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

   1 // The template and inlines for the -*- C++ -*- complex number classes.
   2
   3 // Copyright (C) 1997, 1998, 1999, 2000, 2001 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 2, 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 // You should have received a copy of the GNU General Public License along
  17 // with this library; see the file COPYING.  If not, write to the Free
  18 // Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
  19 // USA.
  20
  21 // As a special exception, you may use this file as part of a free software
  22 // library without restriction.  Specifically, if other files instantiate
  23 // templates or use macros or inline functions from this file, or you compile
  24 // this file and link it with other files to produce an executable, this
  25 // file does not by itself cause the resulting executable to be covered by
  26 // the GNU General Public License.  This exception does not however
  27 // invalidate any other reasons why the executable file might be covered by
  28 // the GNU General Public License.
  29
  30 //
  31 // ISO C++ 14882: 26.2  Complex Numbers
  32 // Note: this is not a conforming implementation.
  33 // Initially implemented by Ulrich Drepper <drepper@cygnus.com>
  34 // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
  35 //
  36
  37 #ifndef _CPP_COMPLEX
  38 #define _CPP_COMPLEX    1
  39
  40 #pragma GCC system_header
  41
  42 #include <bits/c++config.h>
  43 #include <bits/std_cmath.h>
  44 #include <bits/std_sstream.h>
  45
  46 namespace std
  47 {
  48   // Forward declarations
  49   template<typename _Tp> class complex;
  50   template<> class complex<float>;
  51   template<> class complex<double>;
  52   template<> class complex<long double>;
  53
  54   template<typename _Tp> _Tp abs(const complex<_Tp>&);
  55   template<typename _Tp> _Tp arg(const complex<_Tp>&);
  56   template<typename _Tp> _Tp norm(const complex<_Tp>&);
  57
  58   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
  59   template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp&);
  60
  61   // Transcendentals:
  62   template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
  63   template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
  64   template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
  65   template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
  66   template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
  67   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
  68   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
  69   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
  70                                            const complex<_Tp>&);
  71   template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
  72   template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
  73   template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
  74   template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
  75   template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
  76   template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
  77
  78
  79   // 26.2.2  Primary template class complex
  80   template<typename _Tp>
  81     class complex
  82     {
  83     public:
  84       typedef _Tp value_type;
  85
  86       complex(const _Tp& = _Tp(), const _Tp & = _Tp());
  87
  88       // Let's the compiler synthetize the copy constructor
  89       // complex (const complex<_Tp>&);
  90       template<typename _Up>
  91         complex(const complex<_Up>&);
  92
  93       _Tp real() const;
  94       _Tp imag() const;
  95
  96       complex<_Tp>& operator=(const _Tp&);
  97       complex<_Tp>& operator+=(const _Tp&);
  98       complex<_Tp>& operator-=(const _Tp&);
