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 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 /** @file std_complex.h
  38  *  This is an internal header file, included by other library headers.
  39  *  You should not attempt to use it directly.
  40  */
  41
  42 #ifndef _CPP_COMPLEX
  43 #define _CPP_COMPLEX    1
  44
  45 #pragma GCC system_header
  46
  47 #include <bits/c++config.h>
  48 #include <bits/cpp_type_traits.h>
  49 #include <cmath>
  50 #include <sstream>
  51
  52 namespace std
  53 {
  54   // Forward declarations
  55   template<typename _Tp> class complex;
  56   template<> class complex<float>;
  57   template<> class complex<double>;
  58   template<> class complex<long double>;
  59
  60   template<typename _Tp> _Tp abs(const complex<_Tp>&);
  61   template<typename _Tp> _Tp arg(const complex<_Tp>&);
  62   template<typename _Tp> _Tp norm(const complex<_Tp>&);
  63
  64   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
  65   template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
  66
  67   // Transcendentals:
  68   template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
  69   template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
  70   template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
  71   template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
  72   template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
  73   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
  74   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
  75   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
  76                                            const complex<_Tp>&);
  77   template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
  78   template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
  79   template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
  80   template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
  81   template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
  82   template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
  83
  84
  85   // 26.2.2  Primary template class complex
  86   template<typename _Tp>
  87     class complex
  88     {
  89     public:
  90       typedef _Tp value_type;
  91
  92       complex(const _Tp& = _Tp(), const _Tp & = _Tp());
  93
  94       // Let's the compiler synthetize the copy constructor
  95       // complex (const complex<_Tp>&);
  96       template<typename _Up>
  97         complex(const complex<_Up>&);
  98
  99       _Tp real() const;
 100       _Tp imag() const;
 101
 102       complex<_Tp>& operator=(const _Tp&);
 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
 108       // Let's the compiler synthetize the
 109       // copy and assignment operator
 110       // complex<_Tp>& operator= (const complex<_Tp>&);
 111       template<typename _Up>
 112         complex<_Tp>& operator=(const complex<_Up>&);
 113       template<typename _Up>
 114         complex<_Tp>& operator+=(const complex<_Up>&);
 115       template<typename _Up>
 116         complex<_Tp>& operator-=(const complex<_Up>&);
 117       template<typename _Up>
 118         complex<_Tp>& operator*=(const complex<_Up>&);
 119       template<typename _Up>
 120         complex<_Tp>& operator/=(const complex<_Up>&);
 121
 122     private:
 123       _Tp _M_real, _M_imag;
 124     };
 125
 126   template<typename _Tp>
 127     inline _Tp
 128     complex<_Tp>::real() const { return _M_real; }
 129
 130   template<typename _Tp>
 131     inline _Tp
 132     complex<_Tp>::imag() const { return _M_imag; }
 133
 134   template<typename _Tp>
 135     inline
 136     complex<_Tp>::complex(const _Tp& __r, const _Tp& __i)
 137     : _M_real(__r), _M_imag(__i) { }
 138
 139   template<typename _Tp>
 140     template<typename _Up>
 141     inline
 142     complex<_Tp>::complex(const complex<_Up>& __z)
 143     : _M_real(__z.real()), _M_imag(__z.imag()) { }
 144
 145   template<typename _Tp>
 146     complex<_Tp>&
 147     complex<_Tp>::operator=(const _Tp& __t)
 148     {
 149      _M_real = __t;
 150      _M_imag = _Tp();
 151      return *this;
 152     }
 153
 154   // 26.2.5/1
 155   template<typename _Tp>
 156     inline complex<_Tp>&
 157     complex<_Tp>::operator+=(const _Tp& __t)
 158     {
 159       _M_real += __t;
 160       return *this;
 161     }
 162
 163   // 26.2.5/3
 164   template<typename _Tp>
 165     inline complex<_Tp>&
 166     complex<_Tp>::operator-=(const _Tp& __t)
 167     {
 168       _M_real -= __t;
 169       return *this;
 170     }
 171
 172   // 26.2.5/5
 173   template<typename _Tp>
 174     complex<_Tp>&
 175     complex<_Tp>::operator*=(const _Tp& __t)
 176     {
 177       _M_real *= __t;
 178       _M_imag *= __t;
 179       return *this;
 180     }
 181
 182   // 26.2.5/7
 183   template<typename _Tp>
 184     complex<_Tp>&
 185     complex<_Tp>::operator/=(const _Tp& __t)
 186     {
 187       _M_real /= __t;
 188       _M_imag /= __t;
 189       return *this;
 190     }
 191
 192   template<typename _Tp>
 193     template<typename _Up>
 194     complex<_Tp>&
 195     complex<_Tp>::operator=(const complex<_Up>& __z)
 196     {
 197       _M_real = __z.real();
 198       _M_imag = __z.imag();
 199       return *this;
 200     }
 201
 202   // 26.2.5/9
 203   template<typename _Tp>
 204     template<typename _Up>
 205     complex<_Tp>&
 206     complex<_Tp>::operator+=(const complex<_Up>& __z)
 207     {
 208       _M_real += __z.real();
 209       _M_imag += __z.imag();
 210       return *this;
 211     }
 212
 213   // 26.2.5/11
 214   template<typename _Tp>
 215     template<typename _Up>
 216     complex<_Tp>&
 217     complex<_Tp>::operator-=(const complex<_Up>& __z)
 218     {
 219       _M_real -= __z.real();
 220       _M_imag -= __z.imag();
 221       return *this;
 222     }
 223
 224   // 26.2.5/13
 225   // XXX: This is a grammar school implementation.
