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() { return _M_real; } 146 147 constexpr _Tp 148 imag() { 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 constexpr _Tp 535 real(const complex<_Tp>& __z) 536 { return __z.real(); } 537 538 template<typename _Tp> 539 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 : _M_value{ __r, __i } { } 1051 #else 1052 { 1053 __real__ _M_value = __r; 1054 __imag__ _M_value = __i; 1055 } 1056 #endif 1057 1058 explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&); 1059 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1060 1061 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1062 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1063 // DR 387. std::complex over-encapsulated. 1064 constexpr float 1065 real() { return __real__ _M_value; } 1066 1067 constexpr float 1068 imag() { return __imag__ _M_value; } 1069 #else 1070 float& 1071 real() { return __real__ _M_value; } 1072 1073 const float& 1074 real() const { return __real__ _M_value; } 1075 1076 float& 1077 imag() { return __imag__ _M_value; } 1078 1079 const float& 1080 imag() const { return __imag__ _M_value; } 1081 #endif 1082 1083 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1084 // DR 387. std::complex over-encapsulated. 1085 void 1086 real(float __val) { __real__ _M_value = __val; } 1087 1088 void 1089 imag(float __val) { __imag__ _M_value = __val; } 1090 1091 complex& 1092 operator=(float __f) 1093 { 1094 _M_value = __f; 1095 return *this; 1096 } 1097 1098 complex& 1099 operator+=(float __f) 1100 { 1101 _M_value += __f; 1102 return *this; 1103 } 1104 1105 complex& 1106 operator-=(float __f) 1107 { 1108 _M_value -= __f; 1109 return *this; 1110 } 1111 1112 complex& 1113 operator*=(float __f) 1114 { 1115 _M_value *= __f; 1116 return *this; 1117 } 1118 1119 complex& 1120 operator/=(float __f) 1121 { 1122 _M_value /= __f; 1123 return *this; 1124 } 1125 1126 // Let the compiler synthesize the copy and assignment 1127 // operator. It always does a pretty good job. 1128 // complex& operator=(const complex&); 1129 1130 template<typename _Tp> 1131 complex& 1132 operator=(const complex<_Tp>& __z) 1133 { 1134 __real__ _M_value = __z.real(); 1135 __imag__ _M_value = __z.imag(); 1136 return *this; 1137 } 1138 1139 template<typename _Tp> 1140 complex& 1141 operator+=(const complex<_Tp>& __z) 1142 { 1143 __real__ _M_value += __z.real(); 1144 __imag__ _M_value += __z.imag(); 1145 return *this; 1146 } 1147 1148 template<class _Tp> 1149 complex& 1150 operator-=(const complex<_Tp>& __z) 1151 { 1152 __real__ _M_value -= __z.real(); 1153 __imag__ _M_value -= __z.imag(); 1154 return *this; 1155 } 1156 1157 template<class _Tp> 1158 complex& 1159 operator*=(const complex<_Tp>& __z) 1160 { 1161 _ComplexT __t; 1162 __real__ __t = __z.real(); 1163 __imag__ __t = __z.imag(); 1164 _M_value *= __t; 1165 return *this; 1166 } 1167 1168 template<class _Tp> 1169 complex& 1170 operator/=(const complex<_Tp>& __z) 1171 { 1172 _ComplexT __t; 1173 __real__ __t = __z.real(); 1174 __imag__ __t = __z.imag(); 1175 _M_value /= __t; 1176 return *this; 1177 } 1178 1179 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1180 1181 private: 1182 _ComplexT _M_value; 1183 }; 1184 1185 /// 26.2.3 complex specializations 1186 /// complex<double> specialization 1187 template<> 1188 struct complex<double> 1189 { 1190 typedef double value_type; 1191 typedef __complex__ double _ComplexT; 1192 1193 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1194 1195 _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) 1196 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1197 : _M_value{ __r, __i } { } 1198 #else 1199 { 1200 __real__ _M_value = __r; 1201 __imag__ _M_value = __i; 1202 } 1203 #endif 1204 1205 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1206 : _M_value(__z.