  99       complex<_Tp>& operator*=(const _Tp&);
 100       complex<_Tp>& operator/=(const _Tp&);
 101
 102       // Let's the compiler synthetize the
 103       // copy and assignment operator
 104       // complex<_Tp>& operator= (const complex<_Tp>&);
 105       template<typename _Up>
 106         complex<_Tp>& operator=(const complex<_Up>&);
 107       template<typename _Up>
 108         complex<_Tp>& operator+=(const complex<_Up>&);
 109       template<typename _Up>
 110         complex<_Tp>& operator-=(const complex<_Up>&);
 111       template<typename _Up>
 112         complex<_Tp>& operator*=(const complex<_Up>&);
 113       template<typename _Up>
 114         complex<_Tp>& operator/=(const complex<_Up>&);
 115
 116     private:
 117       _Tp _M_real, _M_imag;
 118     };
 119
 120   template<typename _Tp>
 121     inline _Tp
 122     complex<_Tp>::real() const { return _M_real; }
 123
 124   template<typename _Tp>
 125     inline _Tp
 126     complex<_Tp>::imag() const { return _M_imag; }
 127
 128   template<typename _Tp>
 129     inline
 130     complex<_Tp>::complex(const _Tp& __r, const _Tp& __i)
 131     : _M_real(__r), _M_imag(__i) { }
 132
 133   template<typename _Tp>
 134     template<typename _Up>
 135     inline
 136     complex<_Tp>::complex(const complex<_Up>& __z)
 137     : _M_real(__z.real()), _M_imag(__z.imag()) { }
 138
 139   template<typename _Tp>
 140     complex<_Tp>&
 141     complex<_Tp>::operator=(const _Tp& __t)
 142     {
 143      _M_real = __t;
 144      _M_imag = _Tp();
 145      return *this;
 146     }
 147
 148   // 26.2.5/1
 149   template<typename _Tp>
 150     inline complex<_Tp>&
 151     complex<_Tp>::operator+=(const _Tp& __t)
 152     {
 153       _M_real += __t;
 154       return *this;
 155     }
 156
 157   // 26.2.5/3
 158   template<typename _Tp>
 159     inline complex<_Tp>&
 160     complex<_Tp>::operator-=(const _Tp& __t)
 161     {
 162       _M_real -= __t;
 163       return *this;
 164     }
 165
 166   // 26.2.5/5
 167   template<typename _Tp>
 168     complex<_Tp>&
 169     complex<_Tp>::operator*=(const _Tp& __t)
 170     {
 171       _M_real *= __t;
 172       _M_imag *= __t;
 173       return *this;
 174     }
 175
 176   // 26.2.5/7
 177   template<typename _Tp>
 178     complex<_Tp>&
 179     complex<_Tp>::operator/=(const _Tp& __t)
 180     {
 181       _M_real /= __t;
 182       _M_imag /= __t;
 183       return *this;
 184     }
 185
 186   template<typename _Tp>
 187     template<typename _Up>
 188     complex<_Tp>&
 189     complex<_Tp>::operator=(const complex<_Up>& __z)
 190     {
 191       _M_real = __z.real();
 192       _M_imag = __z.imag();
 193       return *this;
 194     }
 195
 196   // 26.2.5/9
 197   template<typename _Tp>
 198     template<typename _Up>
 199     complex<_Tp>&
 200     complex<_Tp>::operator+=(const complex<_Up>& __z)
 201     {
 202       _M_real += __z.real();
 203       _M_imag += __z.imag();
 204       return *this;
 205     }
 206
 207   // 26.2.5/11
 208   template<typename _Tp>
 209     template<typename _Up>
 210     complex<_Tp>&
 211     complex<_Tp>::operator-=(const complex<_Up>& __z)
 212     {
 213       _M_real -= __z.real();
 214       _M_imag -= __z.imag();
 215       return *this;
 216     }
 217
 218   // 26.2.5/13
 219   // XXX: This is a grammar school implementation.
 220   template<typename _Tp>
 221     template<typename _Up>
 222     complex<_Tp>&
 223     complex<_Tp>::operator*=(const complex<_Up>& __z)
 224     {
 225       const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
 226       _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
 227       _M_real = __r;
 228       return *this;
 229     }
 230
 231   // 26.2.5/15
 232   // XXX: This is a grammar school implementation.
