 template<typename _Tp> 460 inline _GLIBCXX_CONSTEXPR bool 461 operator==(const complex<_Tp>& __x, const _Tp& __y) 462 { return __x.real() == __y && __x.imag() == _Tp(); } 463 464 template<typename _Tp> 465 inline _GLIBCXX_CONSTEXPR bool 466 operator==(const _Tp& __x, const complex<_Tp>& __y) 467 { return __x == __y.real() && _Tp() == __y.imag(); } 468 //@} 469 470 //@{ 471 /// Return false if @a x is equal to @a y. 472 template<typename _Tp> 473 inline _GLIBCXX_CONSTEXPR bool 474 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 475 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 476 477 template<typename _Tp> 478 inline _GLIBCXX_CONSTEXPR bool 479 operator!=(const complex<_Tp>& __x, const _Tp& __y) 480 { return __x.real() != __y || __x.imag() != _Tp(); } 481 482 template<typename _Tp> 483 inline _GLIBCXX_CONSTEXPR bool 484 operator!=(const _Tp& __x, const complex<_Tp>& __y) 485 { return __x != __y.real() || _Tp() != __y.imag(); } 486 //@} 487 488 /// Extraction operator for complex values. 489 template<typename _Tp, typename _CharT, class _Traits> 490 basic_istream<_CharT, _Traits>& 491 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 492 { 493 _Tp __re_x, __im_x; 494 _CharT __ch; 495 __is >> __ch; 496 if (__ch == '(') 497 { 498 __is >> __re_x >> __ch; 499 if (__ch == ',') 500 { 501 __is >> __im_x >> __ch; 502 if (__ch == ')') 503 __x = complex<_Tp>(__re_x, __im_x); 504 else 505 __is.setstate(ios_base::failbit); 506 } 507 else if (__ch == ')') 508 __x = __re_x; 509 else 510 __is.setstate(ios_base::failbit); 511 } 512 else 513 { 514 __is.putback(__ch); 515 __is >> __re_x; 516 __x = __re_x; 517 } 518 return __is; 519 } 520 521 /// Insertion operator for complex values. 522 template<typename _Tp, typename _CharT, class _Traits> 523 basic_ostream<_CharT, _Traits>& 524 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 525 { 526 basic_ostringstream<_CharT, _Traits> __s; 527 __s.flags(__os.flags()); 528 __s.imbue(__os.getloc()); 529 __s.precision(__os.precision()); 530 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 531 return __os << __s.str(); 532 } 533 534 // Values 535#if __cplusplus >= 201103L 536 template<typename _Tp> 537 constexpr _Tp 538 real(const complex<_Tp>& __z) 539 { return __z.real(); } 540 541 template<typename _Tp> 542 constexpr _Tp 543 imag(const complex<_Tp>& __z) 544 { return __z.imag(); } 545#else 546 template<typename _Tp> 547 inline _Tp& 548 real(complex<_Tp>& __z) 549 { return __z.real(); } 550 551 template<typename _Tp> 552 inline const _Tp& 553 real(const complex<_Tp>& __z) 554 { return __z.real(); } 555 556 template<typename _Tp> 557 inline _Tp& 558 imag(complex<_Tp>& __z) 559 { return __z.imag(); } 560 561 template<typename _Tp> 562 inline const _Tp& 563 imag(const complex<_Tp>& __z) 564 { return __z.imag(); } 565#endif 566 567 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 568 template<typename _Tp> 569 inline _Tp 570 __complex_abs(const complex<_Tp>& __z) 571 { 572 _Tp __x = __z.real(); 573 _Tp __y = __z.imag(); 574 const _Tp __s = std::max(abs(__x), abs(__y)); 575 if (__s == _Tp()) // well ... 576 return __s; 577 __x /= __s; 578 __y /= __s; 579 return __s * sqrt(__x * __x + __y * __y); 580 } 581 582#if _GLIBCXX_USE_C99_COMPLEX 583 inline float 584 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 585 586 inline double 587 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 588 589 inline long double 590 __complex_abs(const __complex__ long double& __z) 591 { return __builtin_cabsl(__z); } 592 593 template<typename _Tp> 594 inline _Tp 595 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 596#else 597 template<typename _Tp> 598 inline _Tp 599 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 600#endif 601 602 603 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 604 template<typename _Tp> 605 inline _Tp 606 __complex_arg(const complex<_Tp>& __z) 607 { return atan2(__z.imag(), __z.real()); } 608 609#if _GLIBCXX_USE_C99_COMPLEX 610 inline float 611 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 612 613 inline double 614 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 615 616 inline long double 617 __complex_arg(const __complex__ long double& __z) 618 { return __builtin_cargl(__z); } 619 620 template<typename _Tp> 621 inline _Tp 622 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 623#else 624 template<typename _Tp> 625 inline _Tp 626 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 627#endif 628 629 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 630 // As defined, norm() is -not- a norm is the common mathematical 631 // sens used in numerics. The helper class _Norm_helper<> tries to 632 // distinguish between builtin floating point and the rest, so as 633 // to deliver an answer as close as possible to the real value. 