__rep()) { } 1207 1208 explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); 1209 1210 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1211 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1212 // DR 387. std::complex over-encapsulated. 1213 constexpr double 1214 real() { return __real__ _M_value; } 1215 1216 constexpr double 1217 imag() { return __imag__ _M_value; } 1218 #else 1219 double& 1220 real() { return __real__ _M_value; } 1221 1222 const double& 1223 real() const { return __real__ _M_value; } 1224 1225 double& 1226 imag() { return __imag__ _M_value; } 1227 1228 const double& 1229 imag() const { return __imag__ _M_value; } 1230 #endif 1231 1232 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1233 // DR 387. std::complex over-encapsulated. 1234 void 1235 real(double __val) { __real__ _M_value = __val; } 1236 1237 void 1238 imag(double __val) { __imag__ _M_value = __val; } 1239 1240 complex& 1241 operator=(double __d) 1242 { 1243 _M_value = __d; 1244 return *this; 1245 } 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 // The compiler will synthesize this, efficiently. 1276 // complex& operator=(const complex&); 1277 1278 template<typename _Tp> 1279 complex& 1280 operator=(const complex<_Tp>& __z) 1281 { 1282 __real__ _M_value = __z.real(); 1283 __imag__ _M_value = __z.imag(); 1284 return *this; 1285 } 1286 1287 template<typename _Tp> 1288 complex& 1289 operator+=(const complex<_Tp>& __z) 1290 { 1291 __real__ _M_value += __z.real(); 1292 __imag__ _M_value += __z.imag(); 1293 return *this; 1294 } 1295 1296 template<typename _Tp> 1297 complex& 1298 operator-=(const complex<_Tp>& __z) 1299 { 1300 __real__ _M_value -= __z.real(); 1301 __imag__ _M_value -= __z.imag(); 1302 return *this; 1303 } 1304 1305 template<typename _Tp> 1306 complex& 1307 operator*=(const complex<_Tp>& __z) 1308 { 1309 _ComplexT __t; 1310 __real__ __t = __z.real(); 1311 __imag__ __t = __z.imag(); 1312 _M_value *= __t; 1313 return *this; 1314 } 1315 1316 template<typename _Tp> 1317 complex& 1318 operator/=(const complex<_Tp>& __z) 1319 { 1320 _ComplexT __t; 1321 __real__ __t = __z.real(); 1322 __imag__ __t = __z.imag(); 1323 _M_value /= __t; 1324 return *this; 1325 } 1326 1327 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1328 1329 private: 1330 _ComplexT _M_value; 1331 }; 1332 1333 /// 26.2.3 complex specializations 1334 /// complex<long double> specialization 1335 template<> 1336 struct complex<long double> 1337 { 1338 typedef long double value_type; 1339 typedef __complex__ long double _ComplexT; 1340 1341 _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } 1342 1343 _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, 1344 long double __i = 0.0L) 1345 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1346 : _M_value{ __r, __i } { } 1347 #else 1348 { 1349 __real__ _M_value = __r; 1350 __imag__ _M_value = __i; 1351 } 1352 #endif 1353 1354 _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) 1355 : _M_value(__z.__rep()) { } 1356 1357 _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) 1358 : _M_value(__z.__rep()) { } 1359 1360 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1361 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1362 // DR 387. std::complex over-encapsulated. 1363 constexpr long double 1364 real() { return __real__ _M_value; } 1365 1366 constexpr long double 1367 imag() { return __imag__ _M_value; } 1368 #else 1369 long double& 1370 real() { return __real__ _M_value; } 1371 1372 const long double& 1373 real() const { return __real__ _M_value; } 1374 1375 long double& 1376 imag() { return __imag__ _M_value; } 1377 1378 const long double& 1379 imag() const { return __imag__ _M_value; } 1380 #endif 1381 1382 // _GLIBCXX_RESOLVE_LIB_DEFECTS 1383 // DR 387. std::complex over-encapsulated. 