 233   template<typename _Tp>
 234     template<typename _Up>
 235     complex<_Tp>&
 236     complex<_Tp>::operator/=(const complex<_Up>& __z)
 237     {
 238       const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
 239       const _Tp __n = norm(__z);
 240       _M_imag = (_M_real * __z.imag() - _M_imag * __z.real()) / __n;
 241       _M_real = __r / __n;
 242       return *this;
 243     }
 244
 245   // Operators:
 246   template<typename _Tp>
 247     inline complex<_Tp>
 248     operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
 249     { return complex<_Tp> (__x) += __y; }
 250
 251   template<typename _Tp>
 252     inline complex<_Tp>
 253     operator+(const complex<_Tp>& __x, const _Tp& __y)
 254     { return complex<_Tp> (__x) += __y; }
 255
 256   template<typename _Tp>
 257     inline complex<_Tp>
 258     operator+(const _Tp& __x, const complex<_Tp>& __y)
 259     { return complex<_Tp> (__y) += __x; }
 260
 261   template<typename _Tp>
 262     inline complex<_Tp>
 263     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
 264     { return complex<_Tp> (__x) -= __y; }
 265
 266   template<typename _Tp>
 267     inline complex<_Tp>
 268     operator-(const complex<_Tp>& __x, const _Tp& __y)
 269     { return complex<_Tp> (__x) -= __y; }
 270
 271   template<typename _Tp>
 272     inline complex<_Tp>
 273     operator-(const _Tp& __x, const complex<_Tp>& __y)
 274     { return complex<_Tp> (__x) -= __y; }
 275
 276   template<typename _Tp>
 277     inline complex<_Tp>
 278     operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
 279     { return complex<_Tp> (__x) *= __y; }
 280
 281   template<typename _Tp>
 282     inline complex<_Tp>
 283     operator*(const complex<_Tp>& __x, const _Tp& __y)
 284     { return complex<_Tp> (__x) *= __y; }
 285
 286   template<typename _Tp>
 287     inline complex<_Tp>
 288     operator*(const _Tp& __x, const complex<_Tp>& __y)
 289     { return complex<_Tp> (__y) *= __x; }
 290
 291   template<typename _Tp>
 292     inline complex<_Tp>
 293     operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
 294     { return complex<_Tp> (__x) /= __y; }
 295
 296   template<typename _Tp>
 297     inline complex<_Tp>
 298     operator/(const complex<_Tp>& __x, const _Tp& __y)
 299     { return complex<_Tp> (__x) /= __y; }
 300
 301   template<typename _Tp>
 302     inline complex<_Tp>
 303     operator/(const _Tp& __x, const complex<_Tp>& __y)
 304     { return complex<_Tp> (__x) /= __y; }
 305
 306   template<typename _Tp>
 307     inline complex<_Tp>
 308     operator+(const complex<_Tp>& __x)
 309     { return __x; }
 310
 311   template<typename _Tp>
 312     inline complex<_Tp>
 313     operator-(const complex<_Tp>& __x)
 314     {  return complex<_Tp>(-__x.real(), -__x.imag()); }
 315
 316   template<typename _Tp>
 317     inline bool
 318     operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
 319     { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
 320
 321   template<typename _Tp>
 322     inline bool
 323     operator==(const complex<_Tp>& __x, const _Tp& __y)
 324     { return __x.real() == __y && __x.imag() == _Tp(); }
 325
 326   template<typename _Tp>
 327     inline bool
 328     operator==(const _Tp& __x, const complex<_Tp>& __y)
 329     { return __x == __y.real() && _Tp() == __y.imag(); }
 330
 331   template<typename _Tp>
 332     inline bool
 333     operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
 334     { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
 335
 336   template<typename _Tp>
 337     inline bool
 338     operator!=(const complex<_Tp>& __x, const _Tp& __y)
 339     { return __x.real() != __y || __x.imag() != _Tp(); }
 340
 341   template<typename _Tp>
 342     inline bool
 343     operator!=(const _Tp& __x, const complex<_Tp>& __y)
 344     { return __x != __y.real() || _Tp() != __y.imag(); }
 345
 346   template<typename _Tp, typename _CharT, class _Traits>
 347     basic_istream<_CharT, _Traits>&
 348     operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
 349     {
 350       _Tp __re_x, __im_x;
 351       _CharT __ch;
 352       __is >> __ch;
 353       if (__ch == '(')
 354         {
 355           __is >> __re_x >> __ch;
 356           if (__ch == ',')
 357             {
 358               __is >> __im_x >> __ch;
 359               if (__ch == ')')
 360                 __x = complex<_Tp>(__re_x, __im_x);
 361               else
 362                 __is.setstate(ios_base::failbit);
 363             }
 364           else if (__ch == ')')
 365             __x = complex<_Tp>(__re_x, _Tp(0));
 366           else
 367             __is.setstate(ios_base::failbit);
 368         }
 369       else
 370         {
 371           __is.putback(__ch);
 372           __is >> __re_x;
 373           __x = complex<_Tp>(__re_x, _Tp(0));
 374         }
 375       return __is;
 376     }
 377
 378   template<typename _Tp, typename _CharT, class _Traits>
 379     basic_ostream<_CharT, _Traits>&
 380     operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
 381     {
 382       basic_ostringstream<_CharT, _Traits> __s;
 383       __s.flags(__os.flags());
 384       __s.imbue(__os.getloc());
 385       __s.precision(__os.precision());
 386       __s << '(' << __x.real() << "," << __x.imag() << ')';
 387       return __os << __s.str();
 388     }
 389
 390   // Values
 391   template<typename _Tp>
 392     inline _Tp
 393     real(const complex<_Tp>& __z)
 394     { return __z.real(); }
 395
 396   template<typename _Tp>
 397     inline _Tp
 398     imag(const complex<_Tp>& __z)
 399     { return __z.imag(); }
 400
 401   template<typename _Tp>
 402     inline _Tp
 403     abs(const complex<_Tp>& __z)
 404     {
 405       _Tp __x = __z.real();
 406       _Tp __y = __z.imag();
 407       const _Tp __s = abs(__x) + abs(__y);
 408       if (__s == _Tp())  // well ...
