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
   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 2, 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 // You should have received a copy of the GNU General Public License
  19 // along with this library; see the file COPYING.  If not, write to
  20 // the Free Software Foundation, 51 Franklin Street, Fifth Floor,
  21 // Boston, MA 02110-1301, USA.
  22
  23 // As a special exception, you may use this file as part of a free software
  24 // library without restriction.  Specifically, if other files instantiate
  25 // templates or use macros or inline functions from this file, or you compile
  26 // this file and link it with other files to produce an executable, this
  27 // file does not by itself cause the resulting executable to be covered by
  28 // the GNU General Public License.  This exception does not however
  29 // invalidate any other reasons why the executable file might be covered by
  30 // the GNU General Public License.
  31
  32 /** @file include/complex
  33  *  This is a Standard C++ Library header.
  34  */
  35
  36 //
  37 // ISO C++ 14882: 26.2  Complex Numbers
  38 // Note: this is not a conforming implementation.
  39 // Initially implemented by Ulrich Drepper <drepper@cygnus.com>
  40 // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
  41 //
  42
  43 #ifndef _GLIBCXX_COMPLEX
  44 #define _GLIBCXX_COMPLEX 1
  45
  46 #pragma GCC system_header
  47
  48 #include <bits/c++config.h>
  49 #include <bits/cpp_type_traits.h>
  50 #include <ext/type_traits.h>
  51 #include <cmath>
  52 #include <sstream>
  53
  54 _GLIBCXX_BEGIN_NAMESPACE(std)
  55
  56   /**
  57    * @defgroup complex_numbers Complex Numbers
  58    * @ingroup numerics
  59    *
  60    * Classes and functions for complex numbers.
  61    * @{
  62    */
  63
  64   // Forward declarations.
  65   template<typename _Tp> class complex;
  66   template<> class complex<float>;
  67   template<> class complex<double>;
  68   template<> class complex<long double>;
  69
  70   ///  Return magnitude of @a z.
  71   template<typename _Tp> _Tp abs(const complex<_Tp>&);
  72   ///  Return phase angle of @a z.
  73   template<typename _Tp> _Tp arg(const complex<_Tp>&);
  74   ///  Return @a z magnitude squared.
  75   template<typename _Tp> _Tp norm(const complex<_Tp>&);
  76
  77   ///  Return complex conjugate of @a z.
  78   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
  79   ///  Return complex with magnitude @a rho and angle @a theta.
  80   template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
  81
  82   // Transcendentals:
  83   /// Return complex cosine of @a z.
  84   template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
  85   /// Return complex hyperbolic cosine of @a z.
  86   template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
  87   /// Return complex base e exponential of @a z.
  88   template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
  89   /// Return complex natural logarithm of @a z.
  90   template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
  91   /// Return complex base 10 logarithm of @a z.
  92   template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
  93 #ifndef __GXX_EXPERIMENTAL_CXX0X__
  94   // DR 844.
  95   /// Return @a x to the @a y'th power.
  96   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
  97 #endif
  98   /// Return @a x to the @a y'th power.
  99   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
 100   /// Return @a x to the @a y'th power.
 101   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
 102                                           const complex<_Tp>&);
 103   /// Return @a x to the @a y'th power.
 104   template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
 105   /// Return complex sine of @a z.
 106   template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
 107   /// Return complex hyperbolic sine of @a z.
 108   template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
 109   /// Return complex square root of @a z.
 110   template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
 111   /// Return complex tangent of @a z.
 112   template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
 113   /// Return complex hyperbolic tangent of @a z.
 114   template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
 115
 116
 117   // 26.2.2  Primary template class complex
 118   /**
 119    *  Template to represent complex numbers.
 120    *
 121    *  Specializations for float, double, and long double are part of the
 122    *  library.  Results with any other type are not guaranteed.
 123    *
 124    *  @param  Tp  Type of real and imaginary values.
 125   */
 126   template<typename _Tp>
 127     struct complex
 128     {
 129       /// Value typedef.
 130       typedef _Tp value_type;
 131
 132       ///  Default constructor.  First parameter is x, second parameter is y.
 133       ///  Unspecified parameters default to 0.
 134       complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
 135       : _M_real(__r), _M_imag(__i) { }
 136
 137       // Lets the compiler synthesize the copy constructor
 138       // complex (const complex<_Tp>&);
 139       ///  Copy constructor.
 140       template<typename _Up>
 141         complex(const complex<_Up>& __z)
 142         : _M_real(__z.real()), _M_imag(__z.imag()) { }
 143
 144 #ifdef __GXX_EXPERIMENTAL_CXX0X__
 145       // _GLIBCXX_RESOLVE_LIB_DEFECTS
 146       // DR 387. std::complex over-encapsulated.
 147       _Tp real() const
 148       { return _M_real; }
 149
 150       _Tp imag() const
 151       { return _M_imag; }
 152 #else
 153       ///  Return real part of complex number.
 154       _Tp& real()
 155       { return _M_real; }
 156
 157       ///  Return real part of complex number.
 158       const _Tp& real() const
 159       { return _M_real; }
 160
 161       ///  Return imaginary part of complex number.
 162       _Tp& imag()
 163       { return _M_imag; }
 164
 165       ///  Return imaginary part of complex number.
 166       const _Tp& imag() const
 167       { return _M_imag; }
 168 #endif
 169
 170       // _GLIBCXX_RESOLVE_LIB_DEFECTS
 171       // DR 387. std::complex over-encapsulated.
 172       void real(_Tp __val)
 173       { _M_real = __val; }
 174
 175       void imag(_Tp __val)
 176       { _M_imag = __val; }
 177
 178       /// Assign this complex number to scalar @a t.
 179       complex<_Tp>& operator=(const _Tp&);
 180
 181       /// Add @a t to this complex number.
 182       // 26.2.5/1
 183       complex<_Tp>&
 184       operator+=(const _Tp& __t)
 185       {
 186         _M_real += __t;
 187         return *this;
 188       }
 189
 190       /// Subtract @a t from this complex number.
