libstdc++-v3/include/std/complex

   1 // The template and inlines for the -*- C++ -*- complex number classes.
   2
   3 // Copyright (C) 1997-2013 Free Software Foundation, Inc.
   4 //
   5 // This file is part of the GNU ISO C++ Library.  This library is free
   6 // software; you can redistribute it and/or modify it under the
   7 // terms of the GNU General Public License as published by the
   8 // Free Software Foundation; either version 3, or (at your option)
   9 // any later version.
  10
  11 // This library is distributed in the hope that it will be useful,
  12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14 // GNU General Public License for more details.
  15
  16 // Under Section 7 of GPL version 3, you are granted additional
  17 // permissions described in the GCC Runtime Library Exception, version
  18 // 3.1, as published by the Free Software Foundation.
  19
  20 // You should have received a copy of the GNU General Public License and
  21 // a copy of the GCC Runtime Library Exception along with this program;
  22 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  23 // <http://www.gnu.org/licenses/>.
  24
  25 /** @file include/complex
  26  *  This is a Standard C++ Library header.
  27  */
  28
  29 //
  30 // ISO C++ 14882: 26.2  Complex Numbers
  31 // Note: this is not a conforming implementation.
  32 // Initially implemented by Ulrich Drepper <drepper@cygnus.com>
  33 // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
  34 //
  35
  36 #ifndef _GLIBCXX_COMPLEX
  37 #define _GLIBCXX_COMPLEX 1
  38
  39 #pragma GCC system_header
  40
  41 #include <bits/c++config.h>
  42 #include <bits/cpp_type_traits.h>
  43 #include <ext/type_traits.h>
  44 #include <cmath>
  45 #include <sstream>
  46
  47 namespace std _GLIBCXX_VISIBILITY(default)
  48 {
  49 _GLIBCXX_BEGIN_NAMESPACE_VERSION
  50
  51   /**
  52    * @defgroup complex_numbers Complex Numbers
  53    * @ingroup numerics
  54    *
  55    * Classes and functions for complex numbers.
  56    * @{
  57    */
  58
  59   // Forward declarations.
  60   template<typename _Tp> class complex;
  61   template<> class complex<float>;
  62   template<> class complex<double>;
  63   template<> class complex<long double>;
  64
  65   ///  Return magnitude of @a z.
  66   template<typename _Tp> _Tp abs(const complex<_Tp>&);
  67   ///  Return phase angle of @a z.
  68   template<typename _Tp> _Tp arg(const complex<_Tp>&);
  69   ///  Return @a z magnitude squared.
  70   template<typename _Tp> _Tp norm(const complex<_Tp>&);
  71
  72   ///  Return complex conjugate of @a z.
  73   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
  74   ///  Return complex with magnitude @a rho and angle @a theta.
  75   template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
  76
  77   // Transcendentals:
  78   /// Return complex cosine of @a z.
  79   template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
  80   /// Return complex hyperbolic cosine of @a z.
  81   template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
  82   /// Return complex base e exponential of @a z.
  83   template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
  84   /// Return complex natural logarithm of @a z.
  85   template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
  86   /// Return complex base 10 logarithm of @a z.
  87   template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
  88 #if __cplusplus < 201103L
  89   // DR 844.
  90   /// Return @a x to the @a y'th power.
  91   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
  92 #endif
  93   /// Return @a x to the @a y'th power.
  94   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
  95   /// Return @a x to the @a y'th power.
  96   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
  97                                           const complex<_Tp>&);
  98   /// Return @a x to the @a y'th power.
  99   template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
 100   /// Return complex sine of @a z.
 101   template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
 102   /// Return complex hyperbolic sine of @a z.
 103   template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
 104   /// Return complex square root of @a z.
 105   template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
 106   /// Return complex tangent of @a z.
 107   template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
 108   /// Return complex hyperbolic tangent of @a z.
 109   template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
 110
 111
 112   // 26.2.2  Primary template class complex
 113   /**
 114    *  Template to represent complex numbers.
 115    *
 116    *  Specializations for float, double, and long double are part of the
 117    *  library.  Results with any other type are not guaranteed.
 118    *
 119    *  @param  Tp  Type of real and imaginary values.
 120   */
 121   template<typename _Tp>
 122     struct complex
 123     {
 124       /// Value typedef.
 125       typedef _Tp value_type;
 126
 127       ///  Default constructor.  First parameter is x, second parameter is y.
 128       ///  Unspecified parameters default to 0.
 129       _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
 130       : _M_real(__r), _M_imag(__i) { }
 131
 132       // Lets the compiler synthesize the copy constructor
 133       // complex (const complex<_Tp>&);
 134       ///  Copy constructor.
 135       template<typename _Up>
 136         _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
 137         : _M_real(__z.real()), _M_imag(__z.imag()) { }
 138
 139 #if __cplusplus >= 201103L
 140       // _GLIBCXX_RESOLVE_LIB_DEFECTS
 141       // DR 387. std::complex over-encapsulated.
 142       __attribute ((__abi_tag__ ("cxx11")))
 143       constexpr _Tp
 144       real() { return _M_real; }
 145
 146       __attribute ((__abi_tag__ ("cxx11")))
 147       constexpr _Tp
 148       imag() { return _M_imag; }
 149 #else
 150       ///  Return real part of complex number.
 151       _Tp&
 152       real() { return _M_real; }
 153
 154       ///  Return real part of complex number.
 155       const _Tp&
 156       real() const { return _M_real; }
 157
 158       ///  Return imaginary part of complex number.
 159       _Tp&
 160       imag() { return _M_imag; }
 161
 162       ///  Return imaginary part of complex number.
 163       const _Tp&
 164       imag() const { return _M_imag; }
 165 #endif
 166
 167       // _GLIBCXX_RESOLVE_LIB_DEFECTS
 168       // DR 387. std::complex over-encapsulated.
 169       void
 170       real(_Tp __val) { _M_real = __val; }
 171
 172       void
 173       imag(_Tp __val) { _M_imag = __val; }
 174
 175       /// Assign this complex number to scalar @a t.
 176       complex<_Tp>& operator=(const _Tp&);
 177
 178       /// Add @a t to this complex number.
 179       // 26.2.5/1
 180       complex<_Tp>&
 181       operator+=(const _Tp& __t)
 182       {
 183         _M_real += __t;
 184         return *this;
 185       }
 186
 187       /// Subtract @a t from this complex number.
 188       // 26.2.5/3
 189       complex<_Tp>&
 190       operator-=(const _Tp& __t)
 191       {
 192         _M_real -= __t;
 193         return *this;
 194       }
 195
 196       /// Multiply this complex number by @a t.
 197       complex<_Tp>& operator*=(const _Tp&);
 198       /// Divide this complex number by @a t.
 199       complex<_Tp>& operator/=(const _Tp&);
 200
 201       // Lets the compiler synthesize the
 202       // copy and assignment operator
 203       // complex<_Tp>& operator= (const complex<_Tp>&);
 204       /// Assign this complex number to complex @a z.
