libstdc++-v3/include/std/std_complex.h

   1 // The template and inlines for the -*- C++ -*- complex number classes.
   2
   3 // Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002
   4 // Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 2, or (at your option)
  10 // any later version.
  11
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16
  17 // You should have received a copy of the GNU General Public License along
  18 // with this library; see the file COPYING.  If not, write to the Free
  19 // Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
  20 // USA.
  21
  22 // As a special exception, you may use this file as part of a free software
  23 // library without restriction.  Specifically, if other files instantiate
  24 // templates or use macros or inline functions from this file, or you compile
  25 // this file and link it with other files to produce an executable, this
  26 // file does not by itself cause the resulting executable to be covered by
  27 // the GNU General Public License.  This exception does not however
  28 // invalidate any other reasons why the executable file might be covered by
  29 // the GNU General Public License.
  30
  31 //
  32 // ISO C++ 14882: 26.2  Complex Numbers
  33 // Note: this is not a conforming implementation.
  34 // Initially implemented by Ulrich Drepper <drepper@cygnus.com>
  35 // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
  36 //
  37
  38 /** @file complex
  39  *  This is a Standard C++ Library header.  You should @c #include this header
  40  *  in your programs, rather than any of the "st[dl]_*.h" implementation files.
  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 <cmath>
  51 #include <sstream>
  52
  53 namespace std
  54 {
  55   // Forward declarations
  56   template<typename _Tp> class complex;
  57   template<> class complex<float>;
  58   template<> class complex<double>;
  59   template<> class complex<long double>;
  60
  61   template<typename _Tp> _Tp abs(const complex<_Tp>&);
  62   template<typename _Tp> _Tp arg(const complex<_Tp>&);
  63   template<typename _Tp> _Tp norm(const complex<_Tp>&);
  64
  65   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
  66   template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
  67
  68   // Transcendentals:
  69   template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
  70   template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
  71   template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
  72   template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
  73   template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
  74   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
  75   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
  76   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
  77                                            const complex<_Tp>&);
  78   template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
  79   template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
  80   template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
  81   template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
  82   template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
  83   template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
  84
  85
  86   // 26.2.2  Primary template class complex
  87   template<typename _Tp>
  88     class complex
  89     {
  90     public:
  91       typedef _Tp value_type;
  92
  93       complex(const _Tp& = _Tp(), const _Tp & = _Tp());
  94
  95       // Let's the compiler synthetize the copy constructor
  96       // complex (const complex<_Tp>&);
  97       template<typename _Up>
  98         complex(const complex<_Up>&);
  99
 100       _Tp real() const;
 101       _Tp imag() const;
 102
 103       complex<_Tp>& operator=(const _Tp&);
 104       complex<_Tp>& operator+=(const _Tp&);
 105       complex<_Tp>& operator-=(const _Tp&);
 106       complex<_Tp>& operator*=(const _Tp&);
 107       complex<_Tp>& operator/=(const _Tp&);
 108
 109       // Let's the compiler synthetize the
 110       // copy and assignment operator
 111       // complex<_Tp>& operator= (const complex<_Tp>&);
 112       template<typename _Up>
 113         complex<_Tp>& operator=(const complex<_Up>&);
 114       template<typename _Up>
 115         complex<_Tp>& operator+=(const complex<_Up>&);
 116       template<typename _Up>
 117         complex<_Tp>& operator-=(const complex<_Up>&);
 118       template<typename _Up>