1384 void 1385 real(long double __val) { __real__ _M_value = __val; } 1386 1387 void 1388 imag(long double __val) { __imag__ _M_value = __val; } 1389 1390 complex& 1391 operator=(long double __r) 1392 { 1393 _M_value = __r; 1394 return *this; 1395 } 1396 1397 complex& 1398 operator+=(long double __r) 1399 { 1400 _M_value += __r; 1401 return *this; 1402 } 1403 1404 complex& 1405 operator-=(long double __r) 1406 { 1407 _M_value -= __r; 1408 return *this; 1409 } 1410 1411 complex& 1412 operator*=(long double __r) 1413 { 1414 _M_value *= __r; 1415 return *this; 1416 } 1417 1418 complex& 1419 operator/=(long double __r) 1420 { 1421 _M_value /= __r; 1422 return *this; 1423 } 1424 1425 // The compiler knows how to do this efficiently 1426 // complex& operator=(const complex&); 1427 1428 template<typename _Tp> 1429 complex& 1430 operator=(const complex<_Tp>& __z) 1431 { 1432 __real__ _M_value = __z.real(); 1433 __imag__ _M_value = __z.imag(); 1434 return *this; 1435 } 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 _ComplexT __t; 1460 __real__ __t = __z.real(); 1461 __imag__ __t = __z.imag(); 1462 _M_value *= __t; 1463 return *this; 1464 } 1465 1466 template<typename _Tp> 1467 complex& 1468 operator/=(const complex<_Tp>& __z) 1469 { 1470 _ComplexT __t; 1471 __real__ __t = __z.real(); 1472 __imag__ __t = __z.imag(); 1473 _M_value /= __t; 1474 return *this; 1475 } 1476 1477 _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } 1478 1479 private: 1480 _ComplexT _M_value; 1481 }; 1482 1483 // These bits have to be at the end of this file, so that the 1484 // specializations have all been defined. 1485 inline _GLIBCXX_CONSTEXPR 1486 complex<float>::complex(const complex<double>& __z) 1487 : _M_value(__z.__rep()) { } 1488 1489 inline _GLIBCXX_CONSTEXPR 1490 complex<float>::complex(const complex<long double>& __z) 1491 : _M_value(__z.__rep()) { } 1492 1493 inline _GLIBCXX_CONSTEXPR 1494 complex<double>::complex(const complex<long double>& __z) 1495 : _M_value(__z.__rep()) { } 1496 1497 // Inhibit implicit instantiations for required instantiations, 1498 // which are defined via explicit instantiations elsewhere. 1499 // NB: This syntax is a GNU extension. 1500 #if _GLIBCXX_EXTERN_TEMPLATE 1501 extern template istream& operator>>(istream&, complex<float>&); 1502 extern template ostream& operator<<(ostream&, const complex<float>&); 1503 extern template istream& operator>>(istream&, complex<double>&); 1504 extern template ostream& operator<<(ostream&, const complex<double>&); 1505 extern template istream& operator>>(istream&, complex<long double>&); 1506 extern template ostream& operator<<(ostream&, const complex<long double>&); 1507 1508 #ifdef _GLIBCXX_USE_WCHAR_T 1509 extern template wistream& operator>>(wistream&, complex<float>&); 1510 extern template wostream& operator<<(wostream&, const complex<float>&); 1511 extern template wistream& operator>>(wistream&, complex<double>&); 1512 extern template wostream& operator<<(wostream&, const complex<double>&); 1513 extern template wistream& operator>>(wistream&, complex<long double>&); 1514 extern template wostream& operator<<(wostream&, const complex<long double>&); 1515 #endif 1516 #endif 1517 1518 // @} group complex_numbers 1519 1520 _GLIBCXX_END_NAMESPACE_VERSION 1521 } // namespace 1522 1523 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) 1524 { 1525 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1526 1527 // See ext/type_traits.h for the primary template. 1528 template<typename _Tp, typename _Up> 1529 struct __promote_2<std::complex<_Tp>, _Up> 1530 { 1531 public: 1532 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1533 }; 1534 1535 template<typename _Tp, typename _Up> 1536 struct __promote_2<_Tp, std::complex<_Up> > 1537 { 1538 public: 1539 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1540 }; 1541 1542 template<typename _Tp, typename _Up> 1543 struct __promote_2<std::complex<_Tp>, std::complex<_Up> > 1544 { 1545 public: 1546 typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; 1547 }; 1548 1549 _GLIBCXX_END_NAMESPACE_VERSION 1550 } // namespace 1551 1552 #ifdef __GXX_EXPERIMENTAL_CXX0X__ 1553 1554 namespace std _GLIBCXX_VISIBILITY(default) 1555 { 1556 _GLIBCXX_BEGIN_NAMESPACE_VERSION 1557 1558 // Forward declarations. 