 226   template<typename _Tp>
 227     template<typename _Up>
 228     complex<_Tp>&
 229     complex<_Tp>::operator*=(const complex<_Up>& __z)
 230     {
 231       const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
 232       _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
 233       _M_real = __r;
 234       return *this;
 235     }
 236
 237   // 26.2.5/15
 238   // XXX: This is a grammar school implementation.
 239   template<typename _Tp>
 240     template<typename _Up>
 241     complex<_Tp>&
 242     complex<_Tp>::operator/=(const complex<_Up>& __z)
 243     {
 244       const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
 245       const _Tp __n = norm(__z);
 246       _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
 247       _M_real = __r / __n;
 248       return *this;
 249     }
 250
 251   // Operators:
 252   template<typename _Tp>
 253     inline complex<_Tp>
 254     operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
 255     { return complex<_Tp> (__x) += __y; }
 256
 257   template<typename _Tp>
 258     inline complex<_Tp>
 259     operator+(const complex<_Tp>& __x, const _Tp& __y)
 260     { return complex<_Tp> (__x) += __y; }
 261
 262   template<typename _Tp>
 263     inline complex<_Tp>
 264     operator+(const _Tp& __x, const complex<_Tp>& __y)
 265     { return complex<_Tp> (__y) += __x; }
 266
 267   template<typename _Tp>
 268     inline complex<_Tp>
 269     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
 270     { return complex<_Tp> (__x) -= __y; }
 271
 272   template<typename _Tp>
 273     inline complex<_Tp>
 274     operator-(const complex<_Tp>& __x, const _Tp& __y)
 275     { return complex<_Tp> (__x) -= __y; }
 276
 277   template<typename _Tp>
 278     inline complex<_Tp>
 279     operator-(const _Tp& __x, const complex<_Tp>& __y)
 280     { return complex<_Tp> (__x) -= __y; }
 281
 282   template<typename _Tp>
 283     inline complex<_Tp>
 284     operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
 285     { return complex<_Tp> (__x) *= __y; }
 286
 287   template<typename _Tp>
 288     inline complex<_Tp>
 289     operator*(const complex<_Tp>& __x, const _Tp& __y)
 290     { return complex<_Tp> (__x) *= __y; }
 291
 292   template<typename _Tp>
 293     inline complex<_Tp>
 294     operator*(const _Tp& __x, const complex<_Tp>& __y)
 295     { return complex<_Tp> (__y) *= __x; }
 296
 297   template<typename _Tp>
 298     inline complex<_Tp>
 299     operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
 300     { return complex<_Tp> (__x) /= __y; }
 301
 302   template<typename _Tp>
 303     inline complex<_Tp>
 304     operator/(const complex<_Tp>& __x, const _Tp& __y)
 305     { return complex<_Tp> (__x) /= __y; }
 306
 307   template<typename _Tp>
 308     inline complex<_Tp>
 309     operator/(const _Tp& __x, const complex<_Tp>& __y)
 310     { return complex<_Tp> (__x) /= __y; }
 311
 312   template<typename _Tp>
 313     inline complex<_Tp>
 314     operator+(const complex<_Tp>& __x)
 315     { return __x; }
 316
 317   template<typename _Tp>
 318     inline complex<_Tp>
 319     operator-(const complex<_Tp>& __x)
 320     {  return complex<_Tp>(-__x.real(), -__x.imag()); }
 321
 322   template<typename _Tp>
 323     inline bool
 324     operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
 325     { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
 326
 327   template<typename _Tp>
 328     inline bool