 409         return __s;
 410       __x /= __s;
 411       __y /= __s;
 412       return __s * sqrt(__x * __x + __y * __y);
 413     }
 414
 415   template<typename _Tp>
 416     inline _Tp
 417     arg(const complex<_Tp>& __z)
 418     { return atan2(__z.imag(), __z.real()); }
 419
 420   template<typename _Tp>
 421     inline _Tp
 422     norm(const complex<_Tp>& __z)
 423     {
 424       _Tp __res = abs(__z);
 425       return __res * __res;
 426     }
 427
 428   template<typename _Tp>
 429     inline complex<_Tp>
 430     polar(const _Tp& __rho, const _Tp& __theta)
 431     { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
 432
 433   template<typename _Tp>
 434     inline complex<_Tp>
 435     conj(const complex<_Tp>& __z)
 436     { return complex<_Tp>(__z.real(), -__z.imag()); }
 437
 438   // Transcendentals
 439   template<typename _Tp>
 440     inline complex<_Tp>
 441     cos(const complex<_Tp>& __z)
 442     {
 443       const _Tp __x = __z.real();
 444       const _Tp __y = __z.imag();
 445       return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
 446     }
 447
 448   template<typename _Tp>
 449     inline complex<_Tp>
 450     cosh(const complex<_Tp>& __z)
 451     {
 452       const _Tp __x = __z.real();
 453       const _Tp __y = __z.imag();
 454       return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
 455     }
 456
 457   template<typename _Tp>
 458     inline complex<_Tp>
 459     exp(const complex<_Tp>& __z)
 460     { return polar(exp(__z.real()), __z.imag()); }
 461
 462   template<typename _Tp>
 463     inline complex<_Tp>
 464     log(const complex<_Tp>& __z)
 465     { return complex<_Tp>(log(abs(__z)), arg(__z)); }
 466
 467   template<typename _Tp>
 468     inline complex<_Tp>
 469     log10(const complex<_Tp>& __z)
 470     { return log(__z) / log(_Tp(10.0)); }
 471
 472   template<typename _Tp>
 473     inline complex<_Tp>
 474     sin(const complex<_Tp>& __z)
 475     {
 476       const _Tp __x = __z.real();
 477       const _Tp __y = __z.imag();
 478       return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
 479     }
 480
 481   template<typename _Tp>
 482     inline complex<_Tp>
 483     sinh(const complex<_Tp>& __z)
 484     {
 485       const _Tp __x = __z.real();
 486       const _Tp  __y = __z.imag();
 487       return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
 488     }
 489
 490   template<typename _Tp>
 491     complex<_Tp>
 492     sqrt(const complex<_Tp>& __z)
 493     {
 494       _Tp __x = __z.real();
 495       _Tp __y = __z.imag();
 496
 497       if (__x == _Tp())
 498         {
 499           _Tp __t = sqrt(abs(__y) / 2);
 500           return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
 501         }
 502       else
 503         {
 504           _Tp __t = sqrt(2 * (abs(__z) + abs(__x)));
 505           _Tp __u = __t / 2;
 506           return __x > _Tp()
 507             ? complex<_Tp>(__u, __y / __t)
 508             : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
 509         }
 510     }
 511
 512   template<typename _Tp>
 513     inline complex<_Tp>
 514     tan(const complex<_Tp>& __z)
 515     {
 516       return sin(__z) / cos(__z);
 517     }
 518
 519   template<typename _Tp>
 520     inline complex<_Tp>
 521     tanh(const complex<_Tp>& __z)
 522     {
 523       return sinh(__z) / cosh(__z);
 524     }
 525
 526   template<typename _Tp>
 527     inline complex<_Tp>
 528     pow(const complex<_Tp>& __z, int __n)
 529     {
 530       return __pow_helper(__z, __n);
 531     }
 532
 533   template<typename _Tp>