 191       // 26.2.5/3
 192       complex<_Tp>&
 193       operator-=(const _Tp& __t)
 194       {
 195         _M_real -= __t;
 196         return *this;
 197       }
 198
 199       /// Multiply this complex number by @a t.
 200       complex<_Tp>& operator*=(const _Tp&);
 201       /// Divide this complex number by @a t.
 202       complex<_Tp>& operator/=(const _Tp&);
 203
 204       // Lets the compiler synthesize the
 205       // copy and assignment operator
 206       // complex<_Tp>& operator= (const complex<_Tp>&);
 207       /// Assign this complex number to complex @a z.
 208       template<typename _Up>
 209         complex<_Tp>& operator=(const complex<_Up>&);
 210       /// Add @a z to this complex number.
 211       template<typename _Up>
 212         complex<_Tp>& operator+=(const complex<_Up>&);
 213       /// Subtract @a z from this complex number.
 214       template<typename _Up>
 215         complex<_Tp>& operator-=(const complex<_Up>&);
 216       /// Multiply this complex number by @a z.
 217       template<typename _Up>
 218         complex<_Tp>& operator*=(const complex<_Up>&);
 219       /// Divide this complex number by @a z.
 220       template<typename _Up>
 221         complex<_Tp>& operator/=(const complex<_Up>&);
 222
 223       const complex& __rep() const
 224       { return *this; }
 225
 226     private:
 227       _Tp _M_real;
 228       _Tp _M_imag;
 229     };
 230
 231   template<typename _Tp>
 232     complex<_Tp>&
 233     complex<_Tp>::operator=(const _Tp& __t)
 234     {
 235      _M_real = __t;
 236      _M_imag = _Tp();
 237      return *this;
 238     }
 239
 240   // 26.2.5/5
 241   template<typename _Tp>
 242     complex<_Tp>&
 243     complex<_Tp>::operator*=(const _Tp& __t)
 244     {
 245       _M_real *= __t;
 246       _M_imag *= __t;
 247       return *this;
 248     }
 249
 250   // 26.2.5/7
 251   template<typename _Tp>
 252     complex<_Tp>&
 253     complex<_Tp>::operator/=(const _Tp& __t)
 254     {
 255       _M_real /= __t;
 256       _M_imag /= __t;
 257       return *this;
 258     }
 259
 260   template<typename _Tp>
 261     template<typename _Up>
 262     complex<_Tp>&
 263     complex<_Tp>::operator=(const complex<_Up>& __z)
 264     {
 265       _M_real = __z.real();
 266       _M_imag = __z.imag();
 267       return *this;
 268     }
 269
 270   // 26.2.5/9
 271   template<typename _Tp>
 272     template<typename _Up>
 273     complex<_Tp>&
 274     complex<_Tp>::operator+=(const complex<_Up>& __z)
 275     {
 276       _M_real += __z.real();
 277       _M_imag += __z.imag();
 278       return *this;
 279     }
 280
 281   // 26.2.5/11
 282   template<typename _Tp>
 283     template<typename _Up>
 284     complex<_Tp>&
 285     complex<_Tp>::operator-=(const complex<_Up>& __z)
 286     {
 287       _M_real -= __z.real();
 288       _M_imag -= __z.imag();
 289       return *this;
 290     }
 291
 292   // 26.2.5/13
 293   // XXX: This is a grammar school implementation.
 294   template<typename _Tp>
 295     template<typename _Up>
 296     complex<_Tp>&
 297     complex<_Tp>::operator*=(const complex<_Up>& __z)
 298     {
 299       const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
 300       _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
 301       _M_real = __r;
 302       return *this;
 303     }
 304
 305   // 26.2.5/15
 306   // XXX: This is a grammar school implementation.
 307   template<typename _Tp>
 308     template<typename _Up>
 309     complex<_Tp>&
 310     complex<_Tp>::operator/=(const complex<_Up>& __z)
 311     {
 312       const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
 313       const _Tp __n = std::norm(__z);
 314       _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
 315       _M_real = __r / __n;
 316       return *this;
 317     }
 318
 319   // Operators:
 320   //@{
 321   ///  Return new complex value @a x plus @a y.
 322   template<typename _Tp>
 323     inline complex<_Tp>
 324     operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
 325     {
 326       complex<_Tp> __r = __x;
 327       __r += __y;
 328       return __r;
 329     }
 330
 331   template<typename _Tp>
 332     inline complex<_Tp>
 333     operator+(const complex<_Tp>& __x, const _Tp& __y)
 334     {
 335       complex<_Tp> __r = __x;
 336       __r.real() += __y;
 337       return __r;
 338     }
 339
 340   template<typename _Tp>
 341     inline complex<_Tp>
 342     operator+(const _Tp& __x, const complex<_Tp>& __y)
 343     {
 344       complex<_Tp> __r = __y;
 345       __r.real() += __x;
 346       return __r;
 347     }
 348   //@}
 349
 350   //@{
 351   ///  Return new complex value @a x minus @a y.
 352   template<typename _Tp>
 353     inline complex<_Tp>
 354     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
 355     {
 356       complex<_Tp> __r = __x;
 357       __r -= __y;
 358       return __r;
 359     }
 360
 361   template<typename _Tp>
 362     inline complex<_Tp>
 363     operator-(const complex<_Tp>& __x, const _Tp& __y)
 364     {
 365       complex<_Tp> __r = __x;
 366       __r.real() -= __y;
 367       return __r;
 368     }
 369
 370   template<typename _Tp>
 371     inline complex<_Tp>
 372     operator-(const _Tp& __x, const complex<_Tp>& __y)
 373     {
 374       complex<_Tp> __r(__x, -__y.imag());
 375       __r.real() -= __y.real();
 376       return __r;
 377     }
 378   //@}
 379
 380   //@{
 381   ///  Return new complex value @a x times @a y.