 205       template<typename _Up>
 206         complex<_Tp>& operator=(const complex<_Up>&);
 207       /// Add @a z to this complex number.
 208       template<typename _Up>
 209         complex<_Tp>& operator+=(const complex<_Up>&);
 210       /// Subtract @a z from this complex number.
 211       template<typename _Up>
 212         complex<_Tp>& operator-=(const complex<_Up>&);
 213       /// Multiply this complex number by @a z.
 214       template<typename _Up>
 215         complex<_Tp>& operator*=(const complex<_Up>&);
 216       /// Divide this complex number by @a z.
 217       template<typename _Up>
 218         complex<_Tp>& operator/=(const complex<_Up>&);
 219
 220       _GLIBCXX_USE_CONSTEXPR complex __rep() const
 221       { return *this; }
 222
 223     private:
 224       _Tp _M_real;
 225       _Tp _M_imag;
 226     };
 227
 228   template<typename _Tp>
 229     complex<_Tp>&
 230     complex<_Tp>::operator=(const _Tp& __t)
 231     {
 232      _M_real = __t;
 233      _M_imag = _Tp();
 234      return *this;
 235     }
 236
 237   // 26.2.5/5
 238   template<typename _Tp>
 239     complex<_Tp>&
 240     complex<_Tp>::operator*=(const _Tp& __t)
 241     {
 242       _M_real *= __t;
 243       _M_imag *= __t;
 244       return *this;
 245     }
 246
 247   // 26.2.5/7
 248   template<typename _Tp>
 249     complex<_Tp>&
 250     complex<_Tp>::operator/=(const _Tp& __t)
 251     {
 252       _M_real /= __t;
 253       _M_imag /= __t;
 254       return *this;
 255     }
 256
 257   template<typename _Tp>
 258     template<typename _Up>
 259     complex<_Tp>&
 260     complex<_Tp>::operator=(const complex<_Up>& __z)
 261     {
 262       _M_real = __z.real();
 263       _M_imag = __z.imag();
 264       return *this;
 265     }
 266
 267   // 26.2.5/9
 268   template<typename _Tp>
 269     template<typename _Up>
 270     complex<_Tp>&
 271     complex<_Tp>::operator+=(const complex<_Up>& __z)
 272     {
 273       _M_real += __z.real();
 274       _M_imag += __z.imag();
 275       return *this;
 276     }
 277
 278   // 26.2.5/11
 279   template<typename _Tp>
 280     template<typename _Up>
 281     complex<_Tp>&
 282     complex<_Tp>::operator-=(const complex<_Up>& __z)
 283     {
 284       _M_real -= __z.real();
 285       _M_imag -= __z.imag();
 286       return *this;
 287     }
 288
 289   // 26.2.5/13
 290   // XXX: This is a grammar school implementation.
 291   template<typename _Tp>
 292     template<typename _Up>
 293     complex<_Tp>&
 294     complex<_Tp>::operator*=(const complex<_Up>& __z)
 295     {
 296       const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
 297       _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
 298       _M_real = __r;
 299       return *this;
 300     }
 301
 302   // 26.2.5/15
 303   // XXX: This is a grammar school implementation.
 304   template<typename _Tp>
 305     template<typename _Up>
 306     complex<_Tp>&
 307     complex<_Tp>::operator/=(const complex<_Up>& __z)
 308     {
 309       const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
 310       const _Tp __n = std::norm(__z);
 311       _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
 312       _M_real = __r / __n;
 313       return *this;
 314     }
 315
 316   // Operators:
 317   //@{
 318   ///  Return new complex value @a x plus @a y.
 319   template<typename _Tp>
 320     inline complex<_Tp>
 321     operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
 322     {
 323       complex<_Tp> __r = __x;
 324       __r += __y;
 325       return __r;
 326     }
 327
 328   template<typename _Tp>
 329     inline complex<_Tp>
 330     operator+(const complex<_Tp>& __x, const _Tp& __y)
 331     {
 332       complex<_Tp> __r = __x;
 333       __r += __y;
 334       return __r;
 335     }
 336
 337   template<typename _Tp>
 338     inline complex<_Tp>
 339     operator+(const _Tp& __x, const complex<_Tp>& __y)
 340     {
 341       complex<_Tp> __r = __y;
 342       __r += __x;
 343       return __r;
 344     }
 345   //@}
 346
 347   //@{
 348   ///  Return new complex value @a x minus @a y.
 349   template<typename _Tp>
 350     inline complex<_Tp>
 351     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
 352     {
 353       complex<_Tp> __r = __x;
 354       __r -= __y;
 355       return __r;
 356     }
 357
 358   template<typename _Tp>
 359     inline complex<_Tp>
 360     operator-(const complex<_Tp>& __x, const _Tp& __y)
 361     {
 362       complex<_Tp> __r = __x;
 363       __r -= __y;
 364       return __r;
 365     }
 366
 367   template<typename _Tp>
 368     inline complex<_Tp>
 369     operator-(const _Tp& __x, const complex<_Tp>& __y)
 370     {
 371       complex<_Tp> __r(__x, -__y.imag());
 372       __r -= __y.real();
 373       return __r;
 374     }
 375   //@}
 376
 377   //@{
 378   ///  Return new complex value @a x times @a y.
 379   template<typename _Tp>
 380     inline complex<_Tp>
 381     operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
 382     {
 383       complex<_Tp> __r = __x;
 384       __r *= __y;
 385       return __r;
 386     }
 387
 388   template<typename _Tp>
 389     inline complex<_Tp>
 390     operator*(const complex<_Tp>& __x, const _Tp& __y)
 391     {
 392       complex<_Tp> __r = __x;
 393       __r *= __y;
 394       return __r;
 395     }
 396
 397   template<typename _Tp>
 398     inline complex<_Tp>
 399     operator*(const _Tp& __x, const complex<_Tp>& __y)
 400     {
 401       complex<_Tp> __r = __y;
 402       __r *= __x;
 403       return __r;
 404     }
 405   //@}
 406
 407   //@{
 408   ///  Return new complex value @a x divided by @a y.
 409   template<typename _Tp>
 410     inline complex<_Tp>
 411     operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
 412     {
 413       complex<_Tp> __r = __x;
 414       __r /= __y;
 415       return __r;
 416     }
 417
 418   template<typename _Tp>
 419     inline complex<_Tp>
 420     operator/(const complex<_Tp>& __x, const _Tp& __y)
 421     {
 422       complex<_Tp> __r = __x;
 423       __r /= __y;
 424       return __r;
 425     }
 426
 427   template<typename _Tp>
 428     inline complex<_Tp>
 429     operator/(const _Tp& __x, const complex<_Tp>& __y)
 430     {
 431       complex<_Tp> __r = __x;
 432       __r /= __y;
 433       return __r;
 434     }
 435   //@}
 436
 437   ///  Return @a x.
 438   template<typename _Tp>
 439     inline complex<_Tp>
 440     operator+(const complex<_Tp>& __x)
 441     { return __x; }
 442
 443   ///  Return complex negation of @a x.
