1 // The template and inlines for the -*- C++ -*- complex number classes. 2 3 // Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 4 // 2006, 2007, 2008, 2009, 2010, 2011 5 // Free Software Foundation, Inc. 6 // 7 // This file is part of the GNU ISO C++ Library. This library is free 8 // software; you can redistribute it and/or modify it under the 9 // terms of the GNU General Public License as published by the 10 // Free Software Foundation; either version 3, or (at your option) 11 // any later version. 12 13 // This library is distributed in the hope that it will be useful, 14 // but WITHOUT ANY WARRANTY; without even the implied warranty of 15 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 // GNU General Public License for more details. 17 18 // Under Section 7 of GPL version 3, you are granted additional 19 // permissions described in the GCC Runtime Library Exception, version 20 // 3.1, as published by the Free Software Foundation. 21 22 // You should have received a copy of the GNU General Public License and 23 // a copy of the GCC Runtime Library Exception along with this program; 24 // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 25 // <http://www.gnu.org/licenses/>. 26 27 /** @file include/complex 28 * This is a Standard C++ Library header. 29 */ 30 31 // 32 // ISO C++ 14882: 26.2 Complex Numbers 33 // Note: this is not a conforming implementation. 34 // Initially implemented by Ulrich Drepper <drepper (a] cygnus.com> 35 // Improved by Gabriel Dos Reis <dosreis (a] cmla.ens-cachan.fr> 36 // 37 38 #ifndef _GLIBCXX_COMPLEX 39 #define _GLIBCXX_COMPLEX 1 40 41 #pragma GCC system_header 42 43 #include <bits/c++config.h> 44 #include <bits/cpp_type_traits.h> 45 #include <ext/type_traits.h> 46 #include <cmath> 47 #include <sstream> 48 49 namespace std _GLIBCXX_VISIBILITY(default) 50 { 51 _GLIBCXX_BEGIN_NAMESPACE_VERSION 52 53 /** 54 * @defgroup complex_numbers Complex Numbers 55 * @ingroup numerics 56 * 57 * Classes and functions for complex numbers. 58 * @{ 59 */ 60 61 // Forward declarations. 62 template<typename _Tp> class complex; 63 template<> class complex<float>; 64 template<> class complex<double>; 65 template<> class complex<long double>; 66 67 /// Return magnitude of @a z. 68 template<typename _Tp> _Tp abs(const complex<_Tp>&); 69 /// Return phase angle of @a z. 70 template<typename _Tp> _Tp arg(const complex<_Tp>&); 71 /// Return @a z magnitude squared. 72 template<typename _Tp> _Tp norm(const complex<_Tp>&); 73 74 /// Return complex conjugate of @a z. 75 template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); 76 /// Return complex with magnitude @a rho and angle @a theta. 77 template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); 78 79 // Transcendentals: 80 /// Return complex cosine of @a z. 81 template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); 82 /// Return complex hyperbolic cosine of @a z. 83 template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); 84 /// Return complex base e exponential of @a z. 85 template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); 86 /// Return complex natural logarithm of @a z. 87 template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); 88 /// Return complex base 10 logarithm of @a z. 89 template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); 90 #ifndef __GXX_EXPERIMENTAL_CXX0X__ 91 // DR 844. 92 /// Return @a x to the @a y'th power. 93 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); 94 #endif 95 /// Return @a x to the @a y'th power. 96 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); 97 /// Return @a x to the @a y'th power. 98 template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 99 const complex<_Tp>&); 100 /// Return @a x to the @a y'th power. 101 template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); 102 /// Return complex sine of @a z. 103 template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); 104 /// Return complex hyperbolic sine of @a z. 105 template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); 106 /// Return complex square root of @a z. 107 template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); 108 /// Return complex tangent of @a z. 109 template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); 110 /// Return complex hyperbolic tangent of @a z. 111 template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); 112 113 114 // 26.2.2 Primary template class complex 115 /** 116 * Template to represent complex numbers. 117 * 118 * Specializations for float, double, and long double are part of the 119 * library. Results with any other type are not guaranteed. 120 * 121 * @param Tp Type of real and imaginary values. 