 119         complex<_Tp>& operator*=(const complex<_Up>&);
 120       template<typename _Up>
 121         complex<_Tp>& operator/=(const complex<_Up>&);
 122
 123     private:
 124       _Tp _M_real, _M_imag;
 125     };
 126
 127   template<typename _Tp>
 128     inline _Tp
 129     complex<_Tp>::real() const { return _M_real; }
 130
 131   template<typename _Tp>
 132     inline _Tp
 133     complex<_Tp>::imag() const { return _M_imag; }
 134
 135   template<typename _Tp>
 136     inline
 137     complex<_Tp>::complex(const _Tp& __r, const _Tp& __i)
 138     : _M_real(__r), _M_imag(__i) { }
 139
 140   template<typename _Tp>
 141     template<typename _Up>
 142     inline
 143     complex<_Tp>::complex(const complex<_Up>& __z)
 144     : _M_real(__z.real()), _M_imag(__z.imag()) { }
 145
 146   template<typename _Tp>
 147     complex<_Tp>&
 148     complex<_Tp>::operator=(const _Tp& __t)
 149     {
 150      _M_real = __t;
 151      _M_imag = _Tp();
 152      return *this;
 153     }
 154
 155   // 26.2.5/1
 156   template<typename _Tp>
 157     inline complex<_Tp>&
 158     complex<_Tp>::operator+=(const _Tp& __t)
 159     {
 160       _M_real += __t;
 161       return *this;
 162     }
 163
 164   // 26.2.5/3
 165   template<typename _Tp>
 166     inline complex<_Tp>&
 167     complex<_Tp>::operator-=(const _Tp& __t)
 168     {
 169       _M_real -= __t;
 170       return *this;
 171     }
 172
 173   // 26.2.5/5
 174   template<typename _Tp>
 175     complex<_Tp>&
 176     complex<_Tp>::operator*=(const _Tp& __t)
 177     {
 178       _M_real *= __t;
 179       _M_imag *= __t;
 180       return *this;
 181     }
 182
 183   // 26.2.5/7
 184   template<typename _Tp>
 185     complex<_Tp>&
 186     complex<_Tp>::operator/=(const _Tp& __t)
 187     {
 188       _M_real /= __t;
 189       _M_imag /= __t;
 190       return *this;
 191     }
 192
 193   template<typename _Tp>
 194     template<typename _Up>
 195     complex<_Tp>&
 196     complex<_Tp>::operator=(const complex<_Up>& __z)
 197     {
 198       _M_real = __z.real();
 199       _M_imag = __z.imag();
 200       return *this;
 201     }
 202
 203   // 26.2.5/9
 204   template<typename _Tp>
 205     template<typename _Up>
 206     complex<_Tp>&
 207     complex<_Tp>::operator+=(const complex<_Up>& __z)
 208     {
 209       _M_real += __z.real();
 210       _M_imag += __z.imag();
 211       return *this;
 212     }
 213
 214   // 26.2.5/11
 215   template<typename _Tp>
 216     template<typename _Up>
 217     complex<_Tp>&
 218     complex<_Tp>::operator-=(const complex<_Up>& __z)
 219     {
 220       _M_real -= __z.real();
 221       _M_imag -= __z.imag();
 222       return *this;
 223     }
 224
 225   // 26.2.5/13
 226   // XXX: This is a grammar school implementation.
 227   template<typename _Tp>
 228     template<typename _Up>
 229     complex<_Tp>&
 230     complex<_Tp>::operator*=(const complex<_Up>& __z)
 231     {
 232       const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
 233       _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
 234       _M_real = __r;
 235       return *this;
 236     }
 237
 238   // 26.2.5/15
 239   // XXX: This is a grammar school implementation.
 240   template<typename _Tp>
 241     template<typename _Up>
 242     complex<_Tp>&
 243     complex<_Tp>::operator/=(const complex<_Up>& __z)
 244     {
 245       const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
 246       const _Tp __n = std::norm(__z);
 247       _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
 248       _M_real = __r / __n;
 249       return *this;
 250     }
 251
 252   // Operators:
 253   template<typename _Tp>
 254     inline complex<_Tp>
 255     operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
 256     { return complex<_Tp> (__x) += __y; }
 257
 258   template<typename _Tp>
 259     inline complex<_Tp>
 260     operator+(const complex<_Tp>& __x, const _Tp& __y)
 261     { return complex<_Tp> (__x) += __y; }
 262
 263   template<typename _Tp>
 264     inline complex<_Tp>
 265     operator+(const _Tp& __x, const complex<_Tp>& __y)
 266     { return complex<_Tp> (__y) += __x; }
 267
 268   template<typename _Tp>
 269     inline complex<_Tp>
 270     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
 271     { return complex<_Tp> (__x) -= __y; }
 272
 273   template<typename _Tp>
 274     inline complex<_Tp>
 275     operator-(const complex<_Tp>& __x, const _Tp& __y)
 276     { return complex<_Tp> (__x) -= __y; }
 277
 278   template<typename _Tp>
 279     inline complex<_Tp>