634 template<bool> 635 struct _Norm_helper 636 { 637 template<typename _Tp> 638 static inline _Tp _S_do_it(const complex<_Tp>& __z) 639 { 640 const _Tp __x = __z.real(); 641 const _Tp __y = __z.imag(); 642 return __x * __x + __y * __y; 643 } 644 }; 645 646 template<> 647 struct _Norm_helper<true> 648 { 649 template<typename _Tp> 650 static inline _Tp _S_do_it(const complex<_Tp>& __z) 651 { 652 _Tp __res = std::abs(__z); 653 return __res * __res; 654 } 655 }; 656 657 template<typename _Tp> 658 inline _Tp 659 norm(const complex<_Tp>& __z) 660 { 661 return _Norm_helper<__is_floating<_Tp>::__value 662 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 663 } 664 665 template<typename _Tp> 666 inline complex<_Tp> 667 polar(const _Tp& __rho, const _Tp& __theta) 668 { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } 669 670 template<typename _Tp> 671 inline complex<_Tp> 672 conj(const complex<_Tp>& __z) 673 { return complex<_Tp>(__z.real(), -__z.imag()); } 674 675 // Transcendentals 676 677 // 26.2.8/1 cos(__z): Returns the cosine of __z. 678 template<typename _Tp> 679 inline complex<_Tp> 680 __complex_cos(const complex<_Tp>& __z) 681 { 682 const _Tp __x = __z.real(); 683 const _Tp __y = __z.imag(); 684 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 685 } 686 687#if _GLIBCXX_USE_C99_COMPLEX 688 inline __complex__ float 689 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 690 691 inline __complex__ double 692 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 693 694 inline __complex__ long double 695 __complex_cos(const __complex__ long double& __z) 696 { return __builtin_ccosl(__z); } 697 698 template<typename _Tp> 699 inline complex<_Tp> 700 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 701#else 702 template<typename _Tp> 703 inline complex<_Tp> 704 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 705#endif 706 707 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 708 template<typename _Tp> 709 inline complex<_Tp> 710 __complex_cosh(const complex<_Tp>& __z) 711 { 712 const _Tp __x = __z.real(); 713 const _Tp __y = __z.imag(); 714 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 715 } 716 717#if _GLIBCXX_USE_C99_COMPLEX 718 inline __complex__ float 719 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 720 721 inline __complex__ double 722 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 723 724 inline __complex__ long double 725 __complex_cosh(const __complex__ long double& __z) 726 { return __builtin_ccoshl(__z); } 727 728 template<typename _Tp> 729 inline complex<_Tp> 730 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 731#else 732 template<typename _Tp> 733 inline complex<_Tp> 734 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 735#endif 736 737 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 738 template<typename _Tp> 739 inline complex<_Tp> 740 __complex_exp(const complex<_Tp>& __z) 741 { return std::polar(exp(__z.real()), __z.imag()); } 742 743#if _GLIBCXX_USE_C99_COMPLEX 744 inline __complex__ float 745 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 746 747 inline __complex__ double 748 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 749 750 inline __complex__ long double 751 __complex_exp(const __complex__ long double& __z) 752 { return __builtin_cexpl(__z); } 753 754 template<typename _Tp> 755 inline complex<_Tp> 756 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 757#else 758 template<typename _Tp> 759 inline complex<_Tp> 760 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 761#endif 762 763 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 764 // The branch cut is along the negative axis. 765 template<typename _Tp> 766 inline complex<_Tp> 767 __complex_log(const complex<_Tp>& __z) 768 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 769 770#if _GLIBCXX_USE_C99_COMPLEX 771 inline __complex__ float 772 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 773 774 inline __complex__ double 775 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 776 777 inline __complex__ long double 778 __complex_log(const __complex__ long double& __z) 779 { return __builtin_clogl(__z); } 780 781 template<typename _Tp> 782 inline complex<_Tp> 783 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 784#else 785 template<typename _Tp> 786 inline complex<_Tp> 787 log(const complex<_Tp>& __z) { return __complex_log(__z); } 788#endif 789 790 template<typename _Tp> 791 inline complex<_Tp> 792 log10(const complex<_Tp>& __z) 793 { return std::log(__z) / log(_Tp(10.0)); } 794 795 // 26.2.8/10 sin(__z): Returns the sine of __z. 796 template<typename _Tp> 797 inline complex<_Tp> 798 __complex_sin(const complex<_Tp>& __z) 799 { 800 const _Tp __x = __z.real(); 801 const _Tp __y = __z.imag(); 802 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 803 } 804 805#if _GLIBCXX_USE_C99_COMPLEX 806 inline __complex__ float 807 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 808 809 inline __complex__ double 810 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 811 812 inline __complex__ long double 813 __complex_sin(const __complex__ long double& __z) 814 { return __builtin_csinl(__z); } 815 816 template<typename _Tp> 817 inline complex<_Tp> 818 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 819#else 820 template<typename _Tp> 821 inline complex<_Tp> 822 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 823#endif 824 825 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 826 template<typename _Tp> 827 inline complex<_Tp> 828 __complex_sinh(const complex<_Tp>& __z) 829 { 830 const _Tp __x = __z.real(); 831 const _Tp __y = __z.imag(); 832 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 833 } 834 835#if _GLIBCXX_USE_C99_COMPLEX 836 inline __complex__ float 837 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 838 839 inline __complex__ double 840 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 841 842 inline __complex__ long double 843 __complex_sinh(const __complex__ long double& __z) 844 { return __builtin_csinhl(__z); } 845 846 template<typename _Tp> 847 inline complex<_Tp> 848 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 849#else 850 template<typename _Tp> 851 inline complex<_Tp> 852 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 853#endif 854 855 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 856 // The branch cut is on the negative axis. 857 template<typename _Tp> 858 complex<_Tp> 859 __complex_sqrt(const complex<_Tp>& __z) 860 { 861 _Tp __x = __z.real(); 862 _Tp __y = __z.imag(); 863 864 if (__x == _Tp()) 865 { 866 _Tp __t = sqrt(abs(__y) / 2); 867 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 868 } 869 else 870 { 871 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 872 _Tp __u = __t / 2; 873 return __x > _Tp() 874 ? complex<_Tp>(__u, __y / __t) 875 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 876 } 877 } 878 879#if _GLIBCXX_USE_C99_COMPLEX 880 inline __complex__ float 881 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 882 883 inline __complex__ double 884 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 885 886 inline __complex__ long double 887 __complex_sqrt(const __complex__ long double& __z) 888 { return __builtin_csqrtl(__z); } 889 890 template<typename _Tp> 891 inline complex<_Tp> 892 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 893#else 894 template<typename _Tp> 895 inline complex<_Tp> 896 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 897#endif 898 899 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 900 901 template<typename _Tp> 902 inline complex<_Tp> 903 __complex_tan(const complex<_Tp>& __z) 904 { return std::sin(__z) / std::cos(__z); } 905 906#if _GLIBCXX_USE_C99_COMPLEX 907 inline __complex__ float 908 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 909 910 inline __complex__ double 911 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 912 913 inline __complex__ long double 914 __complex_tan(const __complex__ long double& __z) 915 { return __builtin_ctanl(__z); } 916 917 template<typename _Tp> 918 inline complex<_Tp> 919 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 920#else 921 template<typename _Tp> 922 inline complex<_Tp> 923 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 924#endif 925 926 927 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 928 929 template<typename _Tp> 930 inline complex<_Tp> 931 __complex_tanh(const complex<_Tp>& __z) 932 { return std::sinh(__z) / std::cosh(__z); } 933 934#if _GLIBCXX_USE_C99_COMPLEX 935 inline __complex__ float 936 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 937 938 inline __complex__ double 939 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 940 941 inline __complex__ long double 942 __complex_tanh(const __complex__ long double& __z) 943 { return __builtin_ctanhl(__z); } 944 945 template<typename _Tp> 946 inline complex<_Tp> 947 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 948#else 949 template<typename _Tp> 950 inline complex<_Tp> 951 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 952#endif 953 954 955 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 956 // raised to the __y-th power. The branch 957 // cut is on the negative axis. 958#if __cplusplus < 201103L 959 template<typename _Tp> 960 complex<_Tp> 961 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 962 { 963 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 964 965 while (__n >>= 1) 966 { 967 __x *= __x; 968 if (__n % 2) 969 __y *= __x; 970 } 971 972 return __y; 973 } 974 975 // _GLIBCXX_RESOLVE_LIB_DEFECTS 976 // DR 844. complex pow return type is ambiguous. 