 534     inline complex<_Tp>
 535     pow(const complex<_Tp>& __x, const _Tp& __y)
 536     {
 537       return exp(__y * log(__x));
 538     }
 539
 540   template<typename _Tp>
 541     inline complex<_Tp>
 542     pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
 543     {
 544       return exp(__y * log(__x));
 545     }
 546
 547   template<typename _Tp>
 548     inline complex<_Tp>
 549     pow(const _Tp& __x, const complex<_Tp>& __y)
 550     {
 551       return exp(__y * log(__x));
 552     }
 553
 554   // 26.2.3  complex specializations
 555   // complex<float> specialization
 556   template<> class complex<float>
 557   {
 558   public:
 559     typedef float value_type;
 560
 561     complex(float = 0.0f, float = 0.0f);
 562 #ifdef _GLIBCPP_BUGGY_COMPLEX
 563     complex(const complex& __z) : _M_value(__z._M_value) { }
 564 #endif
 565     explicit complex(const complex<double>&);
 566     explicit complex(const complex<long double>&);
 567
 568     float real() const;
 569     float imag() const;
 570
 571     complex<float>& operator=(float);
 572     complex<float>& operator+=(float);
 573     complex<float>& operator-=(float);
 574     complex<float>& operator*=(float);
 575     complex<float>& operator/=(float);
 576
 577     // Let's the compiler synthetize the copy and assignment
 578     // operator.  It always does a pretty good job.
 579     // complex& operator= (const complex&);
 580     template<typename _Tp>
 581       complex<float>&operator=(const complex<_Tp>&);
 582     template<typename _Tp>
 583       complex<float>& operator+=(const complex<_Tp>&);
 584     template<class _Tp>
 585       complex<float>& operator-=(const complex<_Tp>&);
 586     template<class _Tp>
 587       complex<float>& operator*=(const complex<_Tp>&);
 588     template<class _Tp>
 589       complex<float>&operator/=(const complex<_Tp>&);
 590
 591   private:
 592     typedef __complex__ float _ComplexT;
 593     _ComplexT _M_value;
 594
 595     complex(_ComplexT __z) : _M_value(__z) { }
 596
 597     friend class complex<double>;
 598     friend class complex<long double>;
 599   };
 600
 601   inline float
 602   complex<float>::real() const
 603   { return __real__ _M_value; }
 604
 605   inline float
 606   complex<float>::imag() const
 607   { return __imag__ _M_value; }
 608
 609   inline
 610   complex<float>::complex(float r, float i)
 611   {
 612     __real__ _M_value = r;
 613     __imag__ _M_value = i;
 614   }
 615
 616   inline complex<float>&
 617   complex<float>::operator=(float __f)
 618   {
 619     __real__ _M_value = __f;
 620     __imag__ _M_value = 0.0f;
 621     return *this;
 622   }
 623
 624   inline complex<float>&
 625   complex<float>::operator+=(float __f)
 626   {
 627     __real__ _M_value += __f;
 628     return *this;
 629   }
 630
 631   inline complex<float>&
 632   complex<float>::operator-=(float __f)
 633   {
 634     __real__ _M_value -= __f;
 635     return *this;
 636   }
 637
 638   inline complex<float>&
 639   complex<float>::operator*=(float __f)
 640   {
 641     _M_value *= __f;
 642     return *this;
 643   }
 644
 645   inline complex<float>&
 646   complex<float>::operator/=(float __f)
 647   {
 648     _M_value /= __f;
 649     return *this;
 650   }
 651
 652   template<typename _Tp>
 653   inline complex<float>&
 654   complex<float>::operator=(const complex<_Tp>& __z)
 655   {
 656     __real__ _M_value = __z.real();
 657     __imag__ _M_value = __z.imag();
 658     return *this;
 659   }
 660
 661   template<typename _Tp>
 662   inline complex<float>&