 280     operator-(const _Tp& __x, const complex<_Tp>& __y)
 281     { return complex<_Tp> (__x) -= __y; }
 282
 283   template<typename _Tp>
 284     inline complex<_Tp>
 285     operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
 286     { return complex<_Tp> (__x) *= __y; }
 287
 288   template<typename _Tp>
 289     inline complex<_Tp>
 290     operator*(const complex<_Tp>& __x, const _Tp& __y)
 291     { return complex<_Tp> (__x) *= __y; }
 292
 293   template<typename _Tp>
 294     inline complex<_Tp>
 295     operator*(const _Tp& __x, const complex<_Tp>& __y)
 296     { return complex<_Tp> (__y) *= __x; }
 297
 298   template<typename _Tp>
 299     inline complex<_Tp>
 300     operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
 301     { return complex<_Tp> (__x) /= __y; }
 302
 303   template<typename _Tp>
 304     inline complex<_Tp>
 305     operator/(const complex<_Tp>& __x, const _Tp& __y)
 306     { return complex<_Tp> (__x) /= __y; }
 307
 308   template<typename _Tp>
 309     inline complex<_Tp>
 310     operator/(const _Tp& __x, const complex<_Tp>& __y)
 311     { return complex<_Tp> (__x) /= __y; }
 312
 313   template<typename _Tp>
 314     inline complex<_Tp>
 315     operator+(const complex<_Tp>& __x)
 316     { return __x; }
 317
 318   template<typename _Tp>
 319     inline complex<_Tp>
 320     operator-(const complex<_Tp>& __x)
 321     {  return complex<_Tp>(-__x.real(), -__x.imag()); }
 322
 323   template<typename _Tp>
 324     inline bool
 325     operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
 326     { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
 327
 328   template<typename _Tp>
 329     inline bool
 330     operator==(const complex<_Tp>& __x, const _Tp& __y)
 331     { return __x.real() == __y && __x.imag() == _Tp(); }
 332
 333   template<typename _Tp>
 334     inline bool
 335     operator==(const _Tp& __x, const complex<_Tp>& __y)
 336     { return __x == __y.real() && _Tp() == __y.imag(); }
 337
 338   template<typename _Tp>
 339     inline bool
 340     operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
 341     { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
 342
 343   template<typename _Tp>
 344     inline bool
 345     operator!=(const complex<_Tp>& __x, const _Tp& __y)
 346     { return __x.real() != __y || __x.imag() != _Tp(); }
 347
 348   template<typename _Tp>
 349     inline bool
 350     operator!=(const _Tp& __x, const complex<_Tp>& __y)
 351     { return __x != __y.real() || _Tp() != __y.imag(); }
 352
 353   template<typename _Tp, typename _CharT, class _Traits>
 354     basic_istream<_CharT, _Traits>&
 355     operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
 356     {
 357       _Tp __re_x, __im_x;
 358       _CharT __ch;
 359       __is >> __ch;
 360       if (__ch == '(')
 361         {
 362           __is >> __re_x >> __ch;
 363           if (__ch == ',')
 364             {
 365               __is >> __im_x >> __ch;
 366               if (__ch == ')')
 367                 __x = complex<_Tp>(__re_x, __im_x);
 368               else
 369                 __is.setstate(ios_base::failbit);
 370             }
 371           else if (__ch == ')')
 372             __x = complex<_Tp>(__re_x, _Tp(0));
 373           else
 374             __is.setstate(ios_base::failbit);
 375         }
 376       else
 377         {
 378           __is.putback(__ch);
 379           __is >> __re_x;
 380           __x = complex<_Tp>(__re_x, _Tp(0));
 381         }
 382       return __is;
 383     }
 384
 385   template<typename _Tp, typename _CharT, class _Traits>
 386     basic_ostream<_CharT, _Traits>&
 387     operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
 388     {
 389       basic_ostringstream<_CharT, _Traits> __s;
 390       __s.flags(__os.flags());
 391       __s.imbue(__os.getloc());
 392       __s.precision(__os.precision());
 393       __s << '(' << __x.real() << ',' << __x.imag() << ')';
 394       return __os << __s.str();
 395     }
 396
 397   // Values
 398   template<typename _Tp>
 399     inline _Tp
 400     real(const complex<_Tp>& __z)
 401     { return __z.real(); }
 402
 403   template<typename _Tp>
 404     inline _Tp
 405     imag(const complex<_Tp>& __z)
 406     { return __z.imag(); }
 407
 408   template<typename _Tp>
 409     inline _Tp
 410     abs(const complex<_Tp>& __z)
 411     {
 412       _Tp __x = __z.real();
 413       _Tp __y = __z.imag();
 414       const _Tp __s = std::max(abs(__x), abs(__y));
 415       if (__s == _Tp())  // well ...
