libstdc++-v3/include/std/complex

   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@cygnus.com>
  35 // Improved by Gabriel Dos Reis <dosreis@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       : _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() const { return __real__ _M_value; }
1066
1067       constexpr float
1068       imag() const { 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() const { return __real__ _M_value; }
1215
1216       constexpr double
1217       imag() const { 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() const { return __real__ _M_value; }
1365
1366       constexpr long double
1367       imag() const { 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       std::complex<_Tp> __t((__z.real() - __z.imag())
1690                             * (__z.real() + __z.imag()) - _Tp(1.0),
1691                             _Tp(2.0) * __z.real() * __z.imag());
1692       __t = std::sqrt(__t);
1693
1694       return std::log(__t + __z);
1695     }
1696
1697 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1698   inline __complex__ float
1699   __complex_acosh(__complex__ float __z)
1700   { return __builtin_cacoshf(__z); }
1701
1702   inline __complex__ double
1703   __complex_acosh(__complex__ double __z)
1704   { return __builtin_cacosh(__z); }
1705
1706   inline __complex__ long double
1707   __complex_acosh(const __complex__ long double& __z)
1708   { return __builtin_cacoshl(__z); }
1709
1710   template<typename _Tp>
1711     inline std::complex<_Tp>
1712     acosh(const std::complex<_Tp>& __z)
1713     { return __complex_acosh(__z.__rep()); }
1714 #else
1715   /// acosh(__z) [8.1.5].
1716   //  Effects:  Behaves the same as C99 function cacosh, defined
1717   //            in subclause 7.3.6.1.
1718   template<typename _Tp>
1719     inline std::complex<_Tp>
1720     acosh(const std::complex<_Tp>& __z)
1721     { return __complex_acosh(__z); }
1722 #endif
1723
1724   template<typename _Tp>
1725     std::complex<_Tp>
1726     __complex_asinh(const std::complex<_Tp>& __z)
1727     {
1728       std::complex<_Tp> __t((__z.real() - __z.imag())
1729                             * (__z.real() + __z.imag()) + _Tp(1.0),
1730                             _Tp(2.0) * __z.real() * __z.imag());
1731       __t = std::sqrt(__t);
1732
1733       return std::log(__t + __z);
1734     }
1735
1736 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1737   inline __complex__ float
1738   __complex_asinh(__complex__ float __z)
1739   { return __builtin_casinhf(__z); }
1740
1741   inline __complex__ double
1742   __complex_asinh(__complex__ double __z)
1743   { return __builtin_casinh(__z); }
1744
1745   inline __complex__ long double
1746   __complex_asinh(const __complex__ long double& __z)
1747   { return __builtin_casinhl(__z); }
1748
1749   template<typename _Tp>
1750     inline std::complex<_Tp>
1751     asinh(const std::complex<_Tp>& __z)
1752     { return __complex_asinh(__z.__rep()); }
1753 #else
1754   /// asinh(__z) [8.1.6].
1755   //  Effects:  Behaves the same as C99 function casin, defined
1756   //            in subclause 7.3.6.2.
1757   template<typename _Tp>
1758     inline std::complex<_Tp>
1759     asinh(const std::complex<_Tp>& __z)
1760     { return __complex_asinh(__z); }
1761 #endif
1762
1763   template<typename _Tp>
1764     std::complex<_Tp>
1765     __complex_atanh(const std::complex<_Tp>& __z)
1766     {
1767       const _Tp __i2 = __z.imag() * __z.imag();
1768       const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
1769
1770       _Tp __num = _Tp(1.0) + __z.real();
1771       _Tp __den = _Tp(1.0) - __z.real();
1772
1773       __num = __i2 + __num * __num;
1774       __den = __i2 + __den * __den;
1775
1776       return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
1777                                _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
1778     }
1779
1780 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1781   inline __complex__ float
1782   __complex_atanh(__complex__ float __z)
1783   { return __builtin_catanhf(__z); }
1784
1785   inline __complex__ double
1786   __complex_atanh(__complex__ double __z)
1787   { return __builtin_catanh(__z); }
1788
1789   inline __complex__ long double
1790   __complex_atanh(const __complex__ long double& __z)
1791   { return __builtin_catanhl(__z); }
1792
1793   template<typename _Tp>
1794     inline std::complex<_Tp>
1795     atanh(const std::complex<_Tp>& __z)
1796     { return __complex_atanh(__z.__rep()); }
1797 #else
1798   /// atanh(__z) [8.1.7].