 444   template<typename _Tp>
 445     inline complex<_Tp>
 446     operator-(const complex<_Tp>& __x)
 447     {  return complex<_Tp>(-__x.real(), -__x.imag()); }
 448
 449   //@{
 450   ///  Return true if @a x is equal to @a y.
 451   template<typename _Tp>
 452     inline _GLIBCXX_CONSTEXPR bool
 453     operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
 454     { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
 455
 456   template<typename _Tp>
 457     inline _GLIBCXX_CONSTEXPR bool
 458     operator==(const complex<_Tp>& __x, const _Tp& __y)
 459     { return __x.real() == __y && __x.imag() == _Tp(); }
 460
 461   template<typename _Tp>
 462     inline _GLIBCXX_CONSTEXPR bool
 463     operator==(const _Tp& __x, const complex<_Tp>& __y)
 464     { return __x == __y.real() && _Tp() == __y.imag(); }
 465   //@}
 466
 467   //@{
 468   ///  Return false if @a x is equal to @a y.
 469   template<typename _Tp>
 470     inline _GLIBCXX_CONSTEXPR bool
 471     operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
 472     { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
 473
 474   template<typename _Tp>
 475     inline _GLIBCXX_CONSTEXPR bool
 476     operator!=(const complex<_Tp>& __x, const _Tp& __y)
 477     { return __x.real() != __y || __x.imag() != _Tp(); }
 478
 479   template<typename _Tp>
 480     inline _GLIBCXX_CONSTEXPR bool
 481     operator!=(const _Tp& __x, const complex<_Tp>& __y)
 482     { return __x != __y.real() || _Tp() != __y.imag(); }
 483   //@}
 484
 485   ///  Extraction operator for complex values.
 486   template<typename _Tp, typename _CharT, class _Traits>
 487     basic_istream<_CharT, _Traits>&
 488     operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
 489     {
 490       _Tp __re_x, __im_x;
 491       _CharT __ch;
 492       __is >> __ch;
 493       if (__ch == '(')
 494         {
 495           __is >> __re_x >> __ch;
 496           if (__ch == ',')
 497             {
 498               __is >> __im_x >> __ch;
 499               if (__ch == ')')
 500                 __x = complex<_Tp>(__re_x, __im_x);
 501               else
 502                 __is.setstate(ios_base::failbit);
 503             }
 504           else if (__ch == ')')
 505             __x = __re_x;
 506           else
 507             __is.setstate(ios_base::failbit);
 508         }
 509       else
 510         {
 511           __is.putback(__ch);
 512           __is >> __re_x;
 513           __x = __re_x;
 514         }
 515       return __is;
 516     }
 517
 518   ///  Insertion operator for complex values.
 519   template<typename _Tp, typename _CharT, class _Traits>
 520     basic_ostream<_CharT, _Traits>&
 521     operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
 522     {
 523       basic_ostringstream<_CharT, _Traits> __s;
 524       __s.flags(__os.flags());
 525       __s.imbue(__os.getloc());
 526       __s.precision(__os.precision());
 527       __s << '(' << __x.real() << ',' << __x.imag() << ')';
 528       return __os << __s.str();
 529     }
 530
 531   // Values
 532 #if __cplusplus >= 201103L
 533   template<typename _Tp>
 534     constexpr _Tp
 535     real(const complex<_Tp>& __z)
 536     { return __z.real(); }
 537
 538   template<typename _Tp>
 539     constexpr _Tp
 540     imag(const complex<_Tp>& __z)
 541     { return __z.imag(); }
 542 #else
 543   template<typename _Tp>
 544     inline _Tp&
 545     real(complex<_Tp>& __z)
 546     { return __z.real(); }
 547
 548   template<typename _Tp>
 549     inline const _Tp&
 550     real(const complex<_Tp>& __z)
 551     { return __z.real(); }
 552
 553   template<typename _Tp>
 554     inline _Tp&
 555     imag(complex<_Tp>& __z)
 556     { return __z.imag(); }
 557
 558   template<typename _Tp>
 559     inline const _Tp&
 560     imag(const complex<_Tp>& __z)
 561     { return __z.imag(); }
 562 #endif
 563
 564   // 26.2.7/3 abs(__z):  Returns the magnitude of __z.
 565   template<typename _Tp>
 566     inline _Tp
 567     __complex_abs(const complex<_Tp>& __z)
 568     {
 569       _Tp __x = __z.real();
 570       _Tp __y = __z.imag();
 571       const _Tp __s = std::max(abs(__x), abs(__y));
 572       if (__s == _Tp())  // well ...
 573         return __s;
 574       __x /= __s;
 575       __y /= __s;
 576       return __s * sqrt(__x * __x + __y * __y);
 577     }
 578
 579 #if _GLIBCXX_USE_C99_COMPLEX
 580   inline float
 581   __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
 582
 583   inline double
 584   __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
 585
 586   inline long double
 587   __complex_abs(const __complex__ long double& __z)
 588   { return __builtin_cabsl(__z); }
 589
 590   template<typename _Tp>
 591     inline _Tp
 592     abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
 593 #else
 594   template<typename _Tp>
 595     inline _Tp
 596     abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
 597 #endif
 598
 599
 600   // 26.2.7/4: arg(__z): Returns the phase angle of __z.
 601   template<typename _Tp>
 602     inline _Tp
 603     __complex_arg(const complex<_Tp>& __z)
 604     { return  atan2(__z.imag(), __z.real()); }
 605
 606 #if _GLIBCXX_USE_C99_COMPLEX
 607   inline float
 608   __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
 609
 610   inline double
 611   __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
 612
 613   inline long double
 614   __complex_arg(const __complex__ long double& __z)
 615   { return __builtin_cargl(__z); }
 616
 617   template<typename _Tp>
 618     inline _Tp
 619     arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
 620 #else
 621   template<typename _Tp>
 622     inline _Tp
 623     arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
 624 #endif
 625
 626   // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
 627   //     As defined, norm() is -not- a norm is the common mathematical
 628   //     sens used in numerics.  The helper class _Norm_helper<> tries to
 629   //     distinguish between builtin floating point and the rest, so as
 630   //     to deliver an answer as close as possible to the real value.
 631   template<bool>
 632     struct _Norm_helper
 633     {
 634       template<typename _Tp>
 635         static inline _Tp _S_do_it(const complex<_Tp>& __z)
 636         {
 637           const _Tp __x = __z.real();
 638           const _Tp __y = __z.imag();
 639           return __x * __x + __y * __y;
 640         }
 641     };
 642
 643   template<>
 644     struct _Norm_helper<true>
 645     {
 646       template<typename _Tp>
 647         static inline _Tp _S_do_it(const complex<_Tp>& __z)
 648         {
 649           _Tp __res = std::abs(__z);
 650           return __res * __res;
 651         }
 652     };
 653
 654   template<typename _Tp>
 655     inline _Tp
 656     norm(const complex<_Tp>& __z)
 657     {
 658       return _Norm_helper<__is_floating<_Tp>::__value
 659         && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
 660     }
 661
 662   template<typename _Tp>
 663     inline complex<_Tp>
 664     polar(const _Tp& __rho, const _Tp& __theta)
 665     { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
 666
 667   template<typename _Tp>
 668     inline complex<_Tp>
 669     conj(const complex<_Tp>& __z)
 670     { return complex<_Tp>(__z.real(), -__z.imag()); }
 671
 672   // Transcendentals
 673
 674   // 26.2.8/1 cos(__z):  Returns the cosine of __z.