122 */ 123 template<typename _Tp> 124 struct complex 125 { 126 /// Value typedef. 127 typedef _Tp value_type; 128 129 /// Default constructor. First parameter is x, second parameter is y. 130 /// Unspecified parameters default to 0. 131 _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) 132 : _M_real(__r), _M_imag(__i) { } 133 134 // Lets the compiler synthesize the copy constructor 135 // complex (const complex<_Tp>&); 136 /// Copy constructor. 137 template<typename _Up> 138 _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) 139 : _M_real(__z.real()), _M_imag(__z.imag()) { } 140 141 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 142 // _GLIBCXX_RESOLVE_LIB_DEFECTS 143 // DR 387. std::complex over-encapsulated. 144 constexpr _Tp 145 real() const { return _M_real; } 146 147 constexpr _Tp 148 imag() const { return _M_imag; } 149 #else 150 /// Return real part of complex number. 151 _Tp& 152 real() { return _M_real; } 153 154 /// Return real part of complex number. 155 const _Tp& 156 real() const { return _M_real; } 157 158 /// Return imaginary part of complex number. 159 _Tp& 160 imag() { return _M_imag; } 161 162 /// Return imaginary part of complex number. 163 const _Tp& 164 imag() const { return _M_imag; } 165 #endif 166 167 // _GLIBCXX_RESOLVE_LIB_DEFECTS 168 // DR 387. std::complex over-encapsulated. 169 void 170 real(_Tp __val) { _M_real = __val; } 171 172 void 173 imag(_Tp __val) { _M_imag = __val; } 174 175 /// Assign this complex number to scalar @a t. 176 complex<_Tp>& operator=(const _Tp&); 177 178 /// Add @a t to this complex number. 179 // 26.2.5/1 180 complex<_Tp>& 181 operator+=(const _Tp& __t) 182 { 183 _M_real += __t; 184 return *this; 185 } 186 187 /// Subtract @a t from this complex number. 188 // 26.2.5/3 189 complex<_Tp>& 190 operator-=(const _Tp& __t) 191 { 192 _M_real -= __t; 193 return *this; 194 } 195 196 /// Multiply this complex number by @a t. 197 complex<_Tp>& operator*=(const _Tp&); 198 /// Divide this complex number by @a t. 199 complex<_Tp>& operator/=(const _Tp&); 200 201 // Lets the compiler synthesize the 202 // copy and assignment operator 203 // complex<_Tp>& operator= (const complex<_Tp>&); 204 /// Assign this complex number to complex @a z. 205 template<typename _Up> 206 complex<_Tp>& operator=(const complex<_Up>&); 207 /// Add @a z to this complex number. 208 template<typename _Up> 209 complex<_Tp>& operator+=(const complex<_Up>&); 210 /// Subtract @a z from this complex number. 211 template<typename _Up> 212 complex<_Tp>& operator-=(const complex<_Up>&); 213 /// Multiply this complex number by @a z. 214 template<typename _Up> 215 complex<_Tp>& operator*=(const complex<_Up>&); 216 /// Divide this complex number by @a z. 217 template<typename _Up> 218 complex<_Tp>& operator/=(const complex<_Up>&); 219 220 _GLIBCXX_USE_CONSTEXPR complex __rep() const 221 { return *this; } 222 223 private: 224 _Tp _M_real; 225 _Tp _M_imag; 226 }; 227 228 template<typename _Tp> 229 complex<_Tp>& 230 complex<_Tp>::operator=(const _Tp& __t) 231 { 232 _M_real = __t; 233 _M_imag = _Tp(); 234 return *this; 235 } 236 237 // 26.2.5/5 238 template<typename _Tp> 239 complex<_Tp>& 240 complex<_Tp>::operator*=(const _Tp& __t) 241 { 242 _M_real *= __t; 243 _M_imag *= __t; 244 return *this; 245 } 246 247 // 26.2.5/7 248 template<typename _Tp> 249 complex<_Tp>& 250 complex<_Tp>::operator/=(const _Tp& __t) 251 { 252 _M_real /= __t; 253 _M_imag /= __t; 254 return *this; 255 } 256 257 template<typename _Tp> 258 template<typename _Up> 259 complex<_Tp>& 260 complex<_Tp>::operator=(const complex<_Up>& __z) 261 { 262 _M_real = __z.real(); 263 _M_imag = __z.imag(); 264 return *this; 265 } 266 267 // 26.2.5/9 268 template<typename _Tp> 269 template<typename _Up> 270 complex<_Tp>& 271 complex<_Tp>::operator+=(const complex<_Up>& __z) 272 { 273 _M_real += __z.real(); 274 _M_imag += __z.imag(); 275 return *this; 276 } 277 278 // 26.2.5/11 279 template<typename _Tp> 280 template<typename _Up> 281 complex<_Tp>& 282 complex<_Tp>::operator-=(const complex<_Up>& __z) 283 { 284 _M_real -= __z.real(); 285 _M_imag -= __z.imag(); 286 return *this; 287 } 288 289 // 26.2.5/13 290 // XXX: This is a grammar school implementation. 