1799   //  Effects:  Behaves the same as C99 function catanh, defined
1800   //            in subclause 7.3.6.3.
1801   template<typename _Tp>
1802     inline std::complex<_Tp>
1803     atanh(const std::complex<_Tp>& __z)
1804     { return __complex_atanh(__z); }
1805 #endif
1806
1807   template<typename _Tp>
1808     inline _Tp
1809     /// fabs(__z) [8.1.8].
1810     //  Effects:  Behaves the same as C99 function cabs, defined
1811     //            in subclause 7.3.8.1.
1812     fabs(const std::complex<_Tp>& __z)
1813     { return std::abs(__z); }
1814
1815   /// Additional overloads [8.1.9].
1816   template<typename _Tp>
1817     inline typename __gnu_cxx::__promote<_Tp>::__type
1818     arg(_Tp __x)
1819     {
1820       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1821 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
1822       return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
1823                                : __type();
1824 #else
1825       return std::arg(std::complex<__type>(__x));
1826 #endif
1827     }
1828
1829   template<typename _Tp>
1830     inline typename __gnu_cxx::__promote<_Tp>::__type
1831     imag(_Tp)
1832     { return _Tp(); }
1833
1834   template<typename _Tp>
1835     inline typename __gnu_cxx::__promote<_Tp>::__type
1836     norm(_Tp __x)
1837     {
1838       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1839       return __type(__x) * __type(__x);
1840     }
1841
1842   template<typename _Tp>
1843     inline typename __gnu_cxx::__promote<_Tp>::__type
1844     real(_Tp __x)
1845     { return __x; }
1846
1847   template<typename _Tp, typename _Up>
1848     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1849     pow(const std::complex<_Tp>& __x, const _Up& __y)
1850     {
1851       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1852       return std::pow(std::complex<__type>(__x), __type(__y));
1853     }
1854
1855   template<typename _Tp, typename _Up>
1856     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1857     pow(const _Tp& __x, const std::complex<_Up>& __y)
1858     {
1859       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1860       return std::pow(__type(__x), std::complex<__type>(__y));
1861     }
1862
1863   template<typename _Tp, typename _Up>
1864     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1865     pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
1866     {
1867       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1868       return std::pow(std::complex<__type>(__x),
1869                       std::complex<__type>(__y));
1870     }
1871
1872   // Forward declarations.
1873   // DR 781.
1874   template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
1875
1876   template<typename _Tp>
1877     std::complex<_Tp>
1878     __complex_proj(const std::complex<_Tp>& __z)
1879     {
1880       const _Tp __den = (__z.real() * __z.real()
1881                          + __z.imag() * __z.imag() + _Tp(1.0));
1882
1883       return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
1884                                (_Tp(2.0) * __z.imag()) / __den);
1885     }
1886
1887 #if _GLIBCXX_USE_C99_COMPLEX
1888   inline __complex__ float
1889   __complex_proj(__complex__ float __z)
1890   { return __builtin_cprojf(__z); }
1891
1892   inline __complex__ double
1893   __complex_proj(__complex__ double __z)
1894   { return __builtin_cproj(__z); }
1895
1896   inline __complex__ long double
1897   __complex_proj(const __complex__ long double& __z)
1898   { return __builtin_cprojl(__z); }
1899
1900   template<typename _Tp>
1901     inline std::complex<_Tp>
1902     proj(const std::complex<_Tp>& __z)
1903     { return __complex_proj(__z.__rep()); }
1904 #else
1905   template<typename _Tp>
1906     inline std::complex<_Tp>
1907     proj(const std::complex<_Tp>& __z)
1908     { return __complex_proj(__z); }
1909 #endif
1910
1911   // DR 1137.
1912   template<typename _Tp>
1913     inline typename __gnu_cxx::__promote<_Tp>::__type
1914     proj(_Tp __x)
1915     { return __x; }
1916
1917   template<typename _Tp>
1918     inline typename __gnu_cxx::__promote<_Tp>::__type
1919     conj(_Tp __x)
1920     { return __x; }
1921
1922 _GLIBCXX_END_NAMESPACE_VERSION
1923 } // namespace
1924
1925 #endif  // __GXX_EXPERIMENTAL_CXX0X__
1926
1927 #endif  /* _GLIBCXX_COMPLEX */