 382   template<typename _Tp>
 383     inline complex<_Tp>
 384     operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
 385     {
 386       complex<_Tp> __r = __x;
 387       __r *= __y;
 388       return __r;
 389     }
 390
 391   template<typename _Tp>
 392     inline complex<_Tp>
 393     operator*(const complex<_Tp>& __x, const _Tp& __y)
 394     {
 395       complex<_Tp> __r = __x;
 396       __r *= __y;
 397       return __r;
 398     }
 399
 400   template<typename _Tp>
 401     inline complex<_Tp>
 402     operator*(const _Tp& __x, const complex<_Tp>& __y)
 403     {
 404       complex<_Tp> __r = __y;
 405       __r *= __x;
 406       return __r;
 407     }
 408   //@}
 409
 410   //@{
 411   ///  Return new complex value @a x divided by @a y.
 412   template<typename _Tp>
 413     inline complex<_Tp>
 414     operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
 415     {
 416       complex<_Tp> __r = __x;
 417       __r /= __y;
 418       return __r;
 419     }
 420
 421   template<typename _Tp>
 422     inline complex<_Tp>
 423     operator/(const complex<_Tp>& __x, const _Tp& __y)
 424     {
 425       complex<_Tp> __r = __x;
 426       __r /= __y;
 427       return __r;
 428     }
 429
 430   template<typename _Tp>
 431     inline complex<_Tp>
 432     operator/(const _Tp& __x, const complex<_Tp>& __y)
 433     {
 434       complex<_Tp> __r = __x;
 435       __r /= __y;
 436       return __r;
 437     }
 438   //@}
 439
 440   ///  Return @a x.
 441   template<typename _Tp>
 442     inline complex<_Tp>
 443     operator+(const complex<_Tp>& __x)
 444     { return __x; }
 445
 446   ///  Return complex negation of @a x.
 447   template<typename _Tp>
 448     inline complex<_Tp>
 449     operator-(const complex<_Tp>& __x)
 450     {  return complex<_Tp>(-__x.real(), -__x.imag()); }
 451
 452   //@{
 453   ///  Return true if @a x is equal to @a y.
 454   template<typename _Tp>
 455     inline bool
 456     operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
 457     { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
 458
 459   template<typename _Tp>
 460     inline bool
 461     operator==(const complex<_Tp>& __x, const _Tp& __y)
 462     { return __x.real() == __y && __x.imag() == _Tp(); }
 463
 464   template<typename _Tp>
 465     inline bool
 466     operator==(const _Tp& __x, const complex<_Tp>& __y)
 467     { return __x == __y.real() && _Tp() == __y.imag(); }
 468   //@}
 469
 470   //@{
 471   ///  Return false if @a x is equal to @a y.
 472   template<typename _Tp>
 473     inline bool
 474     operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
 475     { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
 476
 477   template<typename _Tp>
 478     inline bool
 479     operator!=(const complex<_Tp>& __x, const _Tp& __y)
 480     { return __x.real() != __y || __x.imag() != _Tp(); }
 481
 482   template<typename _Tp>
 483     inline bool
 484     operator!=(const _Tp& __x, const complex<_Tp>& __y)
 485     { return __x != __y.real() || _Tp() != __y.imag(); }
 486   //@}
 487
 488   ///  Extraction operator for complex values.
 489   template<typename _Tp, typename _CharT, class _Traits>
 490     basic_istream<_CharT, _Traits>&
 491     operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
 492     {
 493       _Tp __re_x, __im_x;
 494       _CharT __ch;
 495       __is >> __ch;
 496       if (__ch == '(')
 497         {
 498           __is >> __re_x >> __ch;
 499           if (__ch == ',')
 500             {
 501               __is >> __im_x >> __ch;
 502               if (__ch == ')')
 503                 __x = complex<_Tp>(__re_x, __im_x);
 504               else
 505                 __is.setstate(ios_base::failbit);
 506             }
 507           else if (__ch == ')')
 508             __x = __re_x;
 509           else
 510             __is.setstate(ios_base::failbit);
 511         }
 512       else
 513         {
 514           __is.putback(__ch);
 515           __is >> __re_x;
 516           __x = __re_x;
 517         }
 518       return __is;
 519     }
 520
 521   ///  Insertion operator for complex values.
 522   template<typename _Tp, typename _CharT, class _Traits>
 523     basic_ostream<_CharT, _Traits>&
 524     operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
 525     {
 526       basic_ostringstream<_CharT, _Traits> __s;
 527       __s.flags(__os.flags());
 528       __s.imbue(__os.getloc());
 529       __s.precision(__os.precision());
 530       __s << '(' << __x.real() << ',' << __x.imag() << ')';
 531       return __os << __s.str();
 532     }
 533
 534   // Values
 535 #ifdef __GXX_EXPERIMENTAL_CXX0X__
 536   template<typename _Tp>
 537     inline _Tp
 538     real(const complex<_Tp>& __z)
 539     { return __z.real(); }
 540
 541   template<typename _Tp>
 542     inline _Tp
 543     imag(const complex<_Tp>& __z)
 544     { return __z.imag(); }
 545 #else
 546   template<typename _Tp>
 547     inline _Tp&
 548     real(complex<_Tp>& __z)
 549     { return __z.real(); }
 550
 551   template<typename _Tp>
 552     inline const _Tp&
 553     real(const complex<_Tp>& __z)
 554     { return __z.real(); }
 555
 556   template<typename _Tp>
 557     inline _Tp&
 558     imag(complex<_Tp>& __z)
 559     { return __z.imag(); }
 560
 561   template<typename _Tp>
 562     inline const _Tp&
 563     imag(const complex<_Tp>& __z)
 564     { return __z.imag(); }
 565 #endif
 566
 567   // 26.2.7/3 abs(__z):  Returns the magnitude of __z.
 568   template<typename _Tp>
 569     inline _Tp
 570     __complex_abs(const complex<_Tp>& __z)
 571     {
 572       _Tp __x = __z.real();
 573       _Tp __y = __z.imag();
 574       const _Tp __s = std::max(abs(__x), abs(__y));
 575       if (__s == _Tp())  // well ...