 416         return __s;
 417       __x /= __s;
 418       __y /= __s;
 419       return __s * sqrt(__x * __x + __y * __y);
 420     }
 421
 422   template<typename _Tp>
 423     inline _Tp
 424     arg(const complex<_Tp>& __z)
 425     { return atan2(__z.imag(), __z.real()); }
 426
 427   // 26.2.7/5: norm(__z) returns the squared magintude of __z.
 428   //     As defined, norm() is -not- a norm is the common mathematical
 429   //     sens used in numerics.  The helper class _Norm_helper<> tries to
 430   //     distinguish between builtin floating point and the rest, so as
 431   //     to deliver an answer as close as possible to the real value.
 432   template<bool>
 433     struct _Norm_helper
 434     {
 435       template<typename _Tp>
 436         static inline _Tp _S_do_it(const complex<_Tp>& __z)
 437         {
 438           const _Tp __x = __z.real();
 439           const _Tp __y = __z.imag();
 440           return __x * __x + __y * __y;
 441         }
 442     };
 443
 444   template<>
 445     struct _Norm_helper<true>
 446     {
 447       template<typename _Tp>
 448         static inline _Tp _S_do_it(const complex<_Tp>& __z)
 449         {
 450           _Tp __res = std::abs(__z);
 451           return __res * __res;
 452         }
 453     };
 454
 455   template<typename _Tp>
 456     inline _Tp
 457     norm(const complex<_Tp>& __z)
 458     {
 459       return _Norm_helper<__is_floating<_Tp>::_M_type && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
 460     }
 461
 462   template<typename _Tp>
 463     inline complex<_Tp>
 464     polar(const _Tp& __rho, const _Tp& __theta)
 465     { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
 466
 467   template<typename _Tp>
 468     inline complex<_Tp>
 469     conj(const complex<_Tp>& __z)
 470     { return complex<_Tp>(__z.real(), -__z.imag()); }
 471
 472   // Transcendentals
 473   template<typename _Tp>
 474     inline complex<_Tp>
 475     cos(const complex<_Tp>& __z)
 476     {
 477       const _Tp __x = __z.real();
 478       const _Tp __y = __z.imag();
 479       return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
 480     }
 481
 482   template<typename _Tp>
 483     inline complex<_Tp>
 484     cosh(const complex<_Tp>& __z)
 485     {
 486       const _Tp __x = __z.real();
 487       const _Tp __y = __z.imag();
 488       return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
 489     }
 490
 491   template<typename _Tp>
 492     inline complex<_Tp>
 493     exp(const complex<_Tp>& __z)
 494     { return std::polar(exp(__z.real()), __z.imag()); }
 495
 496   template<typename _Tp>
 497     inline complex<_Tp>
 498     log(const complex<_Tp>& __z)
 499     { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
 500
 501   template<typename _Tp>
 502     inline complex<_Tp>
 503     log10(const complex<_Tp>& __z)
 504     { return std::log(__z) / log(_Tp(10.0)); }
 505
 506   template<typename _Tp>
 507     inline complex<_Tp>
 508     sin(const complex<_Tp>& __z)
 509     {
 510       const _Tp __x = __z.real();
 511       const _Tp __y = __z.imag();
 512       return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