 675   template<typename _Tp>
 676     inline complex<_Tp>
 677     __complex_cos(const complex<_Tp>& __z)
 678     {
 679       const _Tp __x = __z.real();
 680       const _Tp __y = __z.imag();
 681       return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
 682     }
 683
 684 #if _GLIBCXX_USE_C99_COMPLEX
 685   inline __complex__ float
 686   __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
 687
 688   inline __complex__ double
 689   __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
 690
 691   inline __complex__ long double
 692   __complex_cos(const __complex__ long double& __z)
 693   { return __builtin_ccosl(__z); }
 694
 695   template<typename _Tp>
 696     inline complex<_Tp>
 697     cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
 698 #else
 699   template<typename _Tp>
 700     inline complex<_Tp>
 701     cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
 702 #endif
 703
 704   // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
 705   template<typename _Tp>
 706     inline complex<_Tp>
 707     __complex_cosh(const complex<_Tp>& __z)
 708     {
 709       const _Tp __x = __z.real();
 710       const _Tp __y = __z.imag();
 711       return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
 712     }
 713
 714 #if _GLIBCXX_USE_C99_COMPLEX
 715   inline __complex__ float
 716   __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
 717
 718   inline __complex__ double
 719   __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
 720
 721   inline __complex__ long double
 722   __complex_cosh(const __complex__ long double& __z)
 723   { return __builtin_ccoshl(__z); }
 724
 725   template<typename _Tp>
 726     inline complex<_Tp>
 727     cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
 728 #else
 729   template<typename _Tp>
 730     inline complex<_Tp>
 731     cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
 732 #endif
 733
 734   // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
 735   template<typename _Tp>
 736     inline complex<_Tp>
 737     __complex_exp(const complex<_Tp>& __z)
 738     { return std::polar(exp(__z.real()), __z.imag()); }
 739
 740 #if _GLIBCXX_USE_C99_COMPLEX
 741   inline __complex__ float
 742   __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
 743
 744   inline __complex__ double
 745   __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
 746
 747   inline __complex__ long double
 748   __complex_exp(const __complex__ long double& __z)
 749   { return __builtin_cexpl(__z); }
 750
 751   template<typename _Tp>
 752     inline complex<_Tp>
 753     exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
 754 #else
 755   template<typename _Tp>
 756     inline complex<_Tp>
 757     exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
 758 #endif
 759
 760   // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
 761   //                    The branch cut is along the negative axis.
 762   template<typename _Tp>
 763     inline complex<_Tp>
 764     __complex_log(const complex<_Tp>& __z)
 765     { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
 766
 767 #if _GLIBCXX_USE_C99_COMPLEX
 768   inline __complex__ float
 769   __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
 770
 771   inline __complex__ double
 772   __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
 773
 774   inline __complex__ long double
 775   __complex_log(const __complex__ long double& __z)
 776   { return __builtin_clogl(__z); }
 777
 778   template<typename _Tp>
 779     inline complex<_Tp>
 780     log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
 781 #else
 782   template<typename _Tp>
 783     inline complex<_Tp>
 784     log(const complex<_Tp>& __z) { return __complex_log(__z); }
 785 #endif
 786
 787   template<typename _Tp>
 788     inline complex<_Tp>
 789     log10(const complex<_Tp>& __z)
 790     { return std::log(__z) / log(_Tp(10.0)); }
 791
 792   // 26.2.8/10 sin(__z): Returns the sine of __z.
 793   template<typename _Tp>
 794     inline complex<_Tp>
 795     __complex_sin(const complex<_Tp>& __z)
 796     {
 797       const _Tp __x = __z.real();
 798       const _Tp __y = __z.imag();
 799       return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
 800     }
 801
 802 #if _GLIBCXX_USE_C99_COMPLEX
 803   inline __complex__ float
 804   __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
 805
 806   inline __complex__ double
 807   __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
 808
 809   inline __complex__ long double
 810   __complex_sin(const __complex__ long double& __z)
 811   { return __builtin_csinl(__z); }
 812
 813   template<typename _Tp>
 814     inline complex<_Tp>
 815     sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
 816 #else
 817   template<typename _Tp>
 818     inline complex<_Tp>
 819     sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
 820 #endif
 821
 822   // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
 823   template<typename _Tp>
 824     inline complex<_Tp>
 825     __complex_sinh(const complex<_Tp>& __z)
 826     {
 827       const _Tp __x = __z.real();
 828       const _Tp  __y = __z.imag();
 829       return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
 830     }
 831
 832 #if _GLIBCXX_USE_C99_COMPLEX
 833   inline __complex__ float
 834   __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
 835
 836   inline __complex__ double
 837   __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
 838
 839   inline __complex__ long double
 840   __complex_sinh(const __complex__ long double& __z)
 841   { return __builtin_csinhl(__z); }
 842
 843   template<typename _Tp>
 844     inline complex<_Tp>
 845     sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
 846 #else
 847   template<typename _Tp>
 848     inline complex<_Tp>
 849     sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
 850 #endif
 851
 852   // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
 853   //                     The branch cut is on the negative axis.
 854   template<typename _Tp>
 855     complex<_Tp>
 856     __complex_sqrt(const complex<_Tp>& __z)
 857     {
 858       _Tp __x = __z.real();
 859       _Tp __y = __z.imag();
 860
 861       if (__x == _Tp())
 862         {
 863           _Tp __t = sqrt(abs(__y) / 2);
 864           return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
 865         }
 866       else
 867         {
 868           _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
 869           _Tp __u = __t / 2;
 870           return __x > _Tp()
 871             ? complex<_Tp>(__u, __y / __t)
 872             : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
 873         }
 874     }
 875
 876 #if _GLIBCXX_USE_C99_COMPLEX
 877   inline __complex__ float
 878   __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
 879
 880   inline __complex__ double
 881   __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
 882
 883   inline __complex__ long double
 884   __complex_sqrt(const __complex__ long double& __z)
 885   { return __builtin_csqrtl(__z); }
 886
 887   template<typename _Tp>
 888     inline complex<_Tp>
 889     sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
 890 #else
 891   template<typename _Tp>
 892     inline complex<_Tp>
 893     sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
 894 #endif
 895
 896   // 26.2.8/14 tan(__z):  Return the complex tangent of __z.
