std_complex.h Source File

00001 // The template and inlines for the -*- C++ -*- complex number classes.
00002 
00003 // Copyright (C) 1997, 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
00004 //
00005 // This file is part of the GNU ISO C++ Library.  This library is free
00006 // software; you can redistribute it and/or modify it under the
00007 // terms of the GNU General Public License as published by the
00008 // Free Software Foundation; either version 2, or (at your option)
00009 // any later version.
00010 
00011 // This library is distributed in the hope that it will be useful,
00012 // but WITHOUT ANY WARRANTY; without even the implied warranty of
00013 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00014 // GNU General Public License for more details.
00015 
00016 // You should have received a copy of the GNU General Public License along
00017 // with this library; see the file COPYING.  If not, write to the Free
00018 // Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
00019 // USA.
00020 
00021 // As a special exception, you may use this file as part of a free software
00022 // library without restriction.  Specifically, if other files instantiate
00023 // templates or use macros or inline functions from this file, or you compile
00024 // this file and link it with other files to produce an executable, this
00025 // file does not by itself cause the resulting executable to be covered by
00026 // the GNU General Public License.  This exception does not however
00027 // invalidate any other reasons why the executable file might be covered by
00028 // the GNU General Public License.
00029 
00030 //
00031 // ISO C++ 14882: 26.2  Complex Numbers
00032 // Note: this is not a conforming implementation.
00033 // Initially implemented by Ulrich Drepper <drepper@cygnus.com>
00034 // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
00035 //
00036 
00037 #ifndef _CPP_COMPLEX
00038 #define _CPP_COMPLEX    1
00039 
00040 #pragma GCC system_header
00041 
00042 #include <bits/c++config.h>
00043 #include <bits/cpp_type_traits.h>
00044 #include <bits/std_cmath.h>
00045 #include <bits/std_sstream.h>
00046 
00047 namespace std
00048 {
00049   // Forward declarations
00050   template<typename _Tp> class complex;
00051   template<> class complex<float>;
00052   template<> class complex<double>;
00053   template<> class complex<long double>;
00054 
00055   template<typename _Tp> _Tp abs(const complex<_Tp>&);
00056   template<typename _Tp> _Tp arg(const complex<_Tp>&);
00057   template<typename _Tp> _Tp norm(const complex<_Tp>&);
00058 
00059   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
00060   template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp&);
00061 
00062   // Transcendentals:
00063   template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
00064   template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
00065   template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
00066   template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
00067   template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
00068   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
00069   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
00070   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 
00071                        const complex<_Tp>&);
00072   template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
00073   template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
00074   template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
00075   template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
00076   template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
00077   template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
00078     
00079     
00080   // 26.2.2  Primary template class complex
00081   template<typename _Tp>
00082     class complex
00083     {
00084     public:
00085       typedef _Tp value_type;
00086       
00087       complex(const _Tp& = _Tp(), const _Tp & = _Tp());
00088 
00089       // Let's the compiler synthetize the copy constructor   
00090       // complex (const complex<_Tp>&);
00091       template<typename _Up>