 513     }
 514
 515   template<typename _Tp>
 516     inline complex<_Tp>
 517     sinh(const complex<_Tp>& __z)
 518     {
 519       const _Tp __x = __z.real();
 520       const _Tp  __y = __z.imag();
 521       return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
 522     }
 523
 524   template<typename _Tp>
 525     complex<_Tp>
 526     sqrt(const complex<_Tp>& __z)
 527     {
 528       _Tp __x = __z.real();
 529       _Tp __y = __z.imag();
 530
 531       if (__x == _Tp())
 532         {
 533           _Tp __t = sqrt(abs(__y) / 2);
 534           return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
 535         }
 536       else
 537         {
 538           _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
 539           _Tp __u = __t / 2;
 540           return __x > _Tp()
 541             ? complex<_Tp>(__u, __y / __t)
 542             : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
 543         }
 544     }
 545
 546   template<typename _Tp>
 547     inline complex<_Tp>
 548     tan(const complex<_Tp>& __z)
 549     {
 550       return std::sin(__z) / std::cos(__z);
 551     }
 552
 553   template<typename _Tp>
 554     inline complex<_Tp>
 555     tanh(const complex<_Tp>& __z)
 556     {
 557       return std::sinh(__z) / std::cosh(__z);
 558     }
 559
 560   template<typename _Tp>
 561     inline complex<_Tp>
 562     pow(const complex<_Tp>& __z, int __n)
 563     {
 564       return std::__pow_helper(__z, __n);
 565     }
 566
 567   template<typename _Tp>
 568     complex<_Tp>
 569     pow(const complex<_Tp>& __x, const _Tp& __y)
 570     {
 571       if (__x.imag() == _Tp())
 572         return pow(__x.real(), __y);
 573
 574       complex<_Tp> __t = log(__x);
 575       return std::polar(exp(__y * __t.real()), __y * __t.imag());
 576     }
 577
 578   template<typename _Tp>
 579     inline complex<_Tp>
 580     pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
 581     {
 582       return __x == _Tp() ? _Tp() : exp(__y * log(__x));
 583     }
 584
 585   template<typename _Tp>
 586     inline complex<_Tp>
 587     pow(const _Tp& __x, const complex<_Tp>& __y)
 588     {
 589       return __x == _Tp()
 590         ? _Tp()
 591         : std::polar(pow(__x, __y.real()), __y.imag() * log(__x));
 592     }
 593
 594   // 26.2.3  complex specializations
 595   // complex<float> specialization
 596   template<> class complex<float>
 597   {
 598   public:
 599     typedef float value_type;
 600
 601     complex(float = 0.0f, float = 0.0f);
 602 #ifdef _GLIBCXX_BUGGY_COMPLEX
 603     complex(const complex& __z) : _M_value(__z._M_value) { }
 604 #endif
 605     explicit complex(const complex<double>&);
 606     explicit complex(const complex<long double>&);
 607
 608     float real() const;
 609     float imag() const;
 610
 611     complex<float>& operator=(float);
 612     complex<float>& operator+=(float);
 613     complex<float>& operator-=(float);
 614     complex<float>& operator*=(float);
 615     complex<float>& operator/=(float);
 616
 617     // Let's the compiler synthetize the copy and assignment
 618     // operator.  It always does a pretty good job.