 897
 898   template<typename _Tp>
 899     inline complex<_Tp>
 900     __complex_tan(const complex<_Tp>& __z)
 901     { return std::sin(__z) / std::cos(__z); }
 902
 903 #if _GLIBCXX_USE_C99_COMPLEX
 904   inline __complex__ float
 905   __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
 906
 907   inline __complex__ double
 908   __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
 909
 910   inline __complex__ long double
 911   __complex_tan(const __complex__ long double& __z)
 912   { return __builtin_ctanl(__z); }
 913
 914   template<typename _Tp>
 915     inline complex<_Tp>
 916     tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
 917 #else
 918   template<typename _Tp>
 919     inline complex<_Tp>
 920     tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
 921 #endif
 922
 923
 924   // 26.2.8/15 tanh(__z):  Returns the hyperbolic tangent of __z.
 925
 926   template<typename _Tp>
 927     inline complex<_Tp>
 928     __complex_tanh(const complex<_Tp>& __z)
 929     { return std::sinh(__z) / std::cosh(__z); }
 930
 931 #if _GLIBCXX_USE_C99_COMPLEX
 932   inline __complex__ float
 933   __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
 934
 935   inline __complex__ double
 936   __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
 937
 938   inline __complex__ long double
 939   __complex_tanh(const __complex__ long double& __z)
 940   { return __builtin_ctanhl(__z); }
 941
 942   template<typename _Tp>
 943     inline complex<_Tp>
 944     tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
 945 #else
 946   template<typename _Tp>
 947     inline complex<_Tp>
 948     tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
 949 #endif
 950
 951
 952   // 26.2.8/9  pow(__x, __y): Returns the complex power base of __x
 953   //                          raised to the __y-th power.  The branch
 954   //                          cut is on the negative axis.
 955 #if __cplusplus < 201103L
 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, -(unsigned)__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 #if __cplusplus >= 201103L
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 #if __cplusplus >= 201103L
1062       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1063       // DR 387. std::complex over-encapsulated.
1064       __attribute ((__abi_tag__ ("cxx11")))
1065       constexpr float
1066       real() { return __real__ _M_value; }
1067
1068       __attribute ((__abi_tag__ ("cxx11")))
1069       constexpr float
1070       imag() { return __imag__ _M_value; }
1071 #else
1072       float&
1073       real() { return __real__ _M_value; }
1074
1075       const float&
1076       real() const { return __real__ _M_value; }
1077
1078       float&
1079       imag() { return __imag__ _M_value; }
1080
1081       const float&
1082       imag() const { return __imag__ _M_value; }
1083 #endif
1084
1085       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1086       // DR 387. std::complex over-encapsulated.
1087       void
1088       real(float __val) { __real__ _M_value = __val; }
1089
1090       void
1091       imag(float __val) { __imag__ _M_value = __val; }
1092
1093       complex&
1094       operator=(float __f)
1095       {
1096         _M_value = __f;
1097         return *this;
1098       }
1099
1100       complex&
1101       operator+=(float __f)
1102       {
1103         _M_value += __f;
1104         return *this;
1105       }
1106
1107       complex&
1108       operator-=(float __f)
1109       {
1110         _M_value -= __f;
1111         return *this;
1112       }
1113
1114       complex&
1115       operator*=(float __f)
1116       {
1117         _M_value *= __f;
1118         return *this;
1119       }
1120
1121       complex&
1122       operator/=(float __f)
1123       {
1124         _M_value /= __f;
1125         return *this;
1126       }
1127
1128       // Let the compiler synthesize the copy and assignment
1129       // operator.  It always does a pretty good job.
1130       // complex& operator=(const complex&);
1131
1132       template<typename _Tp>
1133         complex&
1134         operator=(const complex<_Tp>&  __z)
1135         {
1136           __real__ _M_value = __z.real();
1137           __imag__ _M_value = __z.imag();
1138           return *this;
1139         }
1140
1141       template<typename _Tp>
1142         complex&
1143         operator+=(const complex<_Tp>& __z)
1144         {
1145           __real__ _M_value += __z.real();
1146           __imag__ _M_value += __z.imag();
1147           return *this;
1148         }
1149
1150       template<class _Tp>
1151         complex&
1152         operator-=(const complex<_Tp>& __z)
1153         {
1154           __real__ _M_value -= __z.real();
1155           __imag__ _M_value -= __z.imag();
1156           return *this;
1157         }
1158
1159       template<class _Tp>
1160         complex&
1161         operator*=(const complex<_Tp>& __z)
1162         {
1163           _ComplexT __t;
1164           __real__ __t = __z.real();
1165           __imag__ __t = __z.imag();
1166           _M_value *= __t;
1167           return *this;
1168         }
1169
1170       template<class _Tp>
1171         complex&
1172         operator/=(const complex<_Tp>& __z)
1173         {
1174           _ComplexT __t;
1175           __real__ __t = __z.real();
1176           __imag__ __t = __z.imag();
1177           _M_value /= __t;
1178           return *this;
1179         }
1180
1181       _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1182
1183     private:
1184       _ComplexT _M_value;
1185     };
1186
1187   /// 26.2.3  complex specializations
1188   /// complex<double> specialization
1189   template<>
1190     struct complex<double>
1191     {
1192       typedef double value_type;
1193       typedef __complex__ double _ComplexT;
1194
1195       _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1196
1197       _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
1198 #if __cplusplus >= 201103L
1199       : _M_value{ __r, __i } { }
1200 #else
1201       {
1202         __real__ _M_value = __r;
1203         __imag__ _M_value = __i;
1204       }
1205 #endif
1206
1207       _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1208       : _M_value(__z.__rep()) { }
1209
1210       explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
1211
1212 #if __cplusplus >= 201103L
1213       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1214       // DR 387. std::complex over-encapsulated.
1215       __attribute ((__abi_tag__ ("cxx11")))
1216       constexpr double
1217       real() { return __real__ _M_value; }
1218
1219       __attribute ((__abi_tag__ ("cxx11")))
1220       constexpr double
1221       imag() { return __imag__ _M_value; }
1222 #else
1223       double&
1224       real() { return __real__ _M_value; }
1225
1226       const double&
1227       real() const { return __real__ _M_value; }
1228
1229       double&
1230       imag() { return __imag__ _M_value; }
1231
1232       const double&
1233       imag() const { return __imag__ _M_value; }
1234 #endif
1235
1236       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1237       // DR 387. std::complex over-encapsulated.
1238       void
1239       real(double __val) { __real__ _M_value = __val; }
1240
1241       void
1242       imag(double __val) { __imag__ _M_value = __val; }
1243
1244       complex&
1245       operator=(double __d)
1246       {
1247         _M_value = __d;
1248         return *this;
1249       }
1250
1251       complex&
1252       operator+=(double __d)
1253       {
1254         _M_value += __d;
1255         return *this;
1256       }
1257
1258       complex&
1259       operator-=(double __d)
1260       {
1261         _M_value -= __d;
1262         return *this;
1263       }
1264
1265       complex&
1266       operator*=(double __d)
1267       {
1268         _M_value *= __d;
1269         return *this;
1270       }
1271
1272       complex&
1273       operator/=(double __d)
1274       {
1275         _M_value /= __d;
1276         return *this;
1277       }
1278
1279       // The compiler will synthesize this, efficiently.