977 template<typename _Tp> 978 inline complex<_Tp> 979 pow(const complex<_Tp>& __z, int __n) 980 { 981 return __n < 0 982 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) 983 : std::__complex_pow_unsigned(__z, __n); 984 } 985#endif 986 987 template<typename _Tp> 988 complex<_Tp> 989 pow(const complex<_Tp>& __x, const _Tp& __y) 990 { 991#ifndef _GLIBCXX_USE_C99_COMPLEX 992 if (__x == _Tp()) 993 return _Tp(); 994#endif 995 if (__x.imag() == _Tp() && __x.real() > _Tp()) 996 return pow(__x.real(), __y); 997 998 complex<_Tp> __t = std::log(__x); 999 return std::polar(exp(__y * __t.real()), __y * __t.imag()); 1000 } 1001 1002 template<typename _Tp> 1003 inline complex<_Tp> 1004 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1005 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1006 1007#if _GLIBCXX_USE_C99_COMPLEX 1008 inline __complex__ float 1009 __complex_pow(__complex__ float __x, __complex__ float __y) 1010 { return __builtin_cpowf(__x, __y); } 1011 1012 inline __complex__ double 1013 __complex_pow(__complex__ double __x, __complex__ double __y) 1014 { return __builtin_cpow(__x, __y); } 1015 1016 inline __complex__ long double 1017 __complex_pow(const __complex__ long double& __x, 1018 const __complex__ long double& __y) 1019 { return __builtin_cpowl(__x, __y); } 1020 1021 template<typename _Tp> 1022 inline complex<_Tp> 1023 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1024 { return __complex_pow(__x.__rep(), __y.__rep()); } 1025#else 1026 template<typename _Tp> 1027 inline complex<_Tp> 1028 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1029 { return __complex_pow(__x, __y); } 1030#endif 1031 1032 template<typename _Tp> 1033 inline complex<_Tp> 1034 pow(const _Tp& __x, const complex<_Tp>& __y) 1035 { 1036 return __x > _Tp() ? std::polar(pow(__x, __y.real()), 1037 __y.imag() * log(__x)) 1038 : std::pow(complex<_Tp>(__x), __y); 1039 } 1040 1041 /// 26.2.3 complex specializations 1042 /// complex<float> specialization 1043 template<> 1044 struct complex<float> 1045 { 1046 typedef float value_type; 1047 typedef __complex__ float _ComplexT; 1048 1049 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1050 1051 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1052#if __cplusplus >= 201103L 1053 : _M_value{ __r, __i } { } 1054#else 1055 { 1056 __real__ _M_value = __r; 1057 __imag__ _M_value = __i; 1058 } 1059#endif 1060 1061 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1062 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1063 1064#if __cplusplus >= 201103L 1065 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1066 // DR 387. std::complex over-encapsulated. 1067 __attribute ((__abi_tag__ ("cxx11"))) 1068 constexpr float 1069 real() { return __real__ _M_value; } 1070 1071 __attribute ((__abi_tag__ ("cxx11"))) 1072 constexpr float 1073 imag() { return __imag__ _M_value; } 1074#else 1075 float& 1076 real() { return __real__ _M_value; } 1077 1078 const float& 1079 real() const { return __real__ _M_value; } 1080 1081 float& 1082 imag() { return __imag__ _M_value; } 1083 1084 const float& 1085 imag() const { return __imag__ _M_value; } 1086#endif 1087 1088 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1089 // DR 387. std::complex over-encapsulated. 1090 void 1091 real(float __val) { __real__ _M_value = __val; } 1092 1093 void 1094 imag(float __val) { __imag__ _M_value = __val; } 1095 1096 complex& 1097 operator=(float __f) 1098 { 1099 _M_value = __f; 1100 return *this; 1101 } 1102 1103 complex& 1104 operator+=(float __f) 1105 { 1106 _M_value += __f; 1107 return *this; 1108 } 1109 1110 complex& 1111 operator-=(float __f) 1112 { 1113 _M_value -= __f; 1114 return *this; 1115 } 1116 1117 complex& 1118 operator*=(float __f) 1119 { 1120 _M_value *= __f; 1121 return *this; 1122 } 1123 1124 complex& 1125 operator/=(float __f) 1126 { 1127 _M_value /= __f; 1128 return *this; 1129 } 1130 1131 // Let the compiler synthesize the copy and assignment 1132 // operator. It always does a pretty good job. 1133 // complex& operator=(const complex&); 1134 1135 template<typename _Tp> 1136 complex& 1137 operator=(const complex<_Tp>& __z) 1138 { 1139 __real__ _M_value = __z.real(); 1140 __imag__ _M_value = __z.imag(); 1141 return *this; 1142 } 1143 1144 template<typename _Tp> 1145 complex& 1146 operator+=(const complex<_Tp>& __z) 1147 { 1148 __real__ _M_value += __z.real(); 1149 __imag__ _M_value += __z.imag(); 1150 return *this; 1151 } 1152 1153 template<class _Tp> 1154 complex& 1155 operator-=(const complex<_Tp>& __z) 1156 { 1157 __real__ _M_value -= __z.real(); 1158 __imag__ _M_value -= __z.imag(); 1159 return *this; 1160 } 1161 1162 template<class _Tp> 1163 complex& 1164 operator*=(const complex<_Tp>& __z) 1165 { 1166 _ComplexT __t; 1167 __real__ __t = __z.real(); 1168 __imag__ __t = __z.imag(); 1169 _M_value *= __t; 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 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1185 1186 private: 1187 _ComplexT _M_value; 1188 }; 1189 1190 /// 26.2.3 complex specializations 1191 /// complex<double> specialization 1192 template<> 1193 struct complex<double> 1194 { 1195 typedef double value_type; 1196 typedef __complex__ double _ComplexT; 1197 1198 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1199 1200 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1201#if __cplusplus >= 201103L 1202 : _M_value{ __r, __i } { } 1203#else 1204 { 1205 __real__ _M_value = __r; 1206 __imag__ _M_value = __i; 1207 } 1208#endif 1209 1210 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1211 : _M_value(__z.