 619     // complex& operator= (const complex&);
 620     template<typename _Tp>
 621       complex<float>&operator=(const complex<_Tp>&);
 622     template<typename _Tp>
 623       complex<float>& operator+=(const complex<_Tp>&);
 624     template<class _Tp>
 625       complex<float>& operator-=(const complex<_Tp>&);
 626     template<class _Tp>
 627       complex<float>& operator*=(const complex<_Tp>&);
 628     template<class _Tp>
 629       complex<float>&operator/=(const complex<_Tp>&);
 630
 631   private:
 632     typedef __complex__ float _ComplexT;
 633     _ComplexT _M_value;
 634
 635     complex(_ComplexT __z) : _M_value(__z) { }
 636
 637     friend class complex<double>;
 638     friend class complex<long double>;
 639   };
 640
 641   inline float
 642   complex<float>::real() const
 643   { return __real__ _M_value; }
 644
 645   inline float
 646   complex<float>::imag() const
 647   { return __imag__ _M_value; }
 648
 649   inline
 650   complex<float>::complex(float r, float i)
 651   {
 652     __real__ _M_value = r;
 653     __imag__ _M_value = i;
 654   }
 655
 656   inline complex<float>&
 657   complex<float>::operator=(float __f)
 658   {
 659     __real__ _M_value = __f;
 660     __imag__ _M_value = 0.0f;
 661     return *this;
 662   }
 663
 664   inline complex<float>&
 665   complex<float>::operator+=(float __f)
 666   {
 667     __real__ _M_value += __f;
 668     return *this;
 669   }
 670
 671   inline complex<float>&
 672   complex<float>::operator-=(float __f)
 673   {
 674     __real__ _M_value -= __f;
 675     return *this;
 676   }
 677
 678   inline complex<float>&
 679   complex<float>::operator*=(float __f)
 680   {
 681     _M_value *= __f;
 682     return *this;
 683   }
 684
 685   inline complex<float>&
 686   complex<float>::operator/=(float __f)
 687   {
 688     _M_value /= __f;
 689     return *this;
 690   }
 691
 692   template<typename _Tp>
 693   inline complex<float>&
 694   complex<float>::operator=(const complex<_Tp>& __z)
 695   {
 696     __real__ _M_value = __z.real();
 697     __imag__ _M_value = __z.imag();
 698     return *this;
 699   }
 700
 701   template<typename _Tp>
 702   inline complex<float>&
 703   complex<float>::operator+=(const complex<_Tp>& __z)
 704   {
 705     __real__ _M_value += __z.real();
 706     __imag__ _M_value += __z.imag();
 707     return *this;
 708   }
 709
 710   template<typename _Tp>
 711     inline complex<float>&
 712     complex<float>::operator-=(const complex<_Tp>& __z)
 713     {
 714      __real__ _M_value -= __z.real();
 715      __imag__ _M_value -= __z.imag();
 716      return *this;
 717     }
 718
 719   template<typename _Tp>
 720     inline complex<float>&
 721     complex<float>::operator*=(const complex<_Tp>& __z)
 722     {
 723       _ComplexT __t;
 724       __real__ __t = __z.real();
 725       __imag__ __t = __z.imag();
 726       _M_value *= __t;
 727       return *this;
 728     }
 729
 730   template<typename _Tp>
 731     inline complex<float>&
 732     complex<float>::operator/=(const complex<_Tp>& __z)
 733     {
 734       _ComplexT __t;
 735       __real__ __t = __z.real();
 736       __imag__ __t = __z.imag();
 737       _M_value /= __t;
 738       return *this;
 739     }
 740
 741   // 26.2.3  complex specializations
 742   // complex<double> specialization
 743   template<> class complex<double>
 744   {
 745   public:
 746     typedef double value_type;
 747
 748     complex(double  =0.0, double =0.0);
 749 #ifdef _GLIBCXX_BUGGY_COMPLEX
 750     complex(const complex& __z) : _M_value(__z._M_value) { }
 751 #endif
 752     complex(const complex<float>&);
 753     explicit complex(const complex<long double>&);
 754
 755     double real() const;
 756     double imag() const;
 757
 758     complex<double>& operator=(double);
 759     complex<double>& operator+=(double);
 760     complex<double>& operator-=(double);
 761     complex<double>& operator*=(double);
 762     complex<double>& operator/=(double);
 763
 764     // The compiler will synthetize this, efficiently.