291 template<typename _Tp> 292 template<typename _Up> 293 complex<_Tp>& 294 complex<_Tp>::operator*=(const complex<_Up>& __z) 295 { 296 const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); 297 _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); 298 _M_real = __r; 299 return *this; 300 } 301 302 // 26.2.5/15 303 // 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 const _Tp __n = std::norm(__z); 311 _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; 312 _M_real = __r / __n; 313 return *this; 314 } 315 316 // Operators: 317 //@{ 318 /// Return new complex value @a x plus @a y. 319 template<typename _Tp> 320 inline complex<_Tp> 321 operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) 322 { 323 complex<_Tp> __r = __x; 324 __r += __y; 325 return __r; 326 } 327 328 template<typename _Tp> 329 inline complex<_Tp> 330 operator+(const complex<_Tp>& __x, const _Tp& __y) 331 { 332 complex<_Tp> __r = __x; 333 __r += __y; 334 return __r; 335 } 336 337 template<typename _Tp> 338 inline complex<_Tp> 339 operator+(const _Tp& __x, const complex<_Tp>& __y) 340 { 341 complex<_Tp> __r = __y; 342 __r += __x; 343 return __r; 344 } 345 //@} 346 347 //@{ 348 /// Return new complex value @a x minus @a y. 349 template<typename _Tp> 350 inline complex<_Tp> 351 operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) 352 { 353 complex<_Tp> __r = __x; 354 __r -= __y; 355 return __r; 356 } 357 358 template<typename _Tp> 359 inline complex<_Tp> 360 operator-(const complex<_Tp>& __x, const _Tp& __y) 361 { 362 complex<_Tp> __r = __x; 363 __r -= __y; 364 return __r; 365 } 366 367 template<typename _Tp> 368 inline complex<_Tp> 369 operator-(const _Tp& __x, const complex<_Tp>& __y) 370 { 371 complex<_Tp> __r(__x, -__y.imag()); 372 __r -= __y.real(); 373 return __r; 374 } 375 //@} 376 377 //@{ 378 /// Return new complex value @a x times @a y. 379 template<typename _Tp> 380 inline complex<_Tp> 381 operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) 382 { 383 complex<_Tp> __r = __x; 384 __r *= __y; 385 return __r; 386 } 387 388 template<typename _Tp> 389 inline complex<_Tp> 390 operator*(const complex<_Tp>& __x, const _Tp& __y) 391 { 392 complex<_Tp> __r = __x; 393 __r *= __y; 394 return __r; 395 } 396 397 template<typename _Tp> 398 inline complex<_Tp> 399 operator*(const _Tp& __x, const complex<_Tp>& __y) 400 { 401 complex<_Tp> __r = __y; 402 __r *= __x; 403 return __r; 404 } 405 //@} 406 407 //@{ 408 /// Return new complex value @a x divided by @a y. 409 template<typename _Tp> 410 inline complex<_Tp> 411 operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) 412 { 413 complex<_Tp> __r = __x; 414 __r /= __y; 415 return __r; 416 } 417 418 template<typename _Tp> 419 inline complex<_Tp> 420 operator/(const complex<_Tp>& __x, const _Tp& __y) 421 { 422 complex<_Tp> __r = __x; 423 __r /= __y; 424 return __r; 425 } 426 427 template<typename _Tp> 428 inline complex<_Tp> 429 operator/(const _Tp& __x, const complex<_Tp>& __y) 430 { 431 complex<_Tp> __r = __x; 432 __r /= __y; 433 return __r; 434 } 435 //@} 436 437 /// Return @a x. 438 template<typename _Tp> 439 inline complex<_Tp> 440 operator+(const complex<_Tp>& __x) 441 { return __x; } 442 443 /// Return complex negation of @a x. 444 template<typename _Tp> 445 inline complex<_Tp> 446 operator-(const complex<_Tp>& __x) 447 { return complex<_Tp>(-__x.real(), -__x.imag()); } 448 449 //@{ 450 /// Return true if @a x is equal to @a y. 451 template<typename _Tp> 452 inline _GLIBCXX_CONSTEXPR bool 453 operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) 454 { return __x.real() == __y.real() && __x.imag() == __y.imag(); } 455 456 template<typename _Tp> 457 inline _GLIBCXX_CONSTEXPR bool 458 operator==(const complex<_Tp>& __x, const _Tp& __y) 459 { return __x.real() == __y && __x.imag() == _Tp(); } 460 461 template<typename _Tp> 462 inline _GLIBCXX_CONSTEXPR bool 463 operator==(const _Tp& __x, const complex<_Tp>& __y) 464 { return __x == __y.real() && _Tp() == __y.imag(); } 465 //@} 466 467 //@{ 468 /// Return false if @a x is equal to @a y. 469 template<typename _Tp> 470 inline _GLIBCXX_CONSTEXPR bool 471 operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) 472 { return __x.real() != __y.real() || __x.imag() != __y.imag(); } 473 474 template<typename _Tp> 475 inline _GLIBCXX_CONSTEXPR bool 476 operator!=(const complex<_Tp>& __x, const _Tp& __y) 477 { return __x.real() != __y || __x.imag() != _Tp(); } 478 479 template<typename _Tp> 480 inline _GLIBCXX_CONSTEXPR bool 481 operator!=(const _Tp& __x, const complex<_Tp>& __y) 482 { return __x != __y.real() || _Tp() != __y.imag(); } 483 //@} 484 485 /// Extraction operator for complex values. 486 template<typename _Tp, typename _CharT, class _Traits> 487 basic_istream<_CharT, _Traits>& 488 operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) 489 { 490 _Tp __re_x, __im_x; 491 _CharT __ch; 492 __is >> __ch; 493 if (__ch == '(') 494 { 495 __is >> __re_x >> __ch; 496 if (__ch == ',') 497 { 498 __is >> __im_x >> __ch; 499 if (__ch == ')') 500 __x = complex<_Tp>(__re_x, __im_x); 501 else 502 __is.setstate(ios_base::failbit); 503 } 504 else if (__ch == ')') 505 __x = __re_x; 506 else 507 __is.setstate(ios_base::failbit); 508 } 509 else 510 { 511 __is.putback(__ch); 512 __is >> __re_x; 513 __x = __re_x; 514 } 515 return __is; 516 } 517 518 /// Insertion operator for complex values. 