1280       // complex& operator=(const complex&);
1281
1282       template<typename _Tp>
1283         complex&
1284         operator=(const complex<_Tp>& __z)
1285         {
1286           __real__ _M_value = __z.real();
1287           __imag__ _M_value = __z.imag();
1288           return *this;
1289         }
1290
1291       template<typename _Tp>
1292         complex&
1293         operator+=(const complex<_Tp>& __z)
1294         {
1295           __real__ _M_value += __z.real();
1296           __imag__ _M_value += __z.imag();
1297           return *this;
1298         }
1299
1300       template<typename _Tp>
1301         complex&
1302         operator-=(const complex<_Tp>& __z)
1303         {
1304           __real__ _M_value -= __z.real();
1305           __imag__ _M_value -= __z.imag();
1306           return *this;
1307         }
1308
1309       template<typename _Tp>
1310         complex&
1311         operator*=(const complex<_Tp>& __z)
1312         {
1313           _ComplexT __t;
1314           __real__ __t = __z.real();
1315           __imag__ __t = __z.imag();
1316           _M_value *= __t;
1317           return *this;
1318         }
1319
1320       template<typename _Tp>
1321         complex&
1322         operator/=(const complex<_Tp>& __z)
1323         {
1324           _ComplexT __t;
1325           __real__ __t = __z.real();
1326           __imag__ __t = __z.imag();
1327           _M_value /= __t;
1328           return *this;
1329         }
1330
1331       _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1332
1333     private:
1334       _ComplexT _M_value;
1335     };
1336
1337   /// 26.2.3  complex specializations
1338   /// complex<long double> specialization
1339   template<>
1340     struct complex<long double>
1341     {
1342       typedef long double value_type;
1343       typedef __complex__ long double _ComplexT;
1344
1345       _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
1346
1347       _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
1348                                  long double __i = 0.0L)
1349 #if __cplusplus >= 201103L
1350       : _M_value{ __r, __i } { }
1351 #else
1352       {
1353         __real__ _M_value = __r;
1354         __imag__ _M_value = __i;
1355       }
1356 #endif
1357
1358       _GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
1359       : _M_value(__z.__rep()) { }
1360
1361       _GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
1362       : _M_value(__z.__rep()) { }
1363
1364 #if __cplusplus >= 201103L
1365       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1366       // DR 387. std::complex over-encapsulated.
1367       __attribute ((__abi_tag__ ("cxx11")))
1368       constexpr long double
1369       real() { return __real__ _M_value; }
1370
1371       __attribute ((__abi_tag__ ("cxx11")))
1372       constexpr long double
1373       imag() { return __imag__ _M_value; }
1374 #else
1375       long double&
1376       real() { return __real__ _M_value; }
1377
1378       const long double&
1379       real() const { return __real__ _M_value; }
1380
1381       long double&
1382       imag() { return __imag__ _M_value; }
1383
1384       const long double&
1385       imag() const { return __imag__ _M_value; }
1386 #endif
1387
1388       // _GLIBCXX_RESOLVE_LIB_DEFECTS
1389       // DR 387. std::complex over-encapsulated.
1390       void
1391       real(long double __val) { __real__ _M_value = __val; }
1392
1393       void
1394       imag(long double __val) { __imag__ _M_value = __val; }
1395
1396       complex&
1397       operator=(long double __r)
1398       {
1399         _M_value = __r;
1400         return *this;
1401       }
1402
1403       complex&
1404       operator+=(long double __r)
1405       {
1406         _M_value += __r;
1407         return *this;
1408       }
1409
1410       complex&
1411       operator-=(long double __r)
1412       {
1413         _M_value -= __r;
1414         return *this;
1415       }
1416
1417       complex&
1418       operator*=(long double __r)
1419       {
1420         _M_value *= __r;
1421         return *this;
1422       }
1423
1424       complex&
1425       operator/=(long double __r)
1426       {
1427         _M_value /= __r;
1428         return *this;
1429       }
1430
1431       // The compiler knows how to do this efficiently
1432       // complex& operator=(const complex&);
1433
1434       template<typename _Tp>
1435         complex&
1436         operator=(const complex<_Tp>& __z)
1437         {
1438           __real__ _M_value = __z.real();
1439           __imag__ _M_value = __z.imag();
1440           return *this;
1441         }
1442
1443       template<typename _Tp>
1444         complex&
1445         operator+=(const complex<_Tp>& __z)
1446         {
1447           __real__ _M_value += __z.real();
1448           __imag__ _M_value += __z.imag();
1449           return *this;
1450         }
1451
1452       template<typename _Tp>
1453         complex&
1454         operator-=(const complex<_Tp>& __z)
1455         {
1456           __real__ _M_value -= __z.real();
1457           __imag__ _M_value -= __z.imag();
1458           return *this;
1459         }
1460
1461       template<typename _Tp>
1462         complex&
1463         operator*=(const complex<_Tp>& __z)
1464         {
1465           _ComplexT __t;
1466           __real__ __t = __z.real();
1467           __imag__ __t = __z.imag();
1468           _M_value *= __t;
1469           return *this;
1470         }
1471
1472       template<typename _Tp>
1473         complex&
1474         operator/=(const complex<_Tp>& __z)
1475         {
1476           _ComplexT __t;
1477           __real__ __t = __z.real();
1478           __imag__ __t = __z.imag();
1479           _M_value /= __t;
1480           return *this;
1481         }
1482
1483       _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
1484
1485     private:
1486       _ComplexT _M_value;
1487     };
1488
1489   // These bits have to be at the end of this file, so that the
1490   // specializations have all been defined.
1491   inline _GLIBCXX_CONSTEXPR
1492   complex<float>::complex(const complex<double>& __z)
1493   : _M_value(__z.__rep()) { }
1494
1495   inline _GLIBCXX_CONSTEXPR
1496   complex<float>::complex(const complex<long double>& __z)
1497   : _M_value(__z.__rep()) { }
1498
1499   inline _GLIBCXX_CONSTEXPR
1500   complex<double>::complex(const complex<long double>& __z)
1501   : _M_value(__z.__rep()) { }
1502
1503   // Inhibit implicit instantiations for required instantiations,
1504   // which are defined via explicit instantiations elsewhere.
1505   // NB:  This syntax is a GNU extension.
1506 #if _GLIBCXX_EXTERN_TEMPLATE
1507   extern template istream& operator>>(istream&, complex<float>&);
1508   extern template ostream& operator<<(ostream&, const complex<float>&);
1509   extern template istream& operator>>(istream&, complex<double>&);
1510   extern template ostream& operator<<(ostream&, const complex<double>&);
1511   extern template istream& operator>>(istream&, complex<long double>&);
1512   extern template ostream& operator<<(ostream&, const complex<long double>&);
1513
1514 #ifdef _GLIBCXX_USE_WCHAR_T
1515   extern template wistream& operator>>(wistream&, complex<float>&);
1516   extern template wostream& operator<<(wostream&, const complex<float>&);
1517   extern template wistream& operator>>(wistream&, complex<double>&);
1518   extern template wostream& operator<<(wostream&, const complex<double>&);
1519   extern template wistream& operator>>(wistream&, complex<long double>&);
1520   extern template wostream& operator<<(wostream&, const complex<long double>&);
1521 #endif
1522 #endif
1523
1524   // @} group complex_numbers
1525
1526 _GLIBCXX_END_NAMESPACE_VERSION
1527 } // namespace
1528
1529 namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
1530 {
1531 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1532
1533   // See ext/type_traits.h for the primary template.