 663   complex<float>::operator+=(const complex<_Tp>& __z)
 664   {
 665     __real__ _M_value += __z.real();
 666     __imag__ _M_value += __z.imag();
 667     return *this;
 668   }
 669
 670   template<typename _Tp>
 671     inline complex<float>&
 672     complex<float>::operator-=(const complex<_Tp>& __z)
 673     {
 674      __real__ _M_value -= __z.real();
 675      __imag__ _M_value -= __z.imag();
 676      return *this;
 677     }
 678
 679   template<typename _Tp>
 680     inline complex<float>&
 681     complex<float>::operator*=(const complex<_Tp>& __z)
 682     {
 683       _ComplexT __t;
 684       __real__ __t = __z.real();
 685       __imag__ __t = __z.imag();
 686       _M_value *= __t;
 687       return *this;
 688     }
 689
 690   template<typename _Tp>
 691     inline complex<float>&
 692     complex<float>::operator/=(const complex<_Tp>& __z)
 693     {
 694       _ComplexT __t;
 695       __real__ __t = __z.real();
 696       __imag__ __t = __z.imag();
 697       _M_value /= __t;
 698       return *this;
 699     }
 700
 701   // 26.2.3  complex specializations
 702   // complex<double> specialization
 703   template<> class complex<double>
 704   {
 705   public:
 706     typedef double value_type;
 707
 708     complex(double  =0.0, double =0.0);
 709 #ifdef _GLIBCPP_BUGGY_COMPLEX
 710     complex(const complex& __z) : _M_value(__z._M_value) { }
 711 #endif
 712     complex(const complex<float>&);
 713     explicit complex(const complex<long double>&);
 714
 715     double real() const;
 716     double imag() const;
 717
 718     complex<double>& operator=(double);
 719     complex<double>& operator+=(double);
 720     complex<double>& operator-=(double);
 721     complex<double>& operator*=(double);
 722     complex<double>& operator/=(double);
 723
 724     // The compiler will synthetize this, efficiently.
 725     // complex& operator= (const complex&);
 726     template<typename _Tp>
 727       complex<double>& operator=(const complex<_Tp>&);
 728     template<typename _Tp>
 729       complex<double>& operator+=(const complex<_Tp>&);
 730     template<typename _Tp>
 731       complex<double>& operator-=(const complex<_Tp>&);
 732     template<typename _Tp>
 733       complex<double>& operator*=(const complex<_Tp>&);
 734     template<typename _Tp>
 735       complex<double>& operator/=(const complex<_Tp>&);
 736
 737   private:
 738     typedef __complex__ double _ComplexT;
 739     _ComplexT _M_value;
 740
 741     complex(_ComplexT __z) : _M_value(__z) { }
 742
 743     friend class complex<float>;
 744     friend class complex<long double>;
 745   };
 746
 747   inline double
 748   complex<double>::real() const
 749   { return __real__ _M_value; }
 750
 751   inline double
 752   complex<double>::imag() const
 753   { return __imag__ _M_value; }
 754
 755   inline
 756   complex<double>::complex(double __r, double __i)
 757   {
 758     __real__ _M_value = __r;
 759     __imag__ _M_value = __i;
 760   }
 761
 762   inline complex<double>&
 763   complex<double>::operator=(double __d)
 764   {
 765     __real__ _M_value = __d;
 766     __imag__ _M_value = 0.0;
 767     return *this;
 768   }
 769
 770   inline complex<double>&
 771   complex<double>::operator+=(double __d)
 772   {
 773     __real__ _M_value += __d;
 774     return *this;
 775   }
 776
 777   inline complex<double>&
 778   complex<double>::operator-=(double __d)
 779   {
 780     __real__ _M_value -= __d;
 781     return *this;
 782   }
 783
 784   inline complex<double>&
 785   complex<double>::operator*=(double __d)
 786   {