 329     operator==(const complex<_Tp>& __x, const _Tp& __y)
 330     { return __x.real() == __y && __x.imag() == _Tp(); }
 331
 332   template<typename _Tp>
 333     inline bool
 334     operator==(const _Tp& __x, const complex<_Tp>& __y)
 335     { return __x == __y.real() && _Tp() == __y.imag(); }
 336
 337   template<typename _Tp>
 338     inline bool
 339     operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
 340     { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
 341
 342   template<typename _Tp>
 343     inline bool
 344     operator!=(const complex<_Tp>& __x, const _Tp& __y)
 345     { return __x.real() != __y || __x.imag() != _Tp(); }
 346
 347   template<typename _Tp>
 348     inline bool
 349     operator!=(const _Tp& __x, const complex<_Tp>& __y)
 350     { return __x != __y.real() || _Tp() != __y.imag(); }
 351
 352   template<typename _Tp, typename _CharT, class _Traits>
 353     basic_istream<_CharT, _Traits>&
 354     operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
 355     {
 356       _Tp __re_x, __im_x;
 357       _CharT __ch;
 358       __is >> __ch;
 359       if (__ch == '(')
 360         {
 361           __is >> __re_x >> __ch;
 362           if (__ch == ',')
 363             {
 364               __is >> __im_x >> __ch;
 365               if (__ch == ')')
 366                 __x = complex<_Tp>(__re_x, __im_x);
 367               else
 368                 __is.setstate(ios_base::failbit);
 369             }
 370           else if (__ch == ')')
 371             __x = complex<_Tp>(__re_x, _Tp(0));
 372           else
 373             __is.setstate(ios_base::failbit);
 374         }
 375       else
 376         {
 377           __is.putback(__ch);
 378           __is >> __re_x;
 379           __x = complex<_Tp>(__re_x, _Tp(0));
 380         }
 381       return __is;
 382     }
 383
 384   template<typename _Tp, typename _CharT, class _Traits>
 385     basic_ostream<_CharT, _Traits>&
 386     operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
 387     {
 388       basic_ostringstream<_CharT, _Traits> __s;
 389       __s.flags(__os.flags());
 390       __s.imbue(__os.getloc());
 391       __s.precision(__os.precision());
 392       __s << '(' << __x.real() << "," << __x.imag() << ')';
 393       return __os << __s.str();
 394     }
 395
 396   // Values
 397   template<typename _Tp>
 398     inline _Tp
 399     real(const complex<_Tp>& __z)
 400     { return __z.real(); }
 401
 402   template<typename _Tp>
 403     inline _Tp
 404     imag(const complex<_Tp>& __z)
 405     { return __z.imag(); }
 406
 407   template<typename _Tp>
 408     inline _Tp
 409     abs(const complex<_Tp>& __z)
 410     {
 411       _Tp __x = __z.real();
 412       _Tp __y = __z.imag();
 413       const _Tp __s = max(abs(__x), abs(__y));
 414       if (__s == _Tp())  // well ...
 415         return __s;
 416       __x /= __s;
 417       __y /= __s;
 418       return __s * sqrt(__x * __x + __y * __y);
 419     }
 420
 421   template<typename _Tp>
 422     inline _Tp
 423     arg(const complex<_Tp>& __z)
 424     { return atan2(__z.imag(), __z.real()); }
 425
 426   // 26.2.7/5: norm(__z) returns the squared magintude of __z.
 427   //     As defined, norm() is -not- a norm is the common mathematical
 428   //     sens used in numerics.  The helper class _Norm_helper<> tries to
 429   //     distinguish between builtin floating point and the rest, so as
 430   //     to deliver an answer as close as possible to the real value.