__rep()) { } 1212 1213 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1214 1215#if __cplusplus >= 201103L 1216 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1217 // DR 387. std::complex over-encapsulated. 1218 __attribute ((__abi_tag__ ("cxx11"))) 1219 constexpr double 1220 real() { return __real__ _M_value; } 1221 1222 __attribute ((__abi_tag__ ("cxx11"))) 1223 constexpr double 1224 imag() { return __imag__ _M_value; } 1225#else 1226 double& 1227 real() { return __real__ _M_value; } 1228 1229 const double& 1230 real() const { return __real__ _M_value; } 1231 1232 double& 1233 imag() { return __imag__ _M_value; } 1234 1235 const double& 1236 imag() const { return __imag__ _M_value; } 1237#endif 1238 1239 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1240 // DR 387. std::complex over-encapsulated. 1241 void 1242 real(double __val) { __real__ _M_value = __val; } 1243 1244 void 1245 imag(double __val) { __imag__ _M_value = __val; } 1246 1247 complex& 1248 operator=(double __d) 1249 { 1250 _M_value = __d; 1251 return *this; 1252 } 1253 1254 complex& 1255 operator+=(double __d) 1256 { 1257 _M_value += __d; 1258 return *this; 1259 } 1260 1261 complex& 1262 operator-=(double __d) 1263 { 1264 _M_value -= __d; 1265 return *this; 1266 } 1267 1268 complex& 1269 operator*=(double __d) 1270 { 1271 _M_value *= __d; 1272 return *this; 1273 } 1274 1275 complex& 1276 operator/=(double __d) 1277 { 1278 _M_value /= __d; 1279 return *this; 1280 } 1281 1282 // The compiler will synthesize this, efficiently. 1283 // complex& operator=(const complex&); 1284 1285 template<typename _Tp> 1286 complex& 1287 operator=(const complex<_Tp>& __z) 1288 { 1289 __real__ _M_value = __z.real(); 1290 __imag__ _M_value = __z.imag(); 1291 return *this; 1292 } 1293 1294 template<typename _Tp> 1295 complex& 1296 operator+=(const complex<_Tp>& __z) 1297 { 1298 __real__ _M_value += __z.real(); 1299 __imag__ _M_value += __z.imag(); 1300 return *this; 1301 } 1302 1303 template<typename _Tp> 1304 complex& 1305 operator-=(const complex<_Tp>& __z) 1306 { 1307 __real__ _M_value -= __z.real(); 1308 __imag__ _M_value -= __z.imag(); 1309 return *this; 1310 } 1311 1312 template<typename _Tp> 1313 complex& 1314 operator*=(const complex<_Tp>& __z) 1315 { 1316 _ComplexT __t; 1317 __real__ __t = __z.real(); 1318 __imag__ __t = __z.imag(); 1319 _M_value *= __t; 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 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1335 1336 private: 1337 _ComplexT _M_value; 1338 }; 1339 1340 /// 26.2.3 complex specializations 1341 /// complex<long double> specialization 1342 template<> 1343 struct complex<long double> 1344 { 1345 typedef long double value_type; 1346 typedef __complex__ long double _ComplexT; 1347 1348 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1349 1350 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1351 long double __i = 0.0L) 1352#if __cplusplus >= 201103L 1353 : _M_value{ __r, __i } { } 1354#else 1355 { 1356 __real__ _M_value = __r; 1357 __imag__ _M_value = __i; 1358 } 1359#endif 1360 1361 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1362 : _M_value(__z.__rep()) { } 1363 1364 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1365 : _M_value(__z.__rep()) { } 1366 1367#if __cplusplus >= 201103L 1368 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1369 // DR 387. std::complex over-encapsulated. 1370 __attribute ((__abi_tag__ ("cxx11"))) 1371 constexpr long double 1372 real() { return __real__ _M_value; } 1373 1374 __attribute ((__abi_tag__ ("cxx11"))) 1375 constexpr long double 1376 imag() { return __imag__ _M_value; } 1377#else 1378 long double& 1379 real() { return __real__ _M_value; } 1380 1381 const long double& 1382 real() const { return __real__ _M_value; } 1383 1384 long double& 1385 imag() { return __imag__ _M_value; } 1386 1387 const long double& 1388 imag() const { return __imag__ _M_value; } 1389#endif 1390 1391 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1392 // DR 387. std::complex over-encapsulated. 1393 void 1394 real(long double __val) { __real__ _M_value = __val; } 1395 1396 void 1397 imag(long double __val) { __imag__ _M_value = __val; } 1398 1399 complex& 1400 operator=(long double __r) 1401 { 1402 _M_value = __r; 1403 return *this; 1404 } 1405 1406 complex& 1407 operator+=(long double __r) 1408 { 1409 _M_value += __r; 1410 return *this; 1411 } 1412 1413 complex& 1414 operator-=(long double __r) 1415 { 1416 _M_value -= __r; 1417 return *this; 1418 } 1419 1420 complex& 1421 operator*=(long double __r) 1422 { 1423 _M_value *= __r; 1424 return *this; 1425 } 1426 1427 complex& 1428 operator/=(long double __r) 1429 { 1430 _M_value /= __r; 1431 return *this; 1432 } 1433 1434 // The compiler knows how to do this efficiently 1435 // complex& operator=(const