519 template<typename _Tp, typename _CharT, class _Traits> 520 basic_ostream<_CharT, _Traits>& 521 operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) 522 { 523 basic_ostringstream<_CharT, _Traits> __s; 524 __s.flags(__os.flags()); 525 __s.imbue(__os.getloc()); 526 __s.precision(__os.precision()); 527 __s << '(' << __x.real() << ',' << __x.imag() << ')'; 528 return __os << __s.str(); 529 } 530 531 // Values 532 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 533 template<typename _Tp> 534 inline constexpr _Tp 535 real(const complex<_Tp>& __z) 536 { return __z.real(); } 537 538 template<typename _Tp> 539 inline constexpr _Tp 540 imag(const complex<_Tp>& __z) 541 { return __z.imag(); } 542 #else 543 template<typename _Tp> 544 inline _Tp& 545 real(complex<_Tp>& __z) 546 { return __z.real(); } 547 548 template<typename _Tp> 549 inline const _Tp& 550 real(const complex<_Tp>& __z) 551 { return __z.real(); } 552 553 template<typename _Tp> 554 inline _Tp& 555 imag(complex<_Tp>& __z) 556 { return __z.imag(); } 557 558 template<typename _Tp> 559 inline const _Tp& 560 imag(const complex<_Tp>& __z) 561 { return __z.imag(); } 562 #endif 563 564 // 26.2.7/3 abs(__z): Returns the magnitude of __z. 565 template<typename _Tp> 566 inline _Tp 567 __complex_abs(const complex<_Tp>& __z) 568 { 569 _Tp __x = __z.real(); 570 _Tp __y = __z.imag(); 571 const _Tp __s = std::max(abs(__x), abs(__y)); 572 if (__s == _Tp()) // well ... 573 return __s; 574 __x /= __s; 575 __y /= __s; 576 return __s * sqrt(__x * __x + __y * __y); 577 } 578 579 #if _GLIBCXX_USE_C99_COMPLEX 580 inline float 581 __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } 582 583 inline double 584 __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } 585 586 inline long double 587 __complex_abs(const __complex__ long double& __z) 588 { return __builtin_cabsl(__z); } 589 590 template<typename _Tp> 591 inline _Tp 592 abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } 593 #else 594 template<typename _Tp> 595 inline _Tp 596 abs(const complex<_Tp>& __z) { return __complex_abs(__z); } 597 #endif 598 599 600 // 26.2.7/4: arg(__z): Returns the phase angle of __z. 601 template<typename _Tp> 602 inline _Tp 603 __complex_arg(const complex<_Tp>& __z) 604 { return atan2(__z.imag(), __z.real()); } 605 606 #if _GLIBCXX_USE_C99_COMPLEX 607 inline float 608 __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } 609 610 inline double 611 __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } 612 613 inline long double 614 __complex_arg(const __complex__ long double& __z) 615 { return __builtin_cargl(__z); } 616 617 template<typename _Tp> 618 inline _Tp 619 arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } 620 #else 621 template<typename _Tp> 622 inline _Tp 623 arg(const complex<_Tp>& __z) { return __complex_arg(__z); } 624 #endif 625 626 // 26.2.7/5: norm(__z) returns the squared magnitude of __z. 627 // As defined, norm() is -not- a norm is the common mathematical 628 // sens used in numerics. The helper class _Norm_helper<> tries to 629 // distinguish between builtin floating point and the rest, so as 630 // to deliver an answer as close as possible to the real value. 631 template<bool> 632 struct _Norm_helper 633 { 634 template<typename _Tp> 635 static inline _Tp _S_do_it(const complex<_Tp>& __z) 636 { 637 const _Tp __x = __z.real(); 638 const _Tp __y = __z.imag(); 639 return __x * __x + __y * __y; 640 } 641 }; 642 643 template<> 644 struct _Norm_helper<true> 645 { 646 template<typename _Tp> 647 static inline _Tp _S_do_it(const complex<_Tp>& __z) 648 { 649 _Tp __res = std::abs(__z); 650 return __res * __res; 651 } 652 }; 653 654 template<typename _Tp> 655 inline _Tp 656 norm(const complex<_Tp>& __z) 657 { 658 return _Norm_helper<__is_floating<_Tp>::__value 659 && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); 660 } 661 662 template<typename _Tp> 663 inline complex<_Tp> 664 polar(const _Tp& __rho, const _Tp& __theta) 665 { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } 666 667 template<typename _Tp> 668 inline complex<_Tp> 669 conj(const complex<_Tp>& __z) 670 { return complex<_Tp>(__z.real(), -__z.imag()); } 671 672 // Transcendentals 673 674 // 26.2.8/1 cos(__z): Returns the cosine of __z. 675 template<typename _Tp> 676 inline complex<_Tp> 677 __complex_cos(const complex<_Tp>& __z) 678 { 679 const _Tp __x = __z.real(); 680 const _Tp __y = __z.imag(); 681 return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); 682 } 683 684 #if _GLIBCXX_USE_C99_COMPLEX 685 inline __complex__ float 686 __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } 687 688 inline __complex__ double 689 __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } 690 691 inline __complex__ long double 692 __complex_cos(const __complex__ long double& __z) 693 { return __builtin_ccosl(__z); } 694 695 template<typename _Tp> 696 inline complex<_Tp> 697 cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } 698 #else 699 template<typename _Tp> 700 inline complex<_Tp> 701 cos(const complex<_Tp>& __z) { return __complex_cos(__z); } 702 #endif 703 704 // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. 