 765     // complex& operator= (const complex&);
 766     template<typename _Tp>
 767       complex<double>& operator=(const complex<_Tp>&);
 768     template<typename _Tp>
 769       complex<double>& operator+=(const complex<_Tp>&);
 770     template<typename _Tp>
 771       complex<double>& operator-=(const complex<_Tp>&);
 772     template<typename _Tp>
 773       complex<double>& operator*=(const complex<_Tp>&);
 774     template<typename _Tp>
 775       complex<double>& operator/=(const complex<_Tp>&);
 776
 777   private:
 778     typedef __complex__ double _ComplexT;
 779     _ComplexT _M_value;
 780
 781     complex(_ComplexT __z) : _M_value(__z) { }
 782
 783     friend class complex<float>;
 784     friend class complex<long double>;
 785   };
 786
 787   inline double
 788   complex<double>::real() const
 789   { return __real__ _M_value; }
 790
 791   inline double
 792   complex<double>::imag() const
 793   { return __imag__ _M_value; }
 794
 795   inline
 796   complex<double>::complex(double __r, double __i)
 797   {
 798     __real__ _M_value = __r;
 799     __imag__ _M_value = __i;
 800   }
 801
 802   inline complex<double>&
 803   complex<double>::operator=(double __d)
 804   {
 805     __real__ _M_value = __d;
 806     __imag__ _M_value = 0.0;
 807     return *this;
 808   }
 809
 810   inline complex<double>&
 811   complex<double>::operator+=(double __d)
 812   {
 813     __real__ _M_value += __d;
 814     return *this;
 815   }
 816
 817   inline complex<double>&
 818   complex<double>::operator-=(double __d)
 819   {
 820     __real__ _M_value -= __d;
 821     return *this;
 822   }
 823
 824   inline complex<double>&
 825   complex<double>::operator*=(double __d)
 826   {
 827     _M_value *= __d;
 828     return *this;
 829   }
 830
 831   inline complex<double>&
 832   complex<double>::operator/=(double __d)
 833   {
 834     _M_value /= __d;
 835     return *this;
 836   }
 837
 838   template<typename _Tp>
 839     inline complex<double>&
 840     complex<double>::operator=(const complex<_Tp>& __z)
 841     {
 842       __real__ _M_value = __z.real();
 843       __imag__ _M_value = __z.imag();
 844       return *this;
 845     }
 846
 847   template<typename _Tp>
 848     inline complex<double>&
 849     complex<double>::operator+=(const complex<_Tp>& __z)
 850     {
 851       __real__ _M_value += __z.real();
 852       __imag__ _M_value += __z.imag();
 853       return *this;
 854     }
 855
 856   template<typename _Tp>
 857     inline complex<double>&
 858     complex<double>::operator-=(const complex<_Tp>& __z)
 859     {
 860       __real__ _M_value -= __z.real();
 861       __imag__ _M_value -= __z.imag();
 862       return *this;
 863     }
 864
 865   template<typename _Tp>
 866     inline complex<double>&
 867     complex<double>::operator*=(const complex<_Tp>& __z)
 868     {
 869       _ComplexT __t;
 870       __real__ __t = __z.real();
 871       __imag__ __t = __z.imag();
 872       _M_value *= __t;
 873       return *this;
 874     }
 875
 876   template<typename _Tp>
 877     inline complex<double>&
 878     complex<double>::operator/=(const complex<_Tp>& __z)
 879     {
 880       _ComplexT __t;
 881       __real__ __t = __z.real();
 882       __imag__ __t = __z.imag();
 883       _M_value /= __t;
 884       return *this;
 885     }
 886
 887   // 26.2.3  complex specializations
 888   // complex<long double> specialization
 889   template<> class complex<long double>
 890   {
 891   public:
 892     typedef long double value_type;
 893
 894     complex(long double = 0.0L, long double = 0.0L);
 895 #ifdef _GLIBCXX_BUGGY_COMPLEX
 896     complex(const complex& __z) : _M_value(__z._M_value) { }
 897 #endif
 898     complex(const complex<float>&);
 899     complex(const complex<double>&);
 900
 901     long double real() const;
 902     long double imag() const;
 903
 904     complex<long double>& operator= (long double);
 905     complex<long double>& operator+= (long double);
 906     complex<long double>& operator-= (long double);
 907     complex<long double>& operator*= (long double);
 908     complex<long double>& operator/= (long double);
 909
 910     // The compiler knows how to do this efficiently
 911     // complex& operator= (const complex&);
 912     template<typename _Tp>
 913       complex<long double>& operator=(const complex<_Tp>&);
 914     template<typename _Tp>
 915       complex<long double>& operator+=(const complex<_Tp>&);