complex&); 1436 1437 template<typename _Tp> 1438 complex& 1439 operator=(const complex<_Tp>& __z) 1440 { 1441 __real__ _M_value = __z.real(); 1442 __imag__ _M_value = __z.imag(); 1443 return *this; 1444 } 1445 1446 template<typename _Tp> 1447 complex& 1448 operator+=(const complex<_Tp>& __z) 1449 { 1450 __real__ _M_value += __z.real(); 1451 __imag__ _M_value += __z.imag(); 1452 return *this; 1453 } 1454 1455 template<typename _Tp> 1456 complex& 1457 operator-=(const complex<_Tp>& __z) 1458 { 1459 __real__ _M_value -= __z.real(); 1460 __imag__ _M_value -= __z.imag(); 1461 return *this; 1462 } 1463 1464 template<typename _Tp> 1465 complex& 1466 operator*=(const complex<_Tp>& __z) 1467 { 1468 _ComplexT __t; 1469 __real__ __t = __z.real(); 1470 __imag__ __t = __z.imag(); 1471 _M_value *= __t; 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 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1487 1488 private: 1489 _ComplexT _M_value; 1490 }; 1491 1492 // These bits have to be at the end of this file, so that the 1493 // specializations have all been defined. 1494 inline _GLIBCXX_CONSTEXPR 1495 complex<float>::complex(const complex<double>& __z) 1496 : _M_value(__z.__rep()) { } 1497 1498 inline _GLIBCXX_CONSTEXPR 1499 complex<float>::complex(const complex<long double>& __z) 1500 : _M_value(__z.__rep()) { } 1501 1502 inline _GLIBCXX_CONSTEXPR 1503 complex<double>::complex(const complex<long double>& __z) 1504 : _M_value(__z.__rep()) { } 1505 1506 // Inhibit implicit instantiations for required instantiations, 1507 // which are defined via explicit instantiations elsewhere. 1508 // NB: This syntax is a GNU extension. 1509#if _GLIBCXX_EXTERN_TEMPLATE 1510 extern template istream& operator>>(istream&, complex<float>&); 1511 extern template ostream& operator<<(ostream&, const complex<float>&); 1512 extern template istream& operator>>(istream&, complex<double>&); 1513 extern template ostream& operator<<(ostream&, const complex<double>&); 1514 extern template istream& operator>>(istream&, complex<long double>&); 1515 extern template ostream& operator<<(ostream&, const complex<long double>&); 1516 1517#ifdef _GLIBCXX_USE_WCHAR_T 1518 extern template wistream& operator>>(wistream&, complex<float>&); 1519 extern template wostream& operator<<(wostream&, const complex<float>&); 1520 extern template wistream& operator>>(wistream&, complex<double>&); 1521 extern template wostream& operator<<(wostream&, const complex<double>&); 1522 extern template wistream& operator>>(wistream&, complex<long double>&); 1523 extern template wostream& operator<<(wostream&, const complex<long double>&); 1524#endif 1525#endif 1526 1527 // @} group complex_numbers 1528 1529_GLIBCXX_END_NAMESPACE_VERSION 1530} // namespace 1531 1532namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1533{ 1534_GLIBCXX_BEGIN_NAMESPACE_VERSION 1535 1536 // See ext/type_traits.h for the primary template. 1537 template<typename _Tp, typename _Up> 1538 struct __promote_2<std::complex<_Tp>, _Up> 1539 { 1540 public: 1541 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1542 }; 1543 1544 template<typename _Tp, typename _Up> 1545 struct __promote_2<_Tp, std::complex<_Up> > 1546 { 1547 public: 1548 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1549 }; 1550 1551 template<typename _Tp, typename _Up> 1552 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1553 { 1554 public: 1555 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1556 }; 1557 1558_GLIBCXX_END_NAMESPACE_VERSION 1559} // namespace 1560 1561#if __cplusplus >= 201103L 1562 1563namespace std _GLIBCXX_VISIBILITY(default) 1564{ 1565_GLIBCXX_BEGIN_NAMESPACE_VERSION 1566 1567 // Forward declarations. 1568 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1569 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1570 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1571 1572 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1573 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1574 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1575 // DR 595. 1576 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1577 1578 template<typename _Tp> 1579 inline std::complex<_Tp> 1580 __complex_acos(const std::complex<_Tp>& __z) 1581 { 1582 const std::complex<_Tp> __t = std::asin(__z); 1583 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1584 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1585 } 1586 1587#if _GLIBCXX_USE_C99_COMPLEX_TR1 1588 inline __complex__ float 1589 __complex_acos(__complex__ float __z) 1590 { return __builtin_cacosf(__z); } 1591 1592 inline __complex__ double 1593 __complex_acos(__complex__ double __z) 1594 { return __builtin_cacos(__z); } 1595 1596 inline __complex__ long double 1597 __complex_acos(const __complex__ long double& __z) 1598 { return __builtin_cacosl(__z); } 1599 1600 template<typename _Tp> 1601 inline std::complex<_Tp> 1602 acos(const std::complex<_Tp>& __z) 1603 { return __complex_acos(__z.