705 template<typename _Tp> 706 inline complex<_Tp> 707 __complex_cosh(const complex<_Tp>& __z) 708 { 709 const _Tp __x = __z.real(); 710 const _Tp __y = __z.imag(); 711 return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); 712 } 713 714 #if _GLIBCXX_USE_C99_COMPLEX 715 inline __complex__ float 716 __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } 717 718 inline __complex__ double 719 __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } 720 721 inline __complex__ long double 722 __complex_cosh(const __complex__ long double& __z) 723 { return __builtin_ccoshl(__z); } 724 725 template<typename _Tp> 726 inline complex<_Tp> 727 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } 728 #else 729 template<typename _Tp> 730 inline complex<_Tp> 731 cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } 732 #endif 733 734 // 26.2.8/3 exp(__z): Returns the complex base e exponential of x 735 template<typename _Tp> 736 inline complex<_Tp> 737 __complex_exp(const complex<_Tp>& __z) 738 { return std::polar(exp(__z.real()), __z.imag()); } 739 740 #if _GLIBCXX_USE_C99_COMPLEX 741 inline __complex__ float 742 __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } 743 744 inline __complex__ double 745 __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } 746 747 inline __complex__ long double 748 __complex_exp(const __complex__ long double& __z) 749 { return __builtin_cexpl(__z); } 750 751 template<typename _Tp> 752 inline complex<_Tp> 753 exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } 754 #else 755 template<typename _Tp> 756 inline complex<_Tp> 757 exp(const complex<_Tp>& __z) { return __complex_exp(__z); } 758 #endif 759 760 // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. 761 // The branch cut is along the negative axis. 762 template<typename _Tp> 763 inline complex<_Tp> 764 __complex_log(const complex<_Tp>& __z) 765 { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } 766 767 #if _GLIBCXX_USE_C99_COMPLEX 768 inline __complex__ float 769 __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } 770 771 inline __complex__ double 772 __complex_log(__complex__ double __z) { return __builtin_clog(__z); } 773 774 inline __complex__ long double 775 __complex_log(const __complex__ long double& __z) 776 { return __builtin_clogl(__z); } 777 778 template<typename _Tp> 779 inline complex<_Tp> 780 log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } 781 #else 782 template<typename _Tp> 783 inline complex<_Tp> 784 log(const complex<_Tp>& __z) { return __complex_log(__z); } 785 #endif 786 787 template<typename _Tp> 788 inline complex<_Tp> 789 log10(const complex<_Tp>& __z) 790 { return std::log(__z) / log(_Tp(10.0)); } 791 792 // 26.2.8/10 sin(__z): Returns the sine of __z. 793 template<typename _Tp> 794 inline complex<_Tp> 795 __complex_sin(const complex<_Tp>& __z) 796 { 797 const _Tp __x = __z.real(); 798 const _Tp __y = __z.imag(); 799 return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 800 } 801 802 #if _GLIBCXX_USE_C99_COMPLEX 803 inline __complex__ float 804 __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } 805 806 inline __complex__ double 807 __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } 808 809 inline __complex__ long double 810 __complex_sin(const __complex__ long double& __z) 811 { return __builtin_csinl(__z); } 812 813 template<typename _Tp> 814 inline complex<_Tp> 815 sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } 816 #else 817 template<typename _Tp> 818 inline complex<_Tp> 819 sin(const complex<_Tp>& __z) { return __complex_sin(__z); } 820 #endif 821 822 // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. 