00092         complex(const complex<_Up>&);
00093         
00094       _Tp real() const;
00095       _Tp imag() const;
00096 
00097       complex<_Tp>& operator=(const _Tp&);
00098       complex<_Tp>& operator+=(const _Tp&);
00099       complex<_Tp>& operator-=(const _Tp&);
00100       complex<_Tp>& operator*=(const _Tp&);
00101       complex<_Tp>& operator/=(const _Tp&);
00102 
00103       // Let's the compiler synthetize the
00104       // copy and assignment operator
00105       // complex<_Tp>& operator= (const complex<_Tp>&);
00106       template<typename _Up>
00107         complex<_Tp>& operator=(const complex<_Up>&);
00108       template<typename _Up>
00109         complex<_Tp>& operator+=(const complex<_Up>&);
00110       template<typename _Up>
00111         complex<_Tp>& operator-=(const complex<_Up>&);
00112       template<typename _Up>
00113         complex<_Tp>& operator*=(const complex<_Up>&);
00114       template<typename _Up>
00115         complex<_Tp>& operator/=(const complex<_Up>&);
00116 
00117     private:
00118       _Tp _M_real, _M_imag;
00119     };
00120 
00121   template<typename _Tp>
00122     inline _Tp
00123     complex<_Tp>::real() const { return _M_real; }
00124 
00125   template<typename _Tp>
00126     inline _Tp
00127     complex<_Tp>::imag() const { return _M_imag; }
00128 
00129   template<typename _Tp>
00130     inline 
00131     complex<_Tp>::complex(const _Tp& __r, const _Tp& __i)
00132     : _M_real(__r), _M_imag(__i) { }
00133 
00134   template<typename _Tp>
00135     template<typename _Up>
00136     inline 
00137     complex<_Tp>::complex(const complex<_Up>& __z)
00138     : _M_real(__z.real()), _M_imag(__z.imag()) { }
00139         
00140   template<typename _Tp>
00141     complex<_Tp>&
00142     complex<_Tp>::operator=(const _Tp& __t)
00143     {
00144      _M_real = __t;
00145      _M_imag = _Tp();
00146      return *this;
00147     } 
00148 
00149   // 26.2.5/1
00150   template<typename _Tp>
00151     inline complex<_Tp>&
00152     complex<_Tp>::operator+=(const _Tp& __t)
00153     {
00154       _M_real += __t;
00155       return *this;
00156     }
00157 
00158   // 26.2.5/3
00159   template<typename _Tp>
00160     inline complex<_Tp>&
00161     complex<_Tp>::operator-=(const _Tp& __t)
00162     {
00163       _M_real -= __t;
00164       return *this;
00165     }
00166 
00167   // 26.2.5/5
00168   template<typename _Tp>
00169     complex<_Tp>&
00170     complex<_Tp>::operator*=(const _Tp& __t)
00171     {
00172       _M_real *= __t;
00173       _M_imag *= __t;
00174       return *this;
00175     }
00176 
00177   // 26.2.5/7
00178   template<typename _Tp>
00179     complex<_Tp>&
00180     complex<_Tp>::operator/=(const _Tp& __t)
00181     {
00182       _M_real /= __t;
00183       _M_imag /= __t;
00184       return *this;
00185     }
00186 
00187   template<typename _Tp>
00188     template<typename _Up>
00189     complex<_Tp>&
00190     complex<_Tp>::operator=(const complex<_Up>& __z)
00191     {
00192       _M_real = __z.real();
00193       _M_imag = __z.imag();
00194       return *this;
00195     }
00196 
00197   // 26.2.5/9
00198   template<typename _Tp>
00199     template<typename _Up>
00200     complex<_Tp>&
00201     complex<_Tp>::operator+=(const complex<_Up>& __z)
00202     {
00203       _M_real += __z.real();
00204       _M_imag += __z.imag();
00205       return *this;
00206     }
00207 
00208   // 26.2.5/11
00209   template<typename _Tp>
00210     template<typename _Up>
00211     complex<_Tp>&
00212     complex<_Tp>::operator-=(const complex<_Up>& __z)
00213     {
00214       _M_real -= __z.real();
00215       _M_imag -= __z.imag();
00216       return *this;
00217     }
00218 
00219   // 26.2.5/13
00220   // XXX: This is a grammar school implementation.
00221   template<typename _Tp>
00222     template<typename _Up>
00223     complex<_Tp>&
00224     complex<_Tp>::operator*=(const complex<_Up>& __z)
00225     {
00226       const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
00227       _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
00228       _M_real = __r;
00229       return *this;
00230     }
00231 
00232   // 26.2.5/15
00233   // XXX: This is a grammar school implementation.