1534   template<typename _Tp, typename _Up>
1535     struct __promote_2<std::complex<_Tp>, _Up>
1536     {
1537     public:
1538       typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1539     };
1540
1541   template<typename _Tp, typename _Up>
1542     struct __promote_2<_Tp, std::complex<_Up> >
1543     {
1544     public:
1545       typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1546     };
1547
1548   template<typename _Tp, typename _Up>
1549     struct __promote_2<std::complex<_Tp>, std::complex<_Up> >
1550     {
1551     public:
1552       typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
1553     };
1554
1555 _GLIBCXX_END_NAMESPACE_VERSION
1556 } // namespace
1557
1558 #if __cplusplus >= 201103L
1559
1560 namespace std _GLIBCXX_VISIBILITY(default)
1561 {
1562 _GLIBCXX_BEGIN_NAMESPACE_VERSION
1563
1564   // Forward declarations.
1565   template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
1566   template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
1567   template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
1568
1569   template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
1570   template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
1571   template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
1572   // DR 595.
1573   template<typename _Tp> _Tp               fabs(const std::complex<_Tp>&);
1574
1575   template<typename _Tp>
1576     inline std::complex<_Tp>
1577     __complex_acos(const std::complex<_Tp>& __z)
1578     {
1579       const std::complex<_Tp> __t = std::asin(__z);
1580       const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
1581       return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
1582     }
1583
1584 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1585   inline __complex__ float
1586   __complex_acos(__complex__ float __z)
1587   { return __builtin_cacosf(__z); }
1588
1589   inline __complex__ double
1590   __complex_acos(__complex__ double __z)
1591   { return __builtin_cacos(__z); }
1592
1593   inline __complex__ long double
1594   __complex_acos(const __complex__ long double& __z)
1595   { return __builtin_cacosl(__z); }
1596
1597   template<typename _Tp>
1598     inline std::complex<_Tp>
1599     acos(const std::complex<_Tp>& __z)
1600     { return __complex_acos(__z.__rep()); }
1601 #else
1602   /// acos(__z) [8.1.2].
1603   //  Effects:  Behaves the same as C99 function cacos, defined
1604   //            in subclause 7.3.5.1.
1605   template<typename _Tp>
1606     inline std::complex<_Tp>
1607     acos(const std::complex<_Tp>& __z)
1608     { return __complex_acos(__z); }
1609 #endif
1610
1611   template<typename _Tp>
1612     inline std::complex<_Tp>
1613     __complex_asin(const std::complex<_Tp>& __z)
1614     {
1615       std::complex<_Tp> __t(-__z.imag(), __z.real());
1616       __t = std::asinh(__t);
1617       return std::complex<_Tp>(__t.imag(), -__t.real());
1618     }
1619
1620 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1621   inline __complex__ float
1622   __complex_asin(__complex__ float __z)
1623   { return __builtin_casinf(__z); }
1624
1625   inline __complex__ double
1626   __complex_asin(__complex__ double __z)
1627   { return __builtin_casin(__z); }
1628
1629   inline __complex__ long double
1630   __complex_asin(const __complex__ long double& __z)
1631   { return __builtin_casinl(__z); }
1632
1633   template<typename _Tp>
1634     inline std::complex<_Tp>
1635     asin(const std::complex<_Tp>& __z)
1636     { return __complex_asin(__z.__rep()); }
1637 #else
1638   /// asin(__z) [8.1.3].
1639   //  Effects:  Behaves the same as C99 function casin, defined
1640   //            in subclause 7.3.5.2.
1641   template<typename _Tp>
1642     inline std::complex<_Tp>
1643     asin(const std::complex<_Tp>& __z)
1644     { return __complex_asin(__z); }
1645 #endif
1646
1647   template<typename _Tp>
1648     std::complex<_Tp>
1649     __complex_atan(const std::complex<_Tp>& __z)
1650     {
1651       const _Tp __r2 = __z.real() * __z.real();
1652       const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
1653
1654       _Tp __num = __z.imag() + _Tp(1.0);
1655       _Tp __den = __z.imag() - _Tp(1.0);
1656
1657       __num = __r2 + __num * __num;
1658       __den = __r2 + __den * __den;
1659
1660       return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
1661                                _Tp(0.25) * log(__num / __den));
1662     }
1663
1664 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1665   inline __complex__ float
1666   __complex_atan(__complex__ float __z)
1667   { return __builtin_catanf(__z); }
1668
1669   inline __complex__ double
1670   __complex_atan(__complex__ double __z)
1671   { return __builtin_catan(__z); }
1672
1673   inline __complex__ long double
1674   __complex_atan(const __complex__ long double& __z)
1675   { return __builtin_catanl(__z); }
1676
1677   template<typename _Tp>
1678     inline std::complex<_Tp>
1679     atan(const std::complex<_Tp>& __z)
1680     { return __complex_atan(__z.__rep()); }
1681 #else
1682   /// atan(__z) [8.1.4].
1683   //  Effects:  Behaves the same as C99 function catan, defined
1684   //            in subclause 7.3.5.3.
1685   template<typename _Tp>
1686     inline std::complex<_Tp>
1687     atan(const std::complex<_Tp>& __z)
1688     { return __complex_atan(__z); }
1689 #endif
1690
1691   template<typename _Tp>
1692     std::complex<_Tp>
1693     __complex_acosh(const std::complex<_Tp>& __z)
1694     {
1695       // Kahan's formula.
1696       return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
1697                                  + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
1698     }
1699
1700 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1701   inline __complex__ float
1702   __complex_acosh(__complex__ float __z)
1703   { return __builtin_cacoshf(__z); }
1704
1705   inline __complex__ double
1706   __complex_acosh(__complex__ double __z)
1707   { return __builtin_cacosh(__z); }
1708
1709   inline __complex__ long double
1710   __complex_acosh(const __complex__ long double& __z)
1711   { return __builtin_cacoshl(__z); }
1712
1713   template<typename _Tp>
1714     inline std::complex<_Tp>
1715     acosh(const std::complex<_Tp>& __z)
1716     { return __complex_acosh(__z.__rep()); }
1717 #else
1718   /// acosh(__z) [8.1.5].
1719   //  Effects:  Behaves the same as C99 function cacosh, defined
1720   //            in subclause 7.3.6.1.