 787     _M_value *= __d;
 788     return *this;
 789   }
 790
 791   inline complex<double>&
 792   complex<double>::operator/=(double __d)
 793   {
 794     _M_value /= __d;
 795     return *this;
 796   }
 797
 798   template<typename _Tp>
 799     inline complex<double>&
 800     complex<double>::operator=(const complex<_Tp>& __z)
 801     {
 802       __real__ _M_value = __z.real();
 803       __imag__ _M_value = __z.imag();
 804       return *this;
 805     }
 806
 807   template<typename _Tp>
 808     inline complex<double>&
 809     complex<double>::operator+=(const complex<_Tp>& __z)
 810     {
 811       __real__ _M_value += __z.real();
 812       __imag__ _M_value += __z.imag();
 813       return *this;
 814     }
 815
 816   template<typename _Tp>
 817     inline complex<double>&
 818     complex<double>::operator-=(const complex<_Tp>& __z)
 819     {
 820       __real__ _M_value -= __z.real();
 821       __imag__ _M_value -= __z.imag();
 822       return *this;
 823     }
 824
 825   template<typename _Tp>
 826     inline complex<double>&
 827     complex<double>::operator*=(const complex<_Tp>& __z)
 828     {
 829       _ComplexT __t;
 830       __real__ __t = __z.real();
 831       __imag__ __t = __z.imag();
 832       _M_value *= __t;
 833       return *this;
 834     }
 835
 836   template<typename _Tp>
 837     inline complex<double>&
 838     complex<double>::operator/=(const complex<_Tp>& __z)
 839     {
 840       _ComplexT __t;
 841       __real__ __t = __z.real();
 842       __imag__ __t = __z.imag();
 843       _M_value /= __t;
 844       return *this;
 845     }
 846
 847   // 26.2.3  complex specializations
 848   // complex<long double> specialization
 849   template<> class complex<long double>
 850   {
 851   public:
 852     typedef long double value_type;
 853
 854     complex(long double = 0.0L, long double = 0.0L);
 855 #ifdef _GLIBCPP_BUGGY_COMPLEX
 856     complex(const complex& __z) : _M_value(__z._M_value) { }
 857 #endif
 858     complex(const complex<float>&);
 859     complex(const complex<double>&);
 860
 861     long double real() const;
 862     long double imag() const;
 863
 864     complex<long double>& operator= (long double);
 865     complex<long double>& operator+= (long double);
 866     complex<long double>& operator-= (long double);
 867     complex<long double>& operator*= (long double);
 868     complex<long double>& operator/= (long double);
 869
 870     // The compiler knows how to do this efficiently
 871     // complex& operator= (const complex&);
 872     template<typename _Tp>
 873       complex<long double>& operator=(const complex<_Tp>&);
 874     template<typename _Tp>
 875       complex<long double>& operator+=(const complex<_Tp>&);
 876     template<typename _Tp>
 877       complex<long double>& operator-=(const complex<_Tp>&);
 878     template<typename _Tp>
 879       complex<long double>& operator*=(const complex<_Tp>&);
 880     template<typename _Tp>
 881       complex<long double>& operator/=(const complex<_Tp>&);
 882
 883   private:
 884     typedef __complex__ long double _ComplexT;
 885     _ComplexT _M_value;
 886
 887     complex(_ComplexT __z) : _M_value(__z) { }
 888
 889     friend class complex<float>;
 890     friend class complex<double>;
 891   };
 892
 893   inline
 894   complex<long double>::complex(long double __r, long double __i)
 895   {
 896     __real__ _M_value = __r;
 897     __imag__ _M_value = __i;
 898   }
 899
 900   inline long double
 901   complex<long double>::real() const
 902   { return __real__ _M_value; }
 903