__rep()); } 1604#else 1605 /// acos(__z) [8.1.2]. 1606 // Effects: Behaves the same as C99 function cacos, defined 1607 // in subclause 7.3.5.1. 1608 template<typename _Tp> 1609 inline std::complex<_Tp> 1610 acos(const std::complex<_Tp>& __z) 1611 { return __complex_acos(__z); } 1612#endif 1613 1614 template<typename _Tp> 1615 inline std::complex<_Tp> 1616 __complex_asin(const std::complex<_Tp>& __z) 1617 { 1618 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1619 __t = std::asinh(__t); 1620 return std::complex<_Tp>(__t.imag(), -__t.real()); 1621 } 1622 1623#if _GLIBCXX_USE_C99_COMPLEX_TR1 1624 inline __complex__ float 1625 __complex_asin(__complex__ float __z) 1626 { return __builtin_casinf(__z); } 1627 1628 inline __complex__ double 1629 __complex_asin(__complex__ double __z) 1630 { return __builtin_casin(__z); } 1631 1632 inline __complex__ long double 1633 __complex_asin(const __complex__ long double& __z) 1634 { return __builtin_casinl(__z); } 1635 1636 template<typename _Tp> 1637 inline std::complex<_Tp> 1638 asin(const std::complex<_Tp>& __z) 1639 { return __complex_asin(__z.__rep()); } 1640#else 1641 /// asin(__z) [8.1.3]. 1642 // Effects: Behaves the same as C99 function casin, defined 1643 // in subclause 7.3.5.2. 1644 template<typename _Tp> 1645 inline std::complex<_Tp> 1646 asin(const std::complex<_Tp>& __z) 1647 { return __complex_asin(__z); } 1648#endif 1649 1650 template<typename _Tp> 1651 std::complex<_Tp> 1652 __complex_atan(const std::complex<_Tp>& __z) 1653 { 1654 const _Tp __r2 = __z.real() * __z.real(); 1655 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1656 1657 _Tp __num = __z.imag() + _Tp(1.0); 1658 _Tp __den = __z.imag() - _Tp(1.0); 1659 1660 __num = __r2 + __num * __num; 1661 __den = __r2 + __den * __den; 1662 1663 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1664 _Tp(0.25) * log(__num / __den)); 1665 } 1666 1667#if _GLIBCXX_USE_C99_COMPLEX_TR1 1668 inline __complex__ float 1669 __complex_atan(__complex__ float __z) 1670 { return __builtin_catanf(__z); } 1671 1672 inline __complex__ double 1673 __complex_atan(__complex__ double __z) 1674 { return __builtin_catan(__z); } 1675 1676 inline __complex__ long double 1677 __complex_atan(const __complex__ long double& __z) 1678 { return __builtin_catanl(__z); } 1679 1680 template<typename _Tp> 1681 inline std::complex<_Tp> 1682 atan(const std::complex<_Tp>& __z) 1683 { return __complex_atan(__z.__rep()); } 1684#else 1685 /// atan(__z) [8.1.4]. 1686 // Effects: Behaves the same as C99 function catan, defined 1687 // in subclause 7.3.5.3. 1688 template<typename _Tp> 1689 inline std::complex<_Tp> 1690 atan(const std::complex<_Tp>& __z) 1691 { return __complex_atan(__z); } 1692#endif 1693 1694 template<typename _Tp> 1695 std::complex<_Tp> 1696 __complex_acosh(const std::complex<_Tp>& __z) 1697 { 1698 // Kahan's formula. 1699 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1700 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1701 } 1702 1703#if _GLIBCXX_USE_C99_COMPLEX_TR1 1704 inline __complex__ float 1705 __complex_acosh(__complex__ float __z) 1706 { return __builtin_cacoshf(__z); } 1707 1708 inline __complex__ double 1709 __complex_acosh(__complex__ double __z) 1710 { return __builtin_cacosh(__z); } 1711 1712 inline __complex__ long double 1713 __complex_acosh(const __complex__ long double& __z) 1714 { return __builtin_cacoshl(__z); } 1715 1716 template<typename _Tp> 1717 inline std::complex<_Tp> 1718 acosh(const std::complex<_Tp>& __z) 1719 { return __complex_acosh(__z.__rep()); } 1720#else 1721 /// acosh(__z) [8.1.5]. 1722 // Effects: Behaves the same as C99 function cacosh, defined 1723 // in subclause 7.3.6.1. 1724 template<typename _Tp> 1725 inline std::complex<_Tp> 1726 acosh(const std::complex<_Tp>& __z) 1727 { return __complex_acosh(__z); } 1728#endif 1729 1730 template<typename _Tp> 1731 std::complex<_Tp> 1732 __complex_asinh(const std::complex<_Tp>& __z) 1733 { 1734 std::complex<_Tp> __t((__z.real() - __z.imag()) 1735 * (__z.real() + __z.imag()) + _Tp(1.0), 1736 _Tp(2.0) * __z.real() * __z.imag()); 1737 __t = std::sqrt(__t); 1738 1739 return std::log(__t + __z); 1740 } 1741 1742#if _GLIBCXX_USE_C99_COMPLEX_TR1 1743 inline __complex__ float 1744 __complex_asinh(__complex__ float __z) 1745 { return __builtin_casinhf(__z); } 1746 1747 inline __complex__ double 1748 __complex_asinh(__complex__ double __z) 1749 { return __builtin_casinh(__z); } 1750 1751 inline __complex__ long double 1752 __complex_asinh(const __complex__ long double& __z) 1753 { return __builtin_casinhl(__z); } 1754 1755 template<typename _Tp> 1756 inline std::complex<_Tp> 1757 asinh(const std::complex<_Tp>& __z) 1758 { return __complex_asinh(__z.__rep()); } 1759#else 1760 /// asinh(__z) [8.1.6]. 1761 // Effects: Behaves the same as C99 function casin, defined 1762 // in subclause 7.3.6.2. 