 576         return __s;
 577       __x /= __s;
 578       __y /= __s;
 579       return __s * sqrt(__x * __x + __y * __y);
 580     }
 581
 582 #if _GLIBCXX_USE_C99_COMPLEX
 583   inline float
 584   __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
 585
 586   inline double
 587   __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
 588
 589   inline long double
 590   __complex_abs(const __complex__ long double& __z)
 591   { return __builtin_cabsl(__z); }
 592
 593   template<typename _Tp>
 594     inline _Tp
 595     abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
 596 #else
 597   template<typename _Tp>
 598     inline _Tp
 599     abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
 600 #endif
 601
 602
 603   // 26.2.7/4: arg(__z): Returns the phase angle of __z.
 604   template<typename _Tp>
 605     inline _Tp
 606     __complex_arg(const complex<_Tp>& __z)
 607     { return  atan2(__z.imag(), __z.real()); }
 608
 609 #if _GLIBCXX_USE_C99_COMPLEX
 610   inline float
 611   __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
 612
 613   inline double
 614   __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
 615
 616   inline long double
 617   __complex_arg(const __complex__ long double& __z)
 618   { return __builtin_cargl(__z); }
 619
 620   template<typename _Tp>
 621     inline _Tp
 622     arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
 623 #else
 624   template<typename _Tp>
 625     inline _Tp
 626     arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
 627 #endif
 628
 629   // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
 630   //     As defined, norm() is -not- a norm is the common mathematical
 631   //     sens used in numerics.  The helper class _Norm_helper<> tries to
 632   //     distinguish between builtin floating point and the rest, so as
 633   //     to deliver an answer as close as possible to the real value.
 634   template<bool>
 635     struct _Norm_helper
 636     {
 637       template<typename _Tp>
 638         static inline _Tp _S_do_it(const complex<_Tp>& __z)
 639         {
 640           const _Tp __x = __z.real();
 641           const _Tp __y = __z.imag();
 642           return __x * __x + __y * __y;
 643         }
 644     };
 645
 646   template<>
 647     struct _Norm_helper<true>
 648     {
 649       template<typename _Tp>
 650         static inline _Tp _S_do_it(const complex<_Tp>& __z)
 651         {
 652           _Tp __res = std::abs(__z);
 653           return __res * __res;
 654         }
 655     };
 656
 657   template<typename _Tp>
 658     inline _Tp
 659     norm(const complex<_Tp>& __z)
 660     {
 661       return _Norm_helper<__is_floating<_Tp>::__value
 662         && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
 663     }
 664
 665   template<typename _Tp>
 666     inline complex<_Tp>
 667     polar(const _Tp& __rho, const _Tp& __theta)
 668     { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
 669
 670   template<typename _Tp>
 671     inline complex<_Tp>
 672     conj(const complex<_Tp>& __z)
 673     { return complex<_Tp>(__z.real(), -__z.imag()); }
 674
 675   // Transcendentals
 676
 677   // 26.2.8/1 cos(__z):  Returns the cosine of __z.
 678   template<typename _Tp>
 679     inline complex<_Tp>
 680     __complex_cos(const complex<_Tp>& __z)
 681     {
 682       const _Tp __x = __z.real();
 683       const _Tp __y = __z.imag();
 684       return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
 685     }
 686
 687 #if _GLIBCXX_USE_C99_COMPLEX
 688   inline __complex__ float
 689   __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
 690
 691   inline __complex__ double
 692   __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
 693
 694   inline __complex__ long double
 695   __complex_cos(const __complex__ long double& __z)
 696   { return __builtin_ccosl(__z); }
 697
 698   template<typename _Tp>
 699     inline complex<_Tp>
 700     cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
 701 #else
 702   template<typename _Tp>
 703     inline complex<_Tp>
 704     cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
 705 #endif
 706
 707   // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
 708   template<typename _Tp>
 709     inline complex<_Tp>
 710     __complex_cosh(const complex<_Tp>& __z)
 711     {
 712       const _Tp __x = __z.real();
 713       const _Tp __y = __z.imag();
 714       return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
 715     }
 716
 717 #if _GLIBCXX_USE_C99_COMPLEX
 718   inline __complex__ float
 719   __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
 720
 721   inline __complex__ double
 722   __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
 723
 724   inline __complex__ long double
 725   __complex_cosh(const __complex__ long double& __z)
 726   { return __builtin_ccoshl(__z); }
 727
 728   template<typename _Tp>
 729     inline complex<_Tp>
 730     cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
 731 #else
 732   template<typename _Tp>
 733     inline complex<_Tp>
 734     cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
 735 #endif
 736
 737   // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
 738   template<typename _Tp>
 739     inline complex<_Tp>
 740     __complex_exp(const complex<_Tp>& __z)
 741     { return std::polar(exp(__z.real()), __z.imag()); }
 742
 743 #if _GLIBCXX_USE_C99_COMPLEX
 744   inline __complex__ float
 745   __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
 746
 747   inline __complex__ double
 748   __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
 749
 750   inline __complex__ long double
 751   __complex_exp(const __complex__ long double& __z)
 752   { return __builtin_cexpl(__z); }
 753
 754   template<typename _Tp>
 755     inline complex<_Tp>
 756     exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
 757 #else
 758   template<typename _Tp>
 759     inline complex<_Tp>
 760     exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
 761 #endif
 762
 763   // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
 764   //                    The branch cut is along the negative axis.
 765   template<typename _Tp>
 766     inline complex<_Tp>
 767     __complex_log(const complex<_Tp>& __z)
 768     { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
 769
 770 #if _GLIBCXX_USE_C99_COMPLEX
 771   inline __complex__ float
 772   __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
 773
 774   inline __complex__ double
 775   __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
 776
 777   inline __complex__ long double
 778   __complex_log(const __complex__ long double& __z)
 779   { return __builtin_clogl(__z); }
 780
 781   template<typename _Tp>
 782     inline complex<_Tp>
 783     log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
 784 #else
 785   template<typename _Tp>
 786     inline complex<_Tp>
 787     log(const complex<_Tp>& __z) { return __complex_log(__z); }
 788 #endif
 789
 790   template<typename _Tp>
 791     inline complex<_Tp>
 792     log10(const complex<_Tp>& __z)
 793     { return std::log(__z) / log(_Tp(10.0)); }
 794
 795   // 26.2.8/10 sin(__z): Returns the sine of __z.