 431   template<bool>
 432     struct _Norm_helper
 433     {
 434       template<typename _Tp>
 435         static inline _Tp _S_do_it(const complex<_Tp>& __z)
 436         {
 437           const _Tp __x = __z.real();
 438           const _Tp __y = __z.imag();
 439           return __x * __x + __y * __y;
 440         }
 441     };
 442
 443   template<>
 444     struct _Norm_helper<true>
 445     {
 446       template<typename _Tp>
 447         static inline _Tp _S_do_it(const complex<_Tp>& __z)
 448         {
 449           _Tp __res = abs(__z);
 450           return __res * __res;
 451         }
 452     };
 453
 454   template<typename _Tp>
 455     inline _Tp
 456     norm(const complex<_Tp>& __z)
 457     {
 458       return _Norm_helper<__is_floating<_Tp>::_M_type>::_S_do_it(__z);
 459     }
 460
 461   template<typename _Tp>
 462     inline complex<_Tp>
 463     polar(const _Tp& __rho, const _Tp& __theta)
 464     { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
 465
 466   template<typename _Tp>
 467     inline complex<_Tp>
 468     conj(const complex<_Tp>& __z)
 469     { return complex<_Tp>(__z.real(), -__z.imag()); }
 470
 471   // Transcendentals
 472   template<typename _Tp>
 473     inline complex<_Tp>
 474     cos(const complex<_Tp>& __z)
 475     {
 476       const _Tp __x = __z.real();
 477       const _Tp __y = __z.imag();
 478       return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
 479     }
 480
 481   template<typename _Tp>
 482     inline complex<_Tp>
 483     cosh(const complex<_Tp>& __z)
 484     {
 485       const _Tp __x = __z.real();
 486       const _Tp __y = __z.imag();
 487       return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
 488     }
 489
 490   template<typename _Tp>
 491     inline complex<_Tp>
 492     exp(const complex<_Tp>& __z)
 493     { return polar(exp(__z.real()), __z.imag()); }
 494
 495   template<typename _Tp>
 496     inline complex<_Tp>
 497     log(const complex<_Tp>& __z)
 498     { return complex<_Tp>(log(abs(__z)), arg(__z)); }
 499
 500   template<typename _Tp>
 501     inline complex<_Tp>
 502     log10(const complex<_Tp>& __z)
 503     { return log(__z) / log(_Tp(10.0)); }
 504
 505   template<typename _Tp>
 506     inline complex<_Tp>
 507     sin(const complex<_Tp>& __z)
 508     {
 509       const _Tp __x = __z.real();
 510       const _Tp __y = __z.imag();
 511       return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
 512     }
 513
 514   template<typename _Tp>
 515     inline complex<_Tp>
 516     sinh(const complex<_Tp>& __z)
 517     {
 518       const _Tp __x = __z.real();
 519       const _Tp  __y = __z.imag();
 520       return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
 521     }
 522
 523   template<typename _Tp>
 524     complex<_Tp>
 525     sqrt(const complex<_Tp>& __z)
 526     {
 527       _Tp __x = __z.real();
 528       _Tp __y = __z.imag();
 529
 530       if (__x == _Tp())
 531         {
 532           _Tp __t = sqrt(abs(__y) / 2);
 533           return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
 534         }
 535       else
 536         {
 537           _Tp __t = sqrt(2 * (abs(__z) + abs(__x)));
 538           _Tp __u = __t / 2;
 539           return __x > _Tp()
 540             ? complex<_Tp>(__u, __y / __t)
 541             : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
 542         }
 543     }
 544
 545   template<typename _Tp>
 546     inline complex<_Tp>
 547     tan(const complex<_Tp>& __z)
 548     {
 549       return sin(__z) / cos(__z);
 550     }
 551
 552   template<typename _Tp>
 553     inline complex<_Tp>
 554     tanh(const complex<_Tp>& __z)
 555     {
 556       return sinh(__z) / cosh(__z);
 557     }
 558
 559   template<typename _Tp>
 560     inline complex<_Tp>
 561     pow(const complex<_Tp>& __z, int __n)
 562     {
 563       return __pow_helper(__z, __n);
 564     }
 565
 566   template<typename _Tp>
 567     inline complex<_Tp>
 568     pow(const complex<_Tp>& __x, const _Tp& __y)
 569     {
 570       return exp(__y * log(__x));
 571     }
 572
 573   template<typename _Tp>
 574     inline complex<_Tp>
 575     pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
 576     {
 577       return exp(__y * log(__x));
 578     }
 579
 580   template<typename _Tp>
 581     inline complex<_Tp>
 582     pow(const _Tp& __x, const complex<_Tp>& __y)
 583     {
 584       return exp(__y * log(__x));
 585     }
 586
 587   // 26.2.3  complex specializations
 588   // complex<float> specialization
 589   template<> class complex<float>
 590   {
 591   public:
 592     typedef float value_type;
 593
 594     complex(float = 0.0f, float = 0.0f);
 595 #ifdef _GLIBCPP_BUGGY_COMPLEX
 596     complex(const complex& __z) : _M_value(__z._M_value) { }
 597 #endif
 598     explicit complex(const complex<double>&);
 599     explicit complex(const complex<long double>&);
 600
 601     float real() const;
 602     float imag() const;
 603
 604     complex<float>& operator=(float);
 605     complex<float>& operator+=(float);
 606     complex<float>& operator-=(float);
 607     complex<float>& operator*=(float);
 608     complex<float>& operator/=(float);
 609
 610     // Let's the compiler synthetize the copy and assignment
 611     // operator.  It always does a pretty good job.