1559 template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&); 1560 template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&); 1561 template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&); 1562 1563 template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&); 1564 template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&); 1565 template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&); 1566 // DR 595. 1567 template<typename _Tp> _Tp fabs(const std::complex<_Tp>&); 1568 1569 template<typename _Tp> 1570 inline std::complex<_Tp> 1571 __complex_acos(const std::complex<_Tp>& __z) 1572 { 1573 const std::complex<_Tp> __t = std::asin(__z); 1574 const _Tp __pi_2 = 1.5707963267948966192313216916397514L; 1575 return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); 1576 } 1577 1578 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1579 inline __complex__ float 1580 __complex_acos(__complex__ float __z) 1581 { return __builtin_cacosf(__z); } 1582 1583 inline __complex__ double 1584 __complex_acos(__complex__ double __z) 1585 { return __builtin_cacos(__z); } 1586 1587 inline __complex__ long double 1588 __complex_acos(const __complex__ long double& __z) 1589 { return __builtin_cacosl(__z); } 1590 1591 template<typename _Tp> 1592 inline std::complex<_Tp> 1593 acos(const std::complex<_Tp>& __z) 1594 { return __complex_acos(__z.__rep()); } 1595 #else 1596 /// acos(__z) [8.1.2]. 1597 // Effects: Behaves the same as C99 function cacos, defined 1598 // in subclause 7.3.5.1. 1599 template<typename _Tp> 1600 inline std::complex<_Tp> 1601 acos(const std::complex<_Tp>& __z) 1602 { return __complex_acos(__z); } 1603 #endif 1604 1605 template<typename _Tp> 1606 inline std::complex<_Tp> 1607 __complex_asin(const std::complex<_Tp>& __z) 1608 { 1609 std::complex<_Tp> __t(-__z.imag(), __z.real()); 1610 __t = std::asinh(__t); 1611 return std::complex<_Tp>(__t.imag(), -__t.real()); 1612 } 1613 1614 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1615 inline __complex__ float 1616 __complex_asin(__complex__ float __z) 1617 { return __builtin_casinf(__z); } 1618 1619 inline __complex__ double 1620 __complex_asin(__complex__ double __z) 1621 { return __builtin_casin(__z); } 1622 1623 inline __complex__ long double 1624 __complex_asin(const __complex__ long double& __z) 1625 { return __builtin_casinl(__z); } 1626 1627 template<typename _Tp> 1628 inline std::complex<_Tp> 1629 asin(const std::complex<_Tp>& __z) 1630 { return __complex_asin(__z.__rep()); } 1631 #else 1632 /// asin(__z) [8.1.3]. 1633 // Effects: Behaves the same as C99 function casin, defined 1634 // in subclause 7.3.5.2. 1635 template<typename _Tp> 1636 inline std::complex<_Tp> 1637 asin(const std::complex<_Tp>& __z) 1638 { return __complex_asin(__z); } 1639 #endif 1640 1641 template<typename _Tp> 1642 std::complex<_Tp> 1643 __complex_atan(const std::complex<_Tp>& __z) 1644 { 1645 const _Tp __r2 = __z.real() * __z.real(); 1646 const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); 1647 1648 _Tp __num = __z.imag() + _Tp(1.0); 1649 _Tp __den = __z.imag() - _Tp(1.0); 1650 1651 __num = __r2 + __num * __num; 1652 __den = __r2 + __den * __den; 1653 1654 return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), 1655 _Tp(0.25) * log(__num / __den)); 1656 } 1657 1658 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1659 inline __complex__ float 1660 __complex_atan(__complex__ float __z) 1661 { return __builtin_catanf(__z); } 1662 1663 inline __complex__ double 1664 __complex_atan(__complex__ double __z) 1665 { return __builtin_catan(__z); } 1666 1667 inline __complex__ long double 1668 __complex_atan(const __complex__ long double& __z) 1669 { return __builtin_catanl(__z); } 1670 1671 template<typename _Tp> 1672 inline std::complex<_Tp> 1673 atan(const std::complex<_Tp>& __z) 1674 { return __complex_atan(__z.