 796   template<typename _Tp>
 797     inline complex<_Tp>
 798     __complex_sin(const complex<_Tp>& __z)
 799     {
 800       const _Tp __x = __z.real();
 801       const _Tp __y = __z.imag();
 802       return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
 803     }
 804
 805 #if _GLIBCXX_USE_C99_COMPLEX
 806   inline __complex__ float
 807   __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
 808
 809   inline __complex__ double
 810   __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
 811
 812   inline __complex__ long double
 813   __complex_sin(const __complex__ long double& __z)
 814   { return __builtin_csinl(__z); }
 815
 816   template<typename _Tp>
 817     inline complex<_Tp>
 818     sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
 819 #else
 820   template<typename _Tp>
 821     inline complex<_Tp>
 822     sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
 823 #endif
 824
 825   // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
 826   template<typename _Tp>
 827     inline complex<_Tp>
 828     __complex_sinh(const complex<_Tp>& __z)
 829     {
 830       const _Tp __x = __z.real();
 831       const _Tp  __y = __z.imag();
 832       return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
 833     }
 834
 835 #if _GLIBCXX_USE_C99_COMPLEX
 836   inline __complex__ float
 837   __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
 838
 839   inline __complex__ double
 840   __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
 841
 842   inline __complex__ long double
 843   __complex_sinh(const __complex__ long double& __z)
 844   { return __builtin_csinhl(__z); }
 845
 846   template<typename _Tp>
 847     inline complex<_Tp>
 848     sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
 849 #else
 850   template<typename _Tp>
 851     inline complex<_Tp>
 852     sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
 853 #endif
 854
 855   // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
 856   //                     The branch cut is on the negative axis.
 857   template<typename _Tp>
 858     complex<_Tp>
 859     __complex_sqrt(const complex<_Tp>& __z)
 860     {
 861       _Tp __x = __z.real();
 862       _Tp __y = __z.imag();
 863
 864       if (__x == _Tp())
 865         {
 866           _Tp __t = sqrt(abs(__y) / 2);
 867           return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
 868         }
 869       else
 870         {
 871           _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
 872           _Tp __u = __t / 2;
 873           return __x > _Tp()
 874             ? complex<_Tp>(__u, __y / __t)
 875             : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
 876         }
 877     }
 878
 879 #if _GLIBCXX_USE_C99_COMPLEX
 880   inline __complex__ float
 881   __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
 882
 883   inline __complex__ double
 884   __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
 885
 886   inline __complex__ long double
 887   __complex_sqrt(const __complex__ long double& __z)
 888   { return __builtin_csqrtl(__z); }
 889
 890   template<typename _Tp>
 891     inline complex<_Tp>
 892     sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
 893 #else
 894   template<typename _Tp>
 895     inline complex<_Tp>
 896     sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
 897 #endif
 898
 899   // 26.2.8/14 tan(__z):  Return the complex tangent of __z.
 900
 901   template<typename _Tp>
 902     inline complex<_Tp>
 903     __complex_tan(const complex<_Tp>& __z)
 904     { return std::sin(__z) / std::cos(__z); }
 905
 906 #if _GLIBCXX_USE_C99_COMPLEX
 907   inline __complex__ float
 908   __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
 909
 910   inline __complex__ double
 911   __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
 912
 913   inline __complex__ long double
 914   __complex_tan(const __complex__ long double& __z)
 915   { return __builtin_ctanl(__z); }
 916
 917   template<typename _Tp>
 918     inline complex<_Tp>
 919     tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
 920 #else
 921   template<typename _Tp>
 922     inline complex<_Tp>
 923     tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
 924 #endif
 925
 926
 927   // 26.2.8/15 tanh(__z):  Returns the hyperbolic tangent of __z.
 928
 929   template<typename _Tp>
 930     inline complex<_Tp>
 931     __complex_tanh(const complex<_Tp>& __z)
 932     { return std::sinh(__z) / std::cosh(__z); }
 933
 934 #if _GLIBCXX_USE_C99_COMPLEX
 935   inline __complex__ float
 936   __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
 937
 938   inline __complex__ double
 939   __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
 940
 941   inline __complex__ long double
 942   __complex_tanh(const __complex__ long double& __z)
 943   { return __builtin_ctanhl(__z); }
 944
 945   template<typename _Tp>
 946     inline complex<_Tp>
 947     tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
 948 #else
 949   template<typename _Tp>
 950     inline complex<_Tp>
 951     tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
 952 #endif
 953
 954
 955   // 26.2.8/9  pow(__x, __y): Returns the complex power base of __x
 956   //                          raised to the __y-th power.  The branch
 957   //                          cut is on the negative axis.
 958 #ifndef __GXX_EXPERIMENTAL_CXX0X__
 959   // _GLIBCXX_RESOLVE_LIB_DEFECTS
 960   // DR 844. complex pow return type is ambiguous.