 612     // complex& operator= (const complex&);
 613     template<typename _Tp>
 614       complex<float>&operator=(const complex<_Tp>&);
 615     template<typename _Tp>
 616       complex<float>& operator+=(const complex<_Tp>&);
 617     template<class _Tp>
 618       complex<float>& operator-=(const complex<_Tp>&);
 619     template<class _Tp>
 620       complex<float>& operator*=(const complex<_Tp>&);
 621     template<class _Tp>
 622       complex<float>&operator/=(const complex<_Tp>&);
 623
 624   private:
 625     typedef __complex__ float _ComplexT;
 626     _ComplexT _M_value;
 627
 628     complex(_ComplexT __z) : _M_value(__z) { }
 629
 630     friend class complex<double>;
 631     friend class complex<long double>;
 632   };
 633
 634   inline float
 635   complex<float>::real() const
 636   { return __real__ _M_value; }
 637
 638   inline float
 639   complex<float>::imag() const
 640   { return __imag__ _M_value; }
 641
 642   inline
 643   complex<float>::complex(float r, float i)
 644   {
 645     __real__ _M_value = r;
 646     __imag__ _M_value = i;
 647   }
 648
 649   inline complex<float>&
 650   complex<float>::operator=(float __f)
 651   {
 652     __real__ _M_value = __f;
 653     __imag__ _M_value = 0.0f;
 654     return *this;
 655   }
 656
 657   inline complex<float>&
 658   complex<float>::operator+=(float __f)
 659   {
 660     __real__ _M_value += __f;
 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     _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   template<typename _Tp>
 686   inline complex<float>&
 687   complex<float>::operator=(const complex<_Tp>& __z)
 688   {
 689     __real__ _M_value = __z.real();
 690     __imag__ _M_value = __z.imag();
 691     return *this;
 692   }
 693
 694   template<typename _Tp>
 695   inline complex<float>&
 696   complex<float>::operator+=(const complex<_Tp>& __z)
 697   {
 698     __real__ _M_value += __z.real();
 699     __imag__ _M_value += __z.imag();
 700     return *this;
 701   }
 702
 703   template<typename _Tp>
 704     inline complex<float>&
 705     complex<float>::operator-=(const complex<_Tp>& __z)
 706     {
 707      __real__ _M_value -= __z.real();
 708      __imag__ _M_value -= __z.imag();
 709      return *this;
 710     }
 711
 712   template<typename _Tp>
 713     inline complex<float>&
 714     complex<float>::operator*=(const complex<_Tp>& __z)
 715     {
 716       _ComplexT __t;
 717       __real__ __t = __z.real();
 718       __imag__ __t = __z.imag();
 719       _M_value *= __t;
 720       return *this;
 721     }
 722
 723   template<typename _Tp>
 724     inline complex<float>&
 725     complex<float>::operator/=(const complex<_Tp>& __z)
 726     {
 727       _ComplexT __t;
 728       __real__ __t = __z.real();
 729       __imag__ __t = __z.imag();
 730       _M_value /= __t;
 731       return *this;
 732     }
 733
 734   // 26.2.3  complex specializations
 735   // complex<double> specialization
 736   template<> class complex<double>
 737   {
 738   public:
 739     typedef double value_type;
 740
 741     complex(double  =0.0, double =0.0);
 742 #ifdef _GLIBCPP_BUGGY_COMPLEX
 743     complex(const complex& __z) : _M_value(__z._M_value) { }
 744 #endif
 745     complex(const complex<float>&);
 746     explicit complex(const complex<long double>&);
 747
 748     double real() const;
 749     double imag() const;
 750
 751     complex<double>& operator=(double);
 752     complex<double>& operator+=(double);
 753     complex<double>& operator-=(double);
 754     complex<double>& operator*=(double);
 755     complex<double>& operator/=(double);
 756
 757     // The compiler will synthetize this, efficiently.