__rep()); } 1675 #else 1676 /// atan(__z) [8.1.4]. 1677 // Effects: Behaves the same as C99 function catan, defined 1678 // in subclause 7.3.5.3. 1679 template<typename _Tp> 1680 inline std::complex<_Tp> 1681 atan(const std::complex<_Tp>& __z) 1682 { return __complex_atan(__z); } 1683 #endif 1684 1685 template<typename _Tp> 1686 std::complex<_Tp> 1687 __complex_acosh(const std::complex<_Tp>& __z) 1688 { 1689 // Kahan's formula. 1690 return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) 1691 + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); 1692 } 1693 1694 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1695 inline __complex__ float 1696 __complex_acosh(__complex__ float __z) 1697 { return __builtin_cacoshf(__z); } 1698 1699 inline __complex__ double 1700 __complex_acosh(__complex__ double __z) 1701 { return __builtin_cacosh(__z); } 1702 1703 inline __complex__ long double 1704 __complex_acosh(const __complex__ long double& __z) 1705 { return __builtin_cacoshl(__z); } 1706 1707 template<typename _Tp> 1708 inline std::complex<_Tp> 1709 acosh(const std::complex<_Tp>& __z) 1710 { return __complex_acosh(__z.__rep()); } 1711 #else 1712 /// acosh(__z) [8.1.5]. 1713 // Effects: Behaves the same as C99 function cacosh, defined 1714 // in subclause 7.3.6.1. 1715 template<typename _Tp> 1716 inline std::complex<_Tp> 1717 acosh(const std::complex<_Tp>& __z) 1718 { return __complex_acosh(__z); } 1719 #endif 1720 1721 template<typename _Tp> 1722 std::complex<_Tp> 1723 __complex_asinh(const std::complex<_Tp>& __z) 1724 { 1725 std::complex<_Tp> __t((__z.real() - __z.imag()) 1726 * (__z.real() + __z.imag()) + _Tp(1.0), 1727 _Tp(2.0) * __z.real() * __z.imag()); 1728 __t = std::sqrt(__t); 1729 1730 return std::log(__t + __z); 1731 } 1732 1733 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1734 inline __complex__ float 1735 __complex_asinh(__complex__ float __z) 1736 { return __builtin_casinhf(__z); } 1737 1738 inline __complex__ double 1739 __complex_asinh(__complex__ double __z) 1740 { return __builtin_casinh(__z); } 1741 1742 inline __complex__ long double 1743 __complex_asinh(const __complex__ long double& __z) 1744 { return __builtin_casinhl(__z); } 1745 1746 template<typename _Tp> 1747 inline std::complex<_Tp> 1748 asinh(const std::complex<_Tp>& __z) 1749 { return __complex_asinh(__z.__rep()); } 1750 #else 1751 /// asinh(__z) [8.1.6]. 1752 // Effects: Behaves the same as C99 function casin, defined 1753 // in subclause 7.3.6.2. 1754 template<typename _Tp> 1755 inline std::complex<_Tp> 1756 asinh(const std::complex<_Tp>& __z) 1757 { return __complex_asinh(__z); } 1758 #endif 1759 1760 template<typename _Tp> 1761 std::complex<_Tp> 1762 __complex_atanh(const std::complex<_Tp>& __z) 1763 { 1764 const _Tp __i2 = __z.imag() * __z.imag(); 1765 const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); 1766 1767 _Tp __num = _Tp(1.0) + __z.real(); 1768 _Tp __den = _Tp(1.0) - __z.real(); 1769 1770 __num = __i2 + __num * __num; 1771 __den = __i2 + __den * __den; 1772 1773 return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), 1774 _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); 1775 } 1776 1777 #if _GLIBCXX_USE_C99_COMPLEX_TR1 1778 inline __complex__ float 1779 __complex_atanh(__complex__ float __z) 1780 { return __builtin_catanhf(__z); } 1781 1782 inline __complex__ double 1783 __complex_atanh(__complex__ double __z) 1784 { return __builtin_catanh(__z); } 1785 1786 inline __complex__ long double 1787 __complex_atanh(const __complex__ long double& __z) 1788 { return __builtin_catanhl(__z); } 1789 1790 template<typename _Tp> 1791 inline std::complex<_Tp> 1792 atanh(const std::complex<_Tp>& __z) 1793 { return __complex_atanh(__z.__rep()); } 1794 #else 1795 /// atanh(__z) [8.1.7]. 