823 template<typename _Tp> 824 inline complex<_Tp> 825 __complex_sinh(const complex<_Tp>& __z) 826 { 827 const _Tp __x = __z.real(); 828 const _Tp __y = __z.imag(); 829 return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); 830 } 831 832 #if _GLIBCXX_USE_C99_COMPLEX 833 inline __complex__ float 834 __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } 835 836 inline __complex__ double 837 __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } 838 839 inline __complex__ long double 840 __complex_sinh(const __complex__ long double& __z) 841 { return __builtin_csinhl(__z); } 842 843 template<typename _Tp> 844 inline complex<_Tp> 845 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } 846 #else 847 template<typename _Tp> 848 inline complex<_Tp> 849 sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } 850 #endif 851 852 // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. 853 // The branch cut is on the negative axis. 854 template<typename _Tp> 855 complex<_Tp> 856 __complex_sqrt(const complex<_Tp>& __z) 857 { 858 _Tp __x = __z.real(); 859 _Tp __y = __z.imag(); 860 861 if (__x == _Tp()) 862 { 863 _Tp __t = sqrt(abs(__y) / 2); 864 return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); 865 } 866 else 867 { 868 _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); 869 _Tp __u = __t / 2; 870 return __x > _Tp() 871 ? complex<_Tp>(__u, __y / __t) 872 : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); 873 } 874 } 875 876 #if _GLIBCXX_USE_C99_COMPLEX 877 inline __complex__ float 878 __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } 879 880 inline __complex__ double 881 __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } 882 883 inline __complex__ long double 884 __complex_sqrt(const __complex__ long double& __z) 885 { return __builtin_csqrtl(__z); } 886 887 template<typename _Tp> 888 inline complex<_Tp> 889 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } 890 #else 891 template<typename _Tp> 892 inline complex<_Tp> 893 sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } 894 #endif 895 896 // 26.2.8/14 tan(__z): Return the complex tangent of __z. 897 898 template<typename _Tp> 899 inline complex<_Tp> 900 __complex_tan(const complex<_Tp>& __z) 901 { return std::sin(__z) / std::cos(__z); } 902 903 #if _GLIBCXX_USE_C99_COMPLEX 904 inline __complex__ float 905 __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } 906 907 inline __complex__ double 908 __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } 909 910 inline __complex__ long double 911 __complex_tan(const __complex__ long double& __z) 912 { return __builtin_ctanl(__z); } 913 914 template<typename _Tp> 915 inline complex<_Tp> 916 tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } 917 #else 918 template<typename _Tp> 919 inline complex<_Tp> 920 tan(const complex<_Tp>& __z) { return __complex_tan(__z); } 921 #endif 922 923 924 // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. 925 926 template<typename _Tp> 927 inline complex<_Tp> 928 __complex_tanh(const complex<_Tp>& __z) 929 { return std::sinh(__z) / std::cosh(__z); } 930 931 #if _GLIBCXX_USE_C99_COMPLEX 932 inline __complex__ float 933 __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } 934 935 inline __complex__ double 936 __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } 937 938 inline __complex__ long double 939 __complex_tanh(const __complex__ long double& __z) 940 { return __builtin_ctanhl(__z); } 941 942 template<typename _Tp> 943 inline complex<_Tp> 944 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } 945 #else 946 template<typename _Tp> 947 inline complex<_Tp> 948 tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } 949 #endif 950 951 952 // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x 953 // raised to the __y-th power. The branch 954 // cut is on the negative axis. 955 #ifndef __GXX_EXPERIMENTAL_CXX0X__ 956 template<typename _Tp> 957 complex<_Tp> 958 __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) 959 { 960 complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); 961 962 while (__n >>= 1) 963 { 964 __x *= __x; 965 if (__n % 2) 966 __y *= __x; 967 } 968 969 return __y; 970 } 971 972 // _GLIBCXX_RESOLVE_LIB_DEFECTS 973 // DR 844. complex pow return type is ambiguous. 974 template<typename _Tp> 975 inline complex<_Tp> 976 pow(const complex<_Tp>& __z, int __n) 977 { 978 return __n < 0 979 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -__n) 980 : std::__complex_pow_unsigned(__z, __n); 981 } 982 #endif 983 984 template<typename _Tp> 985 complex<_Tp> 986 pow(const complex<_Tp>& __x, const _Tp& __y) 987 { 988 #ifndef _GLIBCXX_USE_C99_COMPLEX 989 if (__x == _Tp()) 990 return _Tp(); 991 #endif 992 if (__x.imag() == _Tp() && __x.real() > _Tp()) 993 return pow(__x.real(), __y); 994 995 complex<_Tp> __t = std::log(__x); 996 return std::polar(exp(__y * __t.real()), __y * __t.imag()); 997 } 998 999 template<typename _Tp> 1000 inline complex<_Tp> 1001 __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1002 { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } 1003 1004 #if _GLIBCXX_USE_C99_COMPLEX 1005 inline __complex__ float 1006 __complex_pow(__complex__ float __x, __complex__ float __y) 1007 { return __builtin_cpowf(__x, __y); } 1008 1009 inline __complex__ double 1010 __complex_pow(__complex__ double __x, __complex__ double __y) 1011 { return __builtin_cpow(__x, __y); } 1012 1013 inline __complex__ long double 1014 __complex_pow(const __complex__ long double& __x, 1015 const __complex__ long double& __y) 1016 { return __builtin_cpowl(__x, __y); } 1017 1018 template<typename _Tp> 1019 inline complex<_Tp> 1020 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1021 { return __complex_pow(__x.