 904   inline long double
 905   complex<long double>::imag() const
 906   { return __imag__ _M_value; }
 907
 908   inline complex<long double>&
 909   complex<long double>::operator=(long double __r)
 910   {
 911     __real__ _M_value = __r;
 912     __imag__ _M_value = 0.0L;
 913     return *this;
 914   }
 915
 916   inline complex<long double>&
 917   complex<long double>::operator+=(long double __r)
 918   {
 919     __real__ _M_value += __r;
 920     return *this;
 921   }
 922
 923   inline complex<long double>&
 924   complex<long double>::operator-=(long double __r)
 925   {
 926     __real__ _M_value -= __r;
 927     return *this;
 928   }
 929
 930   inline complex<long double>&
 931   complex<long double>::operator*=(long double __r)
 932   {
 933     _M_value *= __r;
 934     return *this;
 935   }
 936
 937   inline complex<long double>&
 938   complex<long double>::operator/=(long double __r)
 939   {
 940     _M_value /= __r;
 941     return *this;
 942   }
 943
 944   template<typename _Tp>
 945     inline complex<long double>&
 946     complex<long double>::operator=(const complex<_Tp>& __z)
 947     {
 948       __real__ _M_value = __z.real();
 949       __imag__ _M_value = __z.imag();
 950       return *this;
 951     }
 952
 953   template<typename _Tp>
 954     inline complex<long double>&
 955     complex<long double>::operator+=(const complex<_Tp>& __z)
 956     {
 957       __real__ _M_value += __z.real();
 958       __imag__ _M_value += __z.imag();
 959       return *this;
 960     }
 961
 962   template<typename _Tp>
 963     inline complex<long double>&
 964     complex<long double>::operator-=(const complex<_Tp>& __z)
 965     {
 966       __real__ _M_value -= __z.real();
 967       __imag__ _M_value -= __z.imag();
 968       return *this;
 969     }
 970
 971   template<typename _Tp>
 972     inline complex<long double>&
 973     complex<long double>::operator*=(const complex<_Tp>& __z)
 974     {
 975       _ComplexT __t;
 976       __real__ __t = __z.real();
 977       __imag__ __t = __z.imag();
 978       _M_value *= __t;
 979       return *this;
 980     }
 981
 982   template<typename _Tp>
 983     inline complex<long double>&
 984     complex<long double>::operator/=(const complex<_Tp>& __z)
 985     {
 986       _ComplexT __t;
 987       __real__ __t = __z.real();
 988       __imag__ __t = __z.imag();
 989       _M_value /= __t;
 990       return *this;
 991     }
 992
 993   // These bits have to be at the end of this file, so that the
 994   // specializations have all been defined.
 995   // ??? No, they have to be there because of compiler limitation at
 996   // inlining.  It suffices that class specializations be defined.
 997   inline
 998   complex<float>::complex(const complex<double>& __z)
 999   : _M_value(_ComplexT(__z._M_value)) { }
1000
1001   inline
1002   complex<float>::complex(const complex<long double>& __z)
1003   : _M_value(_ComplexT(__z._M_value)) { }
1004
1005   inline
1006   complex<double>::complex(const complex<float>& __z)
1007   : _M_value(_ComplexT(__z._M_value)) { }
1008
1009   inline
1010   complex<double>::complex(const complex<long double>& __z)
1011   {
1012     __real__ _M_value = __z.real();
1013     __imag__ _M_value = __z.imag();
1014   }
1015
1016   inline
1017   complex<long double>::complex(const complex<float>& __z)
1018   : _M_value(_ComplexT(__z._M_value)) { }
1019
1020   inline
1021   complex<long double>::complex(const complex<double>& __z)
1022   : _M_value(_ComplexT(__z._M_value)) { }
1023 } // namespace std
1024
1025 #endif  /* _CPP_COMPLEX */