 961   template<typename _Tp>
 962     inline complex<_Tp>
 963     pow(const complex<_Tp>& __z, int __n)
 964     { return std::__pow_helper(__z, __n); }
 965 #endif
 966
 967   template<typename _Tp>
 968     complex<_Tp>
 969     pow(const complex<_Tp>& __x, const _Tp& __y)
 970     {
 971 #ifndef _GLIBCXX_USE_C99_COMPLEX
 972       if (__x == _Tp())
 973         return _Tp();
 974 #endif
 975       if (__x.imag() == _Tp() && __x.real() > _Tp())
 976         return pow(__x.real(), __y);
 977
 978       complex<_Tp> __t = std::log(__x);
 979       return std::polar(exp(__y * __t.real()), __y * __t.imag());
 980     }
 981
 982   template<typename _Tp>
 983     inline complex<_Tp>
 984     __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
 985     { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
 986
 987 #if _GLIBCXX_USE_C99_COMPLEX
 988   inline __complex__ float
 989   __complex_pow(__complex__ float __x, __complex__ float __y)
 990   { return __builtin_cpowf(__x, __y); }
 991
 992   inline __complex__ double
 993   __complex_pow(__complex__ double __x, __complex__ double __y)
 994   { return __builtin_cpow(__x, __y); }
 995
 996   inline __complex__ long double
 997   __complex_pow(const __complex__ long double& __x,
 998                 const __complex__ long double& __y)
 999   { return __builtin_cpowl(__x, __y); }
1000
1001   template<typename _Tp>
1002     inline complex<_Tp>
1003     pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1004     { return __complex_pow(__x.__rep(), __y.__rep()); }
1005 #else
1006   template<typename _Tp>
1007     inline complex<_Tp>
1008     pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
1009     { return __complex_pow(__x, __y); }
1010 #endif
1011
1012   template<typename _Tp>
1013     inline complex<_Tp>
1014     pow(const _Tp& __x, const complex<_Tp>& __y)
1015     {
1016       return __x > _Tp() ? std::polar(pow(__x, __y.real()),
1017                                       __y.imag() * log(__x))
1018                          : std::pow(complex<_Tp>(__x), __y);
1019     }
1020
1021   // 26.2.3  complex specializations
1022   // complex<float> specialization
1023   template<>
1024     struct complex<float>
1025     {
1026       typedef float value_type;
1027       typedef __complex__ float _ComplexT;
1028
1029       complex(_ComplexT __z) : _M_value(__z) { }
1030
1031       complex(float __r = 0.0f, float __i = 0.0f)
1032       {
1033         __real__ _M_value = __r;
1034         __imag__ _M_value = __i;
1035       }
1036
1037       explicit complex(const complex<double>&);
1038       explicit complex(const complex<long double>&);
1039
1040 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1041       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1042       // DR 387. std::complex over-encapsulated.
1043       float real() const
1044       { return __real__ _M_value; }
1045
1046       float imag() const
1047       { return __imag__ _M_value; }
1048 #else
1049       float& real()
1050       { return __real__ _M_value; }
1051
1052       const float& real() const
1053       { return __real__ _M_value; }
1054
1055       float& imag()
1056       { return __imag__ _M_value; }
1057
1058       const float& imag() const
1059       { return __imag__ _M_value; }
1060 #endif
1061
1062       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1063       // DR 387. std::complex over-encapsulated.
1064       void real(float __val)
1065       { __real__ _M_value = __val; }
1066
1067       void imag(float __val)
1068       { __imag__ _M_value = __val; }
1069
1070       complex<float>&
1071       operator=(float __f)
1072       {
1073         __real__ _M_value = __f;
1074         __imag__ _M_value = 0.0f;
1075         return *this;
1076       }
1077
1078       complex<float>&
1079       operator+=(float __f)
1080       {
1081         __real__ _M_value += __f;
1082         return *this;
1083       }
1084
1085       complex<float>&
1086       operator-=(float __f)
1087       {
1088         __real__ _M_value -= __f;
1089         return *this;
1090       }
1091
1092       complex<float>&
1093       operator*=(float __f)
1094       {
1095         _M_value *= __f;
1096         return *this;
1097       }
1098
1099       complex<float>&
1100       operator/=(float __f)
1101       {
1102         _M_value /= __f;
1103         return *this;
1104       }
1105
1106       // Let the compiler synthesize the copy and assignment
1107       // operator.  It always does a pretty good job.
1108       // complex& operator=(const complex&);
1109
1110       template<typename _Tp>
1111         complex<float>&
1112         operator=(const complex<_Tp>&  __z)
1113         {
1114           __real__ _M_value = __z.real();
1115           __imag__ _M_value = __z.imag();
1116           return *this;
1117         }
1118
1119       template<typename _Tp>
1120         complex<float>&
1121         operator+=(const complex<_Tp>& __z)
1122         {
1123           __real__ _M_value += __z.real();
1124           __imag__ _M_value += __z.imag();
1125           return *this;
1126         }
1127
1128       template<class _Tp>
1129         complex<float>&
1130         operator-=(const complex<_Tp>& __z)
1131         {
1132           __real__ _M_value -= __z.real();
1133           __imag__ _M_value -= __z.imag();
1134           return *this;
1135         }
1136
1137       template<class _Tp>
1138         complex<float>&
1139         operator*=(const complex<_Tp>& __z)
1140         {
1141           _ComplexT __t;
1142           __real__ __t = __z.real();
1143           __imag__ __t = __z.imag();
1144           _M_value *= __t;
1145           return *this;
1146         }
1147
1148       template<class _Tp>
1149         complex<float>&
1150         operator/=(const complex<_Tp>& __z)
1151         {
1152           _ComplexT __t;
1153           __real__ __t = __z.real();
1154           __imag__ __t = __z.imag();
1155           _M_value /= __t;
1156           return *this;
1157         }
1158
1159       const _ComplexT& __rep() const { return _M_value; }
1160
1161     private:
1162       _ComplexT _M_value;
1163     };
1164
1165   // 26.2.3  complex specializations
1166   // complex<double> specialization
1167   template<>
1168     struct complex<double>
1169     {
1170       typedef double value_type;
1171       typedef __complex__ double _ComplexT;
1172
1173       complex(_ComplexT __z) : _M_value(__z) { }
1174
1175       complex(double __r = 0.0, double __i = 0.0)
1176       {
1177         __real__ _M_value = __r;
1178         __imag__ _M_value = __i;
1179       }
1180
1181       complex(const complex<float>& __z)
1182       : _M_value(__z.__rep()) { }
1183
1184       explicit complex(const complex<long double>&);
1185
1186 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1187       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1188       // DR 387. std::complex over-encapsulated.
1189       double real() const
1190       { return __real__ _M_value; }
1191
1192       double imag() const
1193       { return __imag__ _M_value; }
1194 #else
1195       double& real()
1196       { return __real__ _M_value; }
1197
1198       const double& real() const
1199       { return __real__ _M_value; }
1200
1201       double& imag()
1202       { return __imag__ _M_value; }
1203
1204       const double& imag() const
1205       { return __imag__ _M_value; }
1206 #endif
1207
1208       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1209       // DR 387. std::complex over-encapsulated.