1763 template<typename _Tp> 1764 inline std::complex<_Tp> 1765 asinh(const std::complex<_Tp>& __z) 1766 { return __complex_asinh(__z); } 1767#endif 1768 1769 template<typename _Tp> 1770 std::complex<_Tp> 1771 __complex_atanh(const std::complex<_Tp>& __z) 1772 { 1773 const _Tp __i2 = __z.imag() * __z.imag(); 1774 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1775 1776 _Tp __num = _Tp(1.0) + __z.real(); 1777 _Tp __den = _Tp(1.0) - __z.real(); 1778 1779 __num = __i2 + __num * __num; 1780 __den = __i2 + __den * __den; 1781 1782 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1783 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1784 } 1785 1786#if _GLIBCXX_USE_C99_COMPLEX_TR1 1787 inline __complex__ float 1788 __complex_atanh(__complex__ float __z) 1789 { return __builtin_catanhf(__z); } 1790 1791 inline __complex__ double 1792 __complex_atanh(__complex__ double __z) 1793 { return __builtin_catanh(__z); } 1794 1795 inline __complex__ long double 1796 __complex_atanh(const __complex__ long double& __z) 1797 { return __builtin_catanhl(__z); } 1798 1799 template<typename _Tp> 1800 inline std::complex<_Tp> 1801 atanh(const std::complex<_Tp>& __z) 1802 { return __complex_atanh(__z.__rep()); } 1803#else 1804 /// atanh(__z) [8.1.7]. 1805 // Effects: Behaves the same as C99 function catanh, defined 1806 // in subclause 7.3.6.3. 1807 template<typename _Tp> 1808 inline std::complex<_Tp> 1809 atanh(const std::complex<_Tp>& __z) 1810 { return __complex_atanh(__z); } 1811#endif 1812 1813 template<typename _Tp> 1814 inline _Tp 1815 /// fabs(__z) [8.1.8]. 1816 // Effects: Behaves the same as C99 function cabs, defined 1817 // in subclause 7.3.8.1. 1818 fabs(const std::complex<_Tp>& __z) 1819 { return std::abs(__z); } 1820 1821 /// Additional overloads [8.1.9]. 1822 template<typename _Tp> 1823 inline typename __gnu_cxx::__promote<_Tp>::__type 1824 arg(_Tp __x) 1825 { 1826 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1827#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1828 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1829 : __type(); 1830#else 1831 return std::arg(std::complex<__type>(__x)); 1832#endif 1833 } 1834 1835 template<typename _Tp> 1836 inline typename __gnu_cxx::__promote<_Tp>::__type 1837 imag(_Tp) 1838 { return _Tp(); } 1839 1840 template<typename _Tp> 1841 inline typename __gnu_cxx::__promote<_Tp>::__type 1842 norm(_Tp __x) 1843 { 1844 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1845 return __type(__x) * __type(__x); 1846 } 1847 1848 template<typename _Tp> 1849 inline typename __gnu_cxx::__promote<_Tp>::__type 1850 real(_Tp __x) 1851 { return __x; } 1852 1853 template<typename _Tp, typename _Up> 1854 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1855 pow(const std::complex<_Tp>& __x, const _Up& __y) 1856 { 1857 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1858 return std::pow(std::complex<__type>(__x), __type(__y)); 1859 } 1860 1861 template<typename _Tp, typename _Up> 1862 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1863 pow(const _Tp& __x, const std::complex<_Up>& __y) 1864 { 1865 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1866 return std::pow(__type(__x), std::complex<__type>(__y)); 1867 } 1868 1869 template<typename _Tp, typename _Up> 1870 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1871 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1872 { 1873 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1874 return std::pow(std::complex<__type>(__x), 1875 std::complex<__type>(__y)); 1876 } 1877 1878 // Forward declarations. 1879 // DR 781. 1880 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); 1881 1882 template<typename _Tp> 1883 std::complex<_Tp> 1884 __complex_proj(const std::complex<_Tp>& __z) 1885 { 1886 const _Tp __den = (__z.real() * __z.real() 1887 + __z.imag() * __z.imag() + _Tp(1.0)); 1888 1889 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, 1890 (_Tp(2.0) * __z.imag()) / __den); 1891 } 1892 1893#if _GLIBCXX_USE_C99_COMPLEX 1894 inline __complex__ float 1895 __complex_proj(__complex__ float __z) 1896 { return __builtin_cprojf(__z); } 1897 1898 inline __complex__ double 1899 __complex_proj(__complex__ double __z) 1900 { return __builtin_cproj(__z); } 1901 1902 inline __complex__ long double 1903 __complex_proj(const __complex__ long double& __z) 1904 { return __builtin_cprojl(__z); } 1905 1906 template<typename _Tp> 1907 inline std::complex<_Tp> 1908 proj(const std::complex<_Tp>& __z) 1909 { return __complex_proj(__z.__rep()); } 1910#else 1911 template<typename _Tp> 1912 inline std::complex<_Tp> 1913 proj(const std::complex<_Tp>& __z) 1914 { return __complex_proj(__z); } 1915#endif 1916 1917 // DR 1137. 1918 template<typename _Tp> 1919 inline typename __gnu_cxx::__promote<_Tp>::__type 1920 proj(_Tp __x) 1921 { return __x; } 1922 1923 template<typename _Tp> 1924 inline typename __gnu_cxx::__promote<_Tp>::__type 1925 conj(_Tp __x) 1926 { return __x; } 1927 1928_GLIBCXX_END_NAMESPACE_VERSION 1929} // namespace 1930 1931#endif // C++11 1932 1933#endif /* _GLIBCXX_COMPLEX */ 1934