1721   template<typename _Tp>
1722     inline std::complex<_Tp>
1723     acosh(const std::complex<_Tp>& __z)
1724     { return __complex_acosh(__z); }
1725 #endif
1726
1727   template<typename _Tp>
1728     std::complex<_Tp>
1729     __complex_asinh(const std::complex<_Tp>& __z)
1730     {
1731       std::complex<_Tp> __t((__z.real() - __z.imag())
1732                             * (__z.real() + __z.imag()) + _Tp(1.0),
1733                             _Tp(2.0) * __z.real() * __z.imag());
1734       __t = std::sqrt(__t);
1735
1736       return std::log(__t + __z);
1737     }
1738
1739 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1740   inline __complex__ float
1741   __complex_asinh(__complex__ float __z)
1742   { return __builtin_casinhf(__z); }
1743
1744   inline __complex__ double
1745   __complex_asinh(__complex__ double __z)
1746   { return __builtin_casinh(__z); }
1747
1748   inline __complex__ long double
1749   __complex_asinh(const __complex__ long double& __z)
1750   { return __builtin_casinhl(__z); }
1751
1752   template<typename _Tp>
1753     inline std::complex<_Tp>
1754     asinh(const std::complex<_Tp>& __z)
1755     { return __complex_asinh(__z.__rep()); }
1756 #else
1757   /// asinh(__z) [8.1.6].
1758   //  Effects:  Behaves the same as C99 function casin, defined
1759   //            in subclause 7.3.6.2.
1760   template<typename _Tp>
1761     inline std::complex<_Tp>
1762     asinh(const std::complex<_Tp>& __z)
1763     { return __complex_asinh(__z); }
1764 #endif
1765
1766   template<typename _Tp>
1767     std::complex<_Tp>
1768     __complex_atanh(const std::complex<_Tp>& __z)
1769     {
1770       const _Tp __i2 = __z.imag() * __z.imag();
1771       const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
1772
1773       _Tp __num = _Tp(1.0) + __z.real();
1774       _Tp __den = _Tp(1.0) - __z.real();
1775
1776       __num = __i2 + __num * __num;
1777       __den = __i2 + __den * __den;
1778
1779       return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
1780                                _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
1781     }
1782
1783 #if _GLIBCXX_USE_C99_COMPLEX_TR1
1784   inline __complex__ float
1785   __complex_atanh(__complex__ float __z)
1786   { return __builtin_catanhf(__z); }
1787
1788   inline __complex__ double
1789   __complex_atanh(__complex__ double __z)
1790   { return __builtin_catanh(__z); }
1791
1792   inline __complex__ long double
1793   __complex_atanh(const __complex__ long double& __z)
1794   { return __builtin_catanhl(__z); }
1795
1796   template<typename _Tp>
1797     inline std::complex<_Tp>
1798     atanh(const std::complex<_Tp>& __z)
1799     { return __complex_atanh(__z.__rep()); }
1800 #else
1801   /// atanh(__z) [8.1.7].
1802   //  Effects:  Behaves the same as C99 function catanh, defined
1803   //            in subclause 7.3.6.3.
1804   template<typename _Tp>
1805     inline std::complex<_Tp>
1806     atanh(const std::complex<_Tp>& __z)
1807     { return __complex_atanh(__z); }
1808 #endif
1809
1810   template<typename _Tp>
1811     inline _Tp
1812     /// fabs(__z) [8.1.8].
1813     //  Effects:  Behaves the same as C99 function cabs, defined
1814     //            in subclause 7.3.8.1.
1815     fabs(const std::complex<_Tp>& __z)
1816     { return std::abs(__z); }
1817
1818   /// Additional overloads [8.1.9].
1819   template<typename _Tp>
1820     inline typename __gnu_cxx::__promote<_Tp>::__type
1821     arg(_Tp __x)
1822     {
1823       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1824 #if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
1825       return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
1826                                : __type();
1827 #else
1828       return std::arg(std::complex<__type>(__x));
1829 #endif
1830     }
1831
1832   template<typename _Tp>
1833     inline typename __gnu_cxx::__promote<_Tp>::__type
1834     imag(_Tp)
1835     { return _Tp(); }
1836
1837   template<typename _Tp>
1838     inline typename __gnu_cxx::__promote<_Tp>::__type
1839     norm(_Tp __x)
1840     {
1841       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
1842       return __type(__x) * __type(__x);
1843     }
1844
1845   template<typename _Tp>
1846     inline typename __gnu_cxx::__promote<_Tp>::__type
1847     real(_Tp __x)
1848     { return __x; }
1849
1850   template<typename _Tp, typename _Up>
1851     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1852     pow(const std::complex<_Tp>& __x, const _Up& __y)
1853     {
1854       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1855       return std::pow(std::complex<__type>(__x), __type(__y));
1856     }
1857
1858   template<typename _Tp, typename _Up>
1859     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1860     pow(const _Tp& __x, const std::complex<_Up>& __y)
1861     {
1862       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1863       return std::pow(__type(__x), std::complex<__type>(__y));
1864     }
1865
1866   template<typename _Tp, typename _Up>
1867     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
1868     pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
1869     {
1870       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
1871       return std::pow(std::complex<__type>(__x),
1872                       std::complex<__type>(__y));
1873     }
1874
1875   // Forward declarations.
1876   // DR 781.
1877   template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
1878
1879   template<typename _Tp>
1880     std::complex<_Tp>
1881     __complex_proj(const std::complex<_Tp>& __z)
1882     {
1883       const _Tp __den = (__z.real() * __z.real()
1884                          + __z.imag() * __z.imag() + _Tp(1.0));
1885
1886       return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
1887                                (_Tp(2.0) * __z.imag()) / __den);
1888     }
1889
1890 #if _GLIBCXX_USE_C99_COMPLEX
1891   inline __complex__ float
1892   __complex_proj(__complex__ float __z)
1893   { return __builtin_cprojf(__z); }
1894
1895   inline __complex__ double
1896   __complex_proj(__complex__ double __z)
1897   { return __builtin_cproj(__z); }
1898
1899   inline __complex__ long double
1900   __complex_proj(const __complex__ long double& __z)
1901   { return __builtin_cprojl(__z); }
1902
1903   template<typename _Tp>
1904     inline std::complex<_Tp>
1905     proj(const std::complex<_Tp>& __z)
1906     { return __complex_proj(__z.__rep()); }
1907 #else
1908   template<typename _Tp>
1909     inline std::complex<_Tp>
1910     proj(const std::complex<_Tp>& __z)
1911     { return __complex_proj(__z); }
1912 #endif
1913
1914   // DR 1137.
1915   template<typename _Tp>
1916     inline typename __gnu_cxx::__promote<_Tp>::__type
1917     proj(_Tp __x)
1918     { return __x; }
1919
1920   template<typename _Tp>
1921     inline typename __gnu_cxx::__promote<_Tp>::__type
1922     conj(_Tp __x)
1923     { return __x; }
1924
1925 _GLIBCXX_END_NAMESPACE_VERSION
1926 } // namespace
1927
1928 #endif  // C++11
1929
1930 #endif  /* _GLIBCXX_COMPLEX */