 758     // complex& operator= (const complex&);
 759     template<typename _Tp>
 760       complex<double>& operator=(const complex<_Tp>&);
 761     template<typename _Tp>
 762       complex<double>& operator+=(const complex<_Tp>&);
 763     template<typename _Tp>
 764       complex<double>& operator-=(const complex<_Tp>&);
 765     template<typename _Tp>
 766       complex<double>& operator*=(const complex<_Tp>&);
 767     template<typename _Tp>
 768       complex<double>& operator/=(const complex<_Tp>&);
 769
 770   private:
 771     typedef __complex__ double _ComplexT;
 772     _ComplexT _M_value;
 773
 774     complex(_ComplexT __z) : _M_value(__z) { }
 775
 776     friend class complex<float>;
 777     friend class complex<long double>;
 778   };
 779
 780   inline double
 781   complex<double>::real() const
 782   { return __real__ _M_value; }
 783
 784   inline double
 785   complex<double>::imag() const
 786   { return __imag__ _M_value; }
 787
 788   inline
 789   complex<double>::complex(double __r, double __i)
 790   {
 791     __real__ _M_value = __r;
 792     __imag__ _M_value = __i;
 793   }
 794
 795   inline complex<double>&
 796   complex<double>::operator=(double __d)
 797   {
 798     __real__ _M_value = __d;
 799     __imag__ _M_value = 0.0;
 800     return *this;
 801   }
 802
 803   inline complex<double>&
 804   complex<double>::operator+=(double __d)
 805   {
 806     __real__ _M_value += __d;
 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     _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   template<typename _Tp>
 832     inline complex<double>&
 833     complex<double>::operator=(const complex<_Tp>& __z)
 834     {
 835       __real__ _M_value = __z.real();
 836       __imag__ _M_value = __z.imag();
 837       return *this;
 838     }
 839
 840   template<typename _Tp>
 841     inline complex<double>&
 842     complex<double>::operator+=(const complex<_Tp>& __z)
 843     {
 844       __real__ _M_value += __z.real();
 845       __imag__ _M_value += __z.imag();
 846       return *this;
 847     }
 848
 849   template<typename _Tp>
 850     inline complex<double>&
 851     complex<double>::operator-=(const complex<_Tp>& __z)
 852     {
 853       __real__ _M_value -= __z.real();
 854       __imag__ _M_value -= __z.imag();
 855       return *this;
 856     }
 857
 858   template<typename _Tp>
 859     inline complex<double>&
 860     complex<double>::operator*=(const complex<_Tp>& __z)
 861     {
 862       _ComplexT __t;
 863       __real__ __t = __z.real();
 864       __imag__ __t = __z.imag();
 865       _M_value *= __t;
 866       return *this;
 867     }
 868
 869   template<typename _Tp>
 870     inline complex<double>&
 871     complex<double>::operator/=(const complex<_Tp>& __z)
 872     {
 873       _ComplexT __t;
 874       __real__ __t = __z.real();
 875       __imag__ __t = __z.imag();
 876       _M_value /= __t;
 877       return *this;
 878     }
 879
 880   // 26.2.3  complex specializations
 881   // complex<long double> specialization
 882   template<> class complex<long double>
 883   {
 884   public:
 885     typedef long double value_type;
 886
 887     complex(long double = 0.0L, long double = 0.0L);
 888 #ifdef _GLIBCPP_BUGGY_COMPLEX
 889     complex(const complex& __z) : _M_value(__z._M_value) { }
 890 #endif
 891     complex(const complex<float>&);
 892     complex(const complex<double>&);
 893
 894     long double real() const;
 895     long double imag() const;
 896
 897     complex<long double>& operator= (long double);
 898     complex<long double>& operator+= (long double);
 899     complex<long double>& operator-= (long double);
 900     complex<long double>& operator*= (long double);
 901     complex<long double>& operator/= (long double);
 902
 903     // The compiler knows how to do this efficiently
 904     // complex& operator= (const complex&);
 905     template<typename _Tp>
 906       complex<long double>& operator=(const complex<_Tp>&);
 907     template<typename _Tp>