1796 // Effects: Behaves the same as C99 function catanh, defined 1797 // in subclause 7.3.6.3. 1798 template<typename _Tp> 1799 inline std::complex<_Tp> 1800 atanh(const std::complex<_Tp>& __z) 1801 { return __complex_atanh(__z); } 1802 #endif 1803 1804 template<typename _Tp> 1805 inline _Tp 1806 /// fabs(__z) [8.1.8]. 1807 // Effects: Behaves the same as C99 function cabs, defined 1808 // in subclause 7.3.8.1. 1809 fabs(const std::complex<_Tp>& __z) 1810 { return std::abs(__z); } 1811 1812 /// Additional overloads [8.1.9]. 1813 template<typename _Tp> 1814 inline typename __gnu_cxx::__promote<_Tp>::__type 1815 arg(_Tp __x) 1816 { 1817 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1818 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) 1819 return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) 1820 : __type(); 1821 #else 1822 return std::arg(std::complex<__type>(__x)); 1823 #endif 1824 } 1825 1826 template<typename _Tp> 1827 inline typename __gnu_cxx::__promote<_Tp>::__type 1828 imag(_Tp) 1829 { return _Tp(); } 1830 1831 template<typename _Tp> 1832 inline typename __gnu_cxx::__promote<_Tp>::__type 1833 norm(_Tp __x) 1834 { 1835 typedef typename __gnu_cxx::__promote<_Tp>::__type __type; 1836 return __type(__x) * __type(__x); 1837 } 1838 1839 template<typename _Tp> 1840 inline typename __gnu_cxx::__promote<_Tp>::__type 1841 real(_Tp __x) 1842 { return __x; } 1843 1844 template<typename _Tp, typename _Up> 1845 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1846 pow(const std::complex<_Tp>& __x, const _Up& __y) 1847 { 1848 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1849 return std::pow(std::complex<__type>(__x), __type(__y)); 1850 } 1851 1852 template<typename _Tp, typename _Up> 1853 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1854 pow(const _Tp& __x, const std::complex<_Up>& __y) 1855 { 1856 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1857 return std::pow(__type(__x), std::complex<__type>(__y)); 1858 } 1859 1860 template<typename _Tp, typename _Up> 1861 inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type> 1862 pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) 1863 { 1864 typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; 1865 return std::pow(std::complex<__type>(__x), 1866 std::complex<__type>(__y)); 1867 } 1868 1869 // Forward declarations. 1870 // DR 781. 1871 template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); 1872 1873 template<typename _Tp> 1874 std::complex<_Tp> 1875 __complex_proj(const std::complex<_Tp>& __z) 1876 { 1877 const _Tp __den = (__z.real() * __z.real() 1878 + __z.imag() * __z.imag() + _Tp(1.0)); 1879 1880 return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, 1881 (_Tp(2.0) * __z.imag()) / __den); 1882 } 1883 1884 #if _GLIBCXX_USE_C99_COMPLEX 1885 inline __complex__ float 1886 __complex_proj(__complex__ float __z) 1887 { return __builtin_cprojf(__z); } 1888 1889 inline __complex__ double 1890 __complex_proj(__complex__ double __z) 1891 { return __builtin_cproj(__z); } 1892 1893 inline __complex__ long double 1894 __complex_proj(const __complex__ long double& __z) 1895 { return __builtin_cprojl(__z); } 1896 1897 template<typename _Tp> 1898 inline std::complex<_Tp> 1899 proj(const std::complex<_Tp>& __z) 1900 { return __complex_proj(__z.__rep()); } 1901 #else 1902 template<typename _Tp> 1903 inline std::complex<_Tp> 1904 proj(const std::complex<_Tp>& __z) 1905 { return __complex_proj(__z); } 1906 #endif 1907 1908 // DR 1137. 1909 template<typename _Tp> 1910 inline typename __gnu_cxx::__promote<_Tp>::__type 1911 proj(_Tp __x) 1912 { return __x; } 1913 1914 template<typename _Tp> 1915 inline typename __gnu_cxx::__promote<_Tp>::__type 1916 conj(_Tp __x) 1917 { return __x; } 1918 1919 _GLIBCXX_END_NAMESPACE_VERSION 1920 } // namespace 1921 1922 #endif // __GXX_EXPERIMENTAL_CXX0X__ 1923 1924 #endif /* _GLIBCXX_COMPLEX */ 1925