1210       void real(double __val)
1211       { __real__ _M_value = __val; }
1212
1213       void imag(double __val)
1214       { __imag__ _M_value = __val; }
1215
1216       complex<double>&
1217       operator=(double __d)
1218       {
1219         __real__ _M_value = __d;
1220         __imag__ _M_value = 0.0;
1221         return *this;
1222       }
1223
1224       complex<double>&
1225       operator+=(double __d)
1226       {
1227         __real__ _M_value += __d;
1228         return *this;
1229       }
1230
1231       complex<double>&
1232       operator-=(double __d)
1233       {
1234         __real__ _M_value -= __d;
1235         return *this;
1236       }
1237
1238       complex<double>&
1239       operator*=(double __d)
1240       {
1241         _M_value *= __d;
1242         return *this;
1243       }
1244
1245       complex<double>&
1246       operator/=(double __d)
1247       {
1248         _M_value /= __d;
1249         return *this;
1250       }
1251
1252       // The compiler will synthesize this, efficiently.
1253       // complex& operator=(const complex&);
1254
1255       template<typename _Tp>
1256         complex<double>&
1257         operator=(const complex<_Tp>& __z)
1258         {
1259           __real__ _M_value = __z.real();
1260           __imag__ _M_value = __z.imag();
1261           return *this;
1262         }
1263
1264       template<typename _Tp>
1265         complex<double>&
1266         operator+=(const complex<_Tp>& __z)
1267         {
1268           __real__ _M_value += __z.real();
1269           __imag__ _M_value += __z.imag();
1270           return *this;
1271         }
1272
1273       template<typename _Tp>
1274         complex<double>&
1275         operator-=(const complex<_Tp>& __z)
1276         {
1277           __real__ _M_value -= __z.real();
1278           __imag__ _M_value -= __z.imag();
1279           return *this;
1280         }
1281
1282       template<typename _Tp>
1283         complex<double>&
1284         operator*=(const complex<_Tp>& __z)
1285         {
1286           _ComplexT __t;
1287           __real__ __t = __z.real();
1288           __imag__ __t = __z.imag();
1289           _M_value *= __t;
1290           return *this;
1291         }
1292
1293       template<typename _Tp>
1294         complex<double>&
1295         operator/=(const complex<_Tp>& __z)
1296         {
1297           _ComplexT __t;
1298           __real__ __t = __z.real();
1299           __imag__ __t = __z.imag();
1300           _M_value /= __t;
1301           return *this;
1302         }
1303
1304       const _ComplexT& __rep() const { return _M_value; }
1305
1306     private:
1307       _ComplexT _M_value;
1308     };
1309
1310   // 26.2.3  complex specializations
1311   // complex<long double> specialization
1312   template<>
1313     struct complex<long double>
1314     {
1315       typedef long double value_type;
1316       typedef __complex__ long double _ComplexT;
1317
1318       complex(_ComplexT __z) : _M_value(__z) { }
1319
1320       complex(long double __r = 0.0L, long double __i = 0.0L)
1321       {
1322         __real__ _M_value = __r;
1323         __imag__ _M_value = __i;
1324       }
1325
1326       complex(const complex<float>& __z)
1327       : _M_value(__z.__rep()) { }
1328
1329       complex(const complex<double>& __z)
1330       : _M_value(__z.__rep()) { }
1331
1332 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1333       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1334       // DR 387. std::complex over-encapsulated.
1335       long double real() const
1336       { return __real__ _M_value; }
1337
1338       long double imag() const
1339       { return __imag__ _M_value; }
1340 #else
1341       long double& real()
1342       { return __real__ _M_value; }
1343
1344       const long double& real() const
1345       { return __real__ _M_value; }
1346
1347       long double& imag()
1348       { return __imag__ _M_value; }
1349
1350       const long double& imag() const
1351       { return __imag__ _M_value; }
1352 #endif
1353
1354       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1355       // DR 387. std::complex over-encapsulated.
1356       void real(long double __val)
1357       { __real__ _M_value = __val; }
1358
1359       void imag(long double __val)
1360       { __imag__ _M_value = __val; }
1361
1362       complex<long double>&
1363       operator=(long double __r)
1364       {
1365         __real__ _M_value = __r;
1366         __imag__ _M_value = 0.0L;
1367         return *this;
1368       }
1369
1370       complex<long double>&
1371       operator+=(long double __r)
1372       {
1373         __real__ _M_value += __r;
1374         return *this;
1375       }
1376
1377       complex<long double>&
1378       operator-=(long double __r)
1379       {
1380         __real__ _M_value -= __r;
1381         return *this;
1382       }
1383
1384       complex<long double>&
1385       operator*=(long double __r)
1386       {
1387         _M_value *= __r;
1388         return *this;
1389       }
1390
1391       complex<long double>&
1392       operator/=(long double __r)
1393       {
1394         _M_value /= __r;
1395         return *this;
1396       }
1397
1398       // The compiler knows how to do this efficiently
1399       // complex& operator=(const complex&);
1400
1401       template<typename _Tp>
1402         complex<long double>&
1403         operator=(const complex<_Tp>& __z)
1404         {
1405           __real__ _M_value = __z.real();
1406           __imag__ _M_value = __z.imag();
1407           return *this;
1408         }
1409
1410       template<typename _Tp>
1411         complex<long double>&
1412         operator+=(const complex<_Tp>& __z)
1413         {
1414           __real__ _M_value += __z.real();
1415           __imag__ _M_value += __z.imag();
1416           return *this;
1417         }
1418
1419       template<typename _Tp>
1420         complex<long double>&
1421         operator-=(const complex<_Tp>& __z)
1422         {
1423           __real__ _M_value -= __z.real();
1424           __imag__ _M_value -= __z.imag();
1425           return *this;
1426         }
1427
1428       template<typename _Tp>
1429         complex<long double>&
1430         operator*=(const complex<_Tp>& __z)
1431         {
1432           _ComplexT __t;
1433           __real__ __t = __z.real();
1434           __imag__ __t = __z.imag();
1435           _M_value *= __t;
1436           return *this;
1437         }
1438
1439       template<typename _Tp>
1440         complex<long double>&
1441         operator/=(const complex<_Tp>& __z)
1442         {
1443           _ComplexT __t;
1444           __real__ __t = __z.real();
1445           __imag__ __t = __z.imag();
1446           _M_value /= __t;
1447           return *this;
1448         }
1449
1450       const _ComplexT& __rep() const { return _M_value; }
1451
1452     private:
1453       _ComplexT _M_value;
1454     };
1455
1456   // These bits have to be at the end of this file, so that the
1457   // specializations have all been defined.