 908       complex<long double>& operator+=(const complex<_Tp>&);
 909     template<typename _Tp>
 910       complex<long double>& operator-=(const complex<_Tp>&);
 911     template<typename _Tp>
 912       complex<long double>& operator*=(const complex<_Tp>&);
 913     template<typename _Tp>
 914       complex<long double>& operator/=(const complex<_Tp>&);
 915
 916   private:
 917     typedef __complex__ long double _ComplexT;
 918     _ComplexT _M_value;
 919
 920     complex(_ComplexT __z) : _M_value(__z) { }
 921
 922     friend class complex<float>;
 923     friend class complex<double>;
 924   };
 925
 926   inline
 927   complex<long double>::complex(long double __r, long double __i)
 928   {
 929     __real__ _M_value = __r;
 930     __imag__ _M_value = __i;
 931   }
 932
 933   inline long double
 934   complex<long double>::real() const
 935   { return __real__ _M_value; }
 936
 937   inline long double
 938   complex<long double>::imag() const
 939   { return __imag__ _M_value; }
 940
 941   inline complex<long double>&
 942   complex<long double>::operator=(long double __r)
 943   {
 944     __real__ _M_value = __r;
 945     __imag__ _M_value = 0.0L;
 946     return *this;
 947   }
 948
 949   inline complex<long double>&
 950   complex<long double>::operator+=(long double __r)
 951   {
 952     __real__ _M_value += __r;
 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     _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   template<typename _Tp>
 978     inline complex<long double>&
 979     complex<long double>::operator=(const complex<_Tp>& __z)
 980     {
 981       __real__ _M_value = __z.real();
 982       __imag__ _M_value = __z.imag();
 983       return *this;
 984     }
 985
 986   template<typename _Tp>
 987     inline complex<long double>&
 988     complex<long double>::operator+=(const complex<_Tp>& __z)
 989     {
 990       __real__ _M_value += __z.real();
 991       __imag__ _M_value += __z.imag();
 992       return *this;
 993     }
 994
 995   template<typename _Tp>
 996     inline complex<long double>&
 997     complex<long double>::operator-=(const complex<_Tp>& __z)
 998     {
 999       __real__ _M_value -= __z.real();
1000       __imag__ _M_value -= __z.imag();
1001       return *this;
1002     }
1003
1004   template<typename _Tp>
1005     inline complex<long double>&
1006     complex<long double>::operator*=(const complex<_Tp>& __z)
1007     {
1008       _ComplexT __t;
1009       __real__ __t = __z.real();
1010       __imag__ __t = __z.imag();
1011       _M_value *= __t;
1012       return *this;
1013     }
1014
1015   template<typename _Tp>
1016     inline complex<long double>&
1017     complex<long double>::operator/=(const complex<_Tp>& __z)
1018     {
1019       _ComplexT __t;
1020       __real__ __t = __z.real();
1021       __imag__ __t = __z.imag();
1022       _M_value /= __t;
1023       return *this;
1024     }
1025
1026   // These bits have to be at the end of this file, so that the
1027   // specializations have all been defined.
1028   // ??? No, they have to be there because of compiler limitation at
1029   // inlining.  It suffices that class specializations be defined.
1030   inline
1031   complex<float>::complex(const complex<double>& __z)
1032   : _M_value(_ComplexT(__z._M_value)) { }
1033
1034   inline
1035   complex<float>::complex(const complex<long double>& __z)
1036   : _M_value(_ComplexT(__z._M_value)) { }
1037
1038   inline
1039   complex<double>::complex(const complex<float>& __z)
1040   : _M_value(_ComplexT(__z._M_value)) { }
1041
1042   inline
1043   complex<double>::complex(const complex<long double>& __z)
1044   {
1045     __real__ _M_value = __z.real();
1046     __imag__ _M_value = __z.imag();
1047   }
1048
1049   inline
1050   complex<long double>::complex(const complex<float>& __z)
1051   : _M_value(_ComplexT(__z._M_value)) { }
1052
1053   inline
1054   complex<long double>::complex(const complex<double>& __z)
1055   : _M_value(_ComplexT(__z._M_value)) { }
1056 } // namespace std
1057
1058 #endif  /* _CPP_COMPLEX */