 916     template<typename _Tp>
 917       complex<long double>& operator-=(const complex<_Tp>&);
 918     template<typename _Tp>
 919       complex<long double>& operator*=(const complex<_Tp>&);
 920     template<typename _Tp>
 921       complex<long double>& operator/=(const complex<_Tp>&);
 922
 923   private:
 924     typedef __complex__ long double _ComplexT;
 925     _ComplexT _M_value;
 926
 927     complex(_ComplexT __z) : _M_value(__z) { }
 928
 929     friend class complex<float>;
 930     friend class complex<double>;
 931   };
 932
 933   inline
 934   complex<long double>::complex(long double __r, long double __i)
 935   {
 936     __real__ _M_value = __r;
 937     __imag__ _M_value = __i;
 938   }
 939
 940   inline long double
 941   complex<long double>::real() const
 942   { return __real__ _M_value; }
 943
 944   inline long double
 945   complex<long double>::imag() const
 946   { return __imag__ _M_value; }
 947
 948   inline complex<long double>&
 949   complex<long double>::operator=(long double __r)
 950   {
 951     __real__ _M_value = __r;
 952     __imag__ _M_value = 0.0L;
 953     return *this;
 954   }
 955
 956   inline complex<long double>&
 957   complex<long double>::operator+=(long double __r)
 958   {
 959     __real__ _M_value += __r;
 960     return *this;
 961   }
 962
 963   inline complex<long double>&
 964   complex<long double>::operator-=(long double __r)
 965   {
 966     __real__ _M_value -= __r;
 967     return *this;
 968   }
 969
 970   inline complex<long double>&
 971   complex<long double>::operator*=(long double __r)
 972   {
 973     _M_value *= __r;
 974     return *this;
 975   }
 976
 977   inline complex<long double>&
 978   complex<long double>::operator/=(long double __r)
 979   {
 980     _M_value /= __r;
 981     return *this;
 982   }
 983
 984   template<typename _Tp>
 985     inline complex<long double>&
 986     complex<long double>::operator=(const complex<_Tp>& __z)
 987     {
 988       __real__ _M_value = __z.real();
 989       __imag__ _M_value = __z.imag();
 990       return *this;
 991     }
 992
 993   template<typename _Tp>
 994     inline complex<long double>&
 995     complex<long double>::operator+=(const complex<_Tp>& __z)
 996     {
 997       __real__ _M_value += __z.real();
 998       __imag__ _M_value += __z.imag();
 999       return *this;
1000     }
1001
1002   template<typename _Tp>
1003     inline complex<long double>&
1004     complex<long double>::operator-=(const complex<_Tp>& __z)
1005     {
1006       __real__ _M_value -= __z.real();
1007       __imag__ _M_value -= __z.imag();
1008       return *this;
1009     }
1010
1011   template<typename _Tp>
1012     inline complex<long double>&
1013     complex<long double>::operator*=(const complex<_Tp>& __z)
1014     {
1015       _ComplexT __t;
1016       __real__ __t = __z.real();
1017       __imag__ __t = __z.imag();
1018       _M_value *= __t;
1019       return *this;
1020     }
1021
1022   template<typename _Tp>
1023     inline complex<long double>&
1024     complex<long double>::operator/=(const complex<_Tp>& __z)
1025     {
1026       _ComplexT __t;
1027       __real__ __t = __z.real();
1028       __imag__ __t = __z.imag();
1029       _M_value /= __t;
1030       return *this;
1031     }
1032
1033   // These bits have to be at the end of this file, so that the
1034   // specializations have all been defined.
1035   // ??? No, they have to be there because of compiler limitation at
1036   // inlining.  It suffices that class specializations be defined.
1037   inline
1038   complex<float>::complex(const complex<double>& __z)
1039   : _M_value(_ComplexT(__z._M_value)) { }
1040
1041   inline
1042   complex<float>::complex(const complex<long double>& __z)
1043   : _M_value(_ComplexT(__z._M_value)) { }
1044
1045   inline
1046   complex<double>::complex(const complex<float>& __z)
1047   : _M_value(_ComplexT(__z._M_value)) { }
1048
1049   inline
1050   complex<double>::complex(const complex<long double>& __z)
1051   {
1052     __real__ _M_value = __z.real();
1053     __imag__ _M_value = __z.imag();
1054   }
1055
1056   inline
1057   complex<long double>::complex(const complex<float>& __z)
1058   : _M_value(_ComplexT(__z._M_value)) { }
1059
1060   inline
1061   complex<long double>::complex(const complex<double>& __z)
1062   : _M_value(_ComplexT(__z._M_value)) { }
1063 } // namespace std
1064
1065 #endif  /* _GLIBCXX_COMPLEX */