1458   inline
1459   complex<float>::complex(const complex<double>& __z)
1460   : _M_value(__z.__rep()) { }
1461
1462   inline
1463   complex<float>::complex(const complex<long double>& __z)
1464   : _M_value(__z.__rep()) { }
1465
1466   inline
1467   complex<double>::complex(const complex<long double>& __z)
1468   : _M_value(__z.__rep()) { }
1469
1470   // Inhibit implicit instantiations for required instantiations,
1471   // which are defined via explicit instantiations elsewhere.
1472   // NB:  This syntax is a GNU extension.
1473 #if _GLIBCXX_EXTERN_TEMPLATE
1474   extern template istream& operator>>(istream&, complex<float>&);
1475   extern template ostream& operator<<(ostream&, const complex<float>&);
1476   extern template istream& operator>>(istream&, complex<double>&);
1477   extern template ostream& operator<<(ostream&, const complex<double>&);
1478   extern template istream& operator>>(istream&, complex<long double>&);
1479   extern template ostream& operator<<(ostream&, const complex<long double>&);
1480
1481 #ifdef _GLIBCXX_USE_WCHAR_T
1482   extern template wistream& operator>>(wistream&, complex<float>&);
1483   extern template wostream& operator<<(wostream&, const complex<float>&);
1484   extern template wistream& operator>>(wistream&, complex<double>&);
1485   extern template wostream& operator<<(wostream&, const complex<double>&);
1486   extern template wistream& operator>>(wistream&, complex<long double>&);
1487   extern template wostream& operator<<(wostream&, const complex<long double>&);
1488 #endif
1489 #endif
1490
1491   // @} group complex_numbers
1492
1493 _GLIBCXX_END_NAMESPACE
1494
1495 _GLIBCXX_BEGIN_NAMESPACE(__gnu_cxx)
1496
1497   // See ext/type_traits.h for the primary template.
1498   template<typename _Tp, typename _Up>
1499     struct __promote_2<std::complex<_Tp>, _Up>
1500     {
1501     public:
1502       typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1503     };
1504
1505   template<typename _Tp, typename _Up>
1506     struct __promote_2<_Tp, std::complex<_Up> >
1507     {
1508     public:
1509       typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1510     };
1511
1512   template<typename _Tp, typename _Up>
1513     struct __promote_2<std::complex<_Tp>, std::complex<_Up> >
1514     {
1515     public:
1516       typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1517     };
1518
1519 _GLIBCXX_END_NAMESPACE
1520
1521 #ifdef __GXX_EXPERIMENTAL_CXX0X__
1522 #  if defined(_GLIBCXX_INCLUDE_AS_TR1)
1523 #    error C++0x header cannot be included from TR1 header
1524 #  endif
1525 #  if defined(_GLIBCXX_INCLUDE_AS_CXX0X)
1526 #    include <tr1_impl/complex>
1527 #  else
1528 #    define _GLIBCXX_INCLUDE_AS_CXX0X
1529 #    define _GLIBCXX_BEGIN_NAMESPACE_TR1
1530 #    define _GLIBCXX_END_NAMESPACE_TR1
1531 #    define _GLIBCXX_TR1
1532 #    include <tr1_impl/complex>
1533 #    undef _GLIBCXX_TR1
1534 #    undef _GLIBCXX_END_NAMESPACE_TR1
1535 #    undef _GLIBCXX_BEGIN_NAMESPACE_TR1
1536 #    undef _GLIBCXX_INCLUDE_AS_CXX0X
1537 #  endif
1538
1539 _GLIBCXX_BEGIN_NAMESPACE(std)
1540
1541   // Forward declarations.
1542   // DR 781.
1543   template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
1544
1545   template<typename _Tp>
1546     std::complex<_Tp>
1547     __complex_proj(const std::complex<_Tp>& __z)
1548     {
1549       const _Tp __den = (__z.real() * __z.real()
1550                          + __z.imag() * __z.imag() + _Tp(1.0));
1551
1552       return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
1553                                (_Tp(2.0) * __z.imag()) / __den);
1554     }
1555
1556 #if _GLIBCXX_USE_C99_COMPLEX
1557   inline __complex__ float
1558   __complex_proj(__complex__ float __z)
1559   { return __builtin_cprojf(__z); }
1560
1561   inline __complex__ double
1562   __complex_proj(__complex__ double __z)
1563   { return __builtin_cproj(__z); }
1564
1565   inline __complex__ long double
1566   __complex_proj(const __complex__ long double& __z)
1567   { return __builtin_cprojl(__z); }
1568
1569   template<typename _Tp>
1570     inline std::complex<_Tp>
1571     proj(const std::complex<_Tp>& __z)
1572     { return __complex_proj(__z.__rep()); }
1573 #else
1574   template<typename _Tp>
1575     inline std::complex<_Tp>
1576     proj(const std::complex<_Tp>& __z)
1577     { return __complex_proj(__z); }
1578 #endif
1579
1580   template<typename _Tp>
1581     inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
1582     proj(_Tp __x)
1583     {
1584       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1585       return std::proj(std::complex<__type>(__x));
1586     }
1587
1588 _GLIBCXX_END_NAMESPACE
1589
1590 #endif
1591
1592 #endif  /* _GLIBCXX_COMPLEX */