__rep(), __y.__rep()); } 1022 #else 1023 template<typename _Tp> 1024 inline complex<_Tp> 1025 pow(const complex<_Tp>& __x, const complex<_Tp>& __y) 1026 { return __complex_pow(__x, __y); } 1027 #endif 1028 1029 template<typename _Tp> 1030 inline complex<_Tp> 1031 pow(const _Tp& __x, const complex<_Tp>& __y) 1032 { 1033 return __x > _Tp() ? std::polar(pow(__x, __y.real()), 1034 __y.imag() * log(__x)) 1035 : std::pow(complex<_Tp>(__x), __y); 1036 } 1037 1038 // 26.2.3 complex specializations 1039 // complex<float> specialization 1040 template<> 1041 struct complex<float> 1042 { 1043 typedef float value_type; 1044 typedef __complex__ float _ComplexT; 1045 1046 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1047 1048 _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) 1049 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1050 // The list-initialization extension to __complex__ types is 1051 // not available in GCC 4.6. Thus libstdc++/48760 cannot be 1052 // fixed in C++0x mode, unfortunately. 1053 : _M_value(__r + __i * 1.0fi) { } 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 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1065 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1066 // DR 387. std::complex over-encapsulated. 1067 constexpr float 1068 real() const { return __real__ _M_value; } 1069 1070 constexpr float 1071 imag() const { return __imag__ _M_value; } 1072 #else 1073 float& 1074 real() { return __real__ _M_value; } 1075 1076 const float& 1077 real() const { return __real__ _M_value; } 1078 1079 float& 1080 imag() { return __imag__ _M_value; } 1081 1082 const float& 1083 imag() const { return __imag__ _M_value; } 1084 #endif 1085 1086 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1087 // DR 387. std::complex over-encapsulated. 1088 void 1089 real(float __val) { __real__ _M_value = __val; } 1090 1091 void 1092 imag(float __val) { __imag__ _M_value = __val; } 1093 1094 complex& 1095 operator=(float __f) 1096 { 1097 _M_value = __f; 1098 return *this; 1099 } 1100 1101 complex& 1102 operator+=(float __f) 1103 { 1104 _M_value += __f; 1105 return *this; 1106 } 1107 1108 complex& 1109 operator-=(float __f) 1110 { 1111 _M_value -= __f; 1112 return *this; 1113 } 1114 1115 complex& 1116 operator*=(float __f) 1117 { 1118 _M_value *= __f; 1119 return *this; 1120 } 1121 1122 complex& 1123 operator/=(float __f) 1124 { 1125 _M_value /= __f; 1126 return *this; 1127 } 1128 1129 // Let the compiler synthesize the copy and assignment 1130 // operator. It always does a pretty good job. 1131 // complex& operator=(const complex&); 1132 1133 template<typename _Tp> 1134 complex& 1135 operator=(const complex<_Tp>& __z) 1136 { 1137 __real__ _M_value = __z.real(); 1138 __imag__ _M_value = __z.imag(); 1139 return *this; 1140 } 1141 1142 template<typename _Tp> 1143 complex& 1144 operator+=(const complex<_Tp>& __z) 1145 { 1146 __real__ _M_value += __z.real(); 1147 __imag__ _M_value += __z.imag(); 1148 return *this; 1149 } 1150 1151 template<class _Tp> 1152 complex& 1153 operator-=(const complex<_Tp>& __z) 1154 { 1155 __real__ _M_value -= __z.real(); 1156 __imag__ _M_value -= __z.imag(); 1157 return *this; 1158 } 1159 1160 template<class _Tp> 1161 complex& 1162 operator*=(const complex<_Tp>& __z) 1163 { 1164 _ComplexT __t; 1165 __real__ __t = __z.real(); 1166 __imag__ __t = __z.imag(); 1167 _M_value *= __t; 1168 return *this; 1169 } 1170 1171 template<class _Tp> 1172 complex& 1173 operator/=(const complex<_Tp>& __z) 1174 { 1175 _ComplexT __t; 1176 __real__ __t = __z.real(); 1177 __imag__ __t = __z.imag(); 1178 _M_value /= __t; 1179 return *this; 1180 } 1181 1182 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1183 1184 private: 1185 _ComplexT _M_value; 1186 }; 1187 1188 // 26.2.3 complex specializations 1189 // complex<double> specialization 1190 template<> 1191 struct complex<double> 1192 { 1193 typedef double value_type; 1194 typedef __complex__ double _ComplexT; 1195 1196 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1197 1198 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1199 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1200 // The list-initialization extension to __complex__ types is 1201 // not available in GCC 4.6. Thus libstdc++/48760 cannot be 1202 // fixed in C++0x mode, unfortunately. 1203 : _M_value(__r + __i * 1.0i) { } 1204 #else 1205 { 1206 __real__ _M_value = __r; 1207 __imag__ _M_value = __i; 1208 } 1209 #endif 1210 1211 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1212 : _M_value(__z.__rep()) { } 1213 1214 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1215 1216 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1217 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1218 // DR 387. std::complex over-encapsulated. 1219 constexpr double 1220 real() const { return __real__ _M_value; } 1221 1222 constexpr double 1223 imag() const { return __imag__ _M_value; } 1224 #else 1225 double& 1226 real() { return __real__ _M_value; } 1227 1228 const double& 1229 real() const { return __real__ _M_value; } 1230 1231 double& 1232 imag() { return __imag__ _M_value; } 1233 1234 const double& 1235 imag() const { return __imag__ _M_value; } 1236 #endif 1237 1238 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1239 // DR 387. std::complex over-encapsulated. 1240 void 1241 real(double __val) { __real__ _M_value = __val; } 1242 1243 void 1244 imag(double __val) { __imag__ _M_value = __val; } 1245 1246 complex& 1247 operator=(double __d) 1248 { 1249 _M_value = __d; 1250 return *this; 1251 } 1252 1253 complex& 1254 operator+=(double __d) 1255 { 1256 _M_value += __d; 1257 return *this; 1258 } 1259 1260 complex& 1261 operator-=(double __d) 1262 { 1263 _M_value -= __d; 1264 return *this; 1265 } 1266 1267 complex& 1268 operator*=(double __d) 1269 { 1270 _M_value *= __d; 1271 return *this; 1272 } 1273 1274 complex& 1275 operator/=(double __d) 1276 { 1277 _M_value /= __d; 1278 return *this; 1279 } 1280 1281 // The compiler will synthesize this, efficiently. 1282 // complex& operator=(const complex&); 1283 1284 template<typename _Tp> 1285 complex& 1286 operator=(const complex<_Tp>& __z) 1287 { 1288 __real__ _M_value = __z.real(); 1289 __imag__ _M_value = __z.imag(); 1290 return *this; 1291 } 1292 1293 template<typename _Tp> 1294 complex& 1295 operator+=(const complex<_Tp>& __z) 1296 { 1297 __real__ _M_value += __z.real(); 1298 __imag__ _M_value += __z.imag(); 1299 return *this; 1300 } 1301 1302 template<typename _Tp> 1303 complex& 1304 operator-=(const complex<_Tp>& __z) 1305 { 1306 __real__ _M_value -= __z.real(); 1307 __imag__ _M_value -= __z.imag(); 1308 return *this; 1309 } 1310 1311 template<typename _Tp> 1312 complex& 1313 operator*=(const complex<_Tp>& __z) 1314 { 1315 _ComplexT __t; 1316 __real__ __t = __z.real(); 1317 __imag__ __t = __z.imag(); 1318 _M_value *= __t; 1319 return *this; 1320 } 1321 1322 template<typename _Tp> 1323 complex& 1324 operator/=(const complex<_Tp>& __z) 1325 { 1326 _ComplexT __t; 1327 __real__ __t = __z.real(); 1328 __imag__ __t = __z.imag(); 1329 _M_value /= __t; 1330 return *this; 1331 } 1332 1333 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1334 1335 private: 1336 _ComplexT _M_value; 1337 }; 1338 1339 // 26.2.3 complex specializations 1340 // complex<long double> specialization 1341 template<> 1342 struct complex<long double> 1343 { 1344 typedef long double value_type; 1345 typedef __complex__ long double _ComplexT; 1346 1347 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1348 1349 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1350 long double __i = 0.0L) 1351 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1352 // The list-initialization extension to __complex__ types is 1353 // not available in GCC 4.6. Thus libstdc++/48760 cannot be 1354 // fixed in C++0x mode, unfortunately. 1355 : _M_value(__r + __i * 1.0Li) { } 1356 #else 1357 { 1358 __real__ _M_value = __r; 1359 __imag__ _M_value = __i; 1360 } 1361 #endif 1362 1363 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1364 : _M_value(__z.__rep()) { } 1365 1366 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1367 : _M_value(__z.__rep()) { } 1368 1369 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1370 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1371 // DR 387. std::complex over-encapsulated. 1372 constexpr long double 1373 real() const { return __real__ _M_value; } 1374 1375 constexpr long double 1376 imag() const { 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 1532 namespace __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 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1562 1563 namespace 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 // __GXX_EXPERIMENTAL_CXX0X__ 1932 1933 #endif /* _GLIBCXX_COMPLEX */ 1934