00234   template<typename _Tp>
00235     template<typename _Up>
00236     complex<_Tp>&
00237     complex<_Tp>::operator/=(const complex<_Up>& __z)
00238     {
00239       const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
00240       const _Tp __n = norm(__z);
00241       _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
00242       _M_real = __r / __n;
00243       return *this;
00244     }
00245     
00246   // Operators:
00247   template<typename _Tp>
00248     inline complex<_Tp>
00249     operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
00250     { return complex<_Tp> (__x) += __y; }
00251 
00252   template<typename _Tp>
00253     inline complex<_Tp>
00254     operator+(const complex<_Tp>& __x, const _Tp& __y)
00255     { return complex<_Tp> (__x) += __y; }
00256 
00257   template<typename _Tp>
00258     inline complex<_Tp>
00259     operator+(const _Tp& __x, const complex<_Tp>& __y)
00260     { return complex<_Tp> (__y) += __x; }
00261 
00262   template<typename _Tp>
00263     inline complex<_Tp>
00264     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
00265     { return complex<_Tp> (__x) -= __y; }
00266     
00267   template<typename _Tp>
00268     inline complex<_Tp>
00269     operator-(const complex<_Tp>& __x, const _Tp& __y)
00270     { return complex<_Tp> (__x) -= __y; }
00271 
00272   template<typename _Tp>
00273     inline complex<_Tp>
00274     operator-(const _Tp& __x, const complex<_Tp>& __y)
00275     { return complex<_Tp> (__x) -= __y; }
00276 
00277   template<typename _Tp>
00278     inline complex<_Tp>
00279     operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
00280     { return complex<_Tp> (__x) *= __y; }
00281 
00282   template<typename _Tp>
00283     inline complex<_Tp>
00284     operator*(const complex<_Tp>& __x, const _Tp& __y)
00285     { return complex<_Tp> (__x) *= __y; }
00286 
00287   template<typename _Tp>
00288     inline complex<_Tp>
00289     operator*(const _Tp& __x, const complex<_Tp>& __y)
00290     { return complex<_Tp> (__y) *= __x; }
00291 
00292   template<typename _Tp>
00293     inline complex<_Tp>
00294     operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
00295     { return complex<_Tp> (__x) /= __y; }
00296     
00297   template<typename _Tp>
00298     inline complex<_Tp>
00299     operator/(const complex<_Tp>& __x, const _Tp& __y)
00300     { return complex<_Tp> (__x) /= __y; }
00301 
00302   template<typename _Tp>
00303     inline complex<_Tp>
00304     operator/(const _Tp& __x, const complex<_Tp>& __y)
00305     { return complex<_Tp> (__x) /= __y; }
00306 
00307   template<typename _Tp>
00308     inline complex<_Tp>
00309     operator+(const complex<_Tp>& __x)
00310     { return __x; }
00311 
00312   template<typename _Tp>
00313     inline complex<_Tp>
00314     operator-(const complex<_Tp>& __x)
00315     {  return complex<_Tp>(-__x.real(), -__x.imag()); }
00316 
00317   template<typename _Tp>
00318     inline bool
00319     operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
00320     { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
00321 
00322   template<typename _Tp>
00323     inline bool
00324     operator==(const complex<_Tp>& __x, const _Tp& __y)
00325     { return __x.real() == __y && __x.imag() == _Tp(); }
00326 
00327   template<typename _Tp>
00328     inline bool
00329     operator==(const _Tp& __x, const complex<_Tp>& __y)
00330     { return __x == __y.real() && _Tp() == __y.imag(); }
00331 
00332   template<typename _Tp>
00333     inline bool
00334     operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
00335     { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
00336 
00337   template<typename _Tp>
00338     inline bool
00339     operator!=(const complex<_Tp>& __x, const _Tp& __y)
00340     { return __x.real() != __y || __x.imag() != _Tp(); }
00341 
00342   template<typename _Tp>
00343     inline bool
00344     operator!=(const _Tp& __x, const complex<_Tp>& __y)
00345     { return __x != __y.real() || _Tp() != __y.imag(); }
00346 
00347   template<typename _Tp, typename _CharT, class _Traits>
00348     basic_istream<_CharT, _Traits>&
00349     operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
00350     {
00351       _Tp __re_x, __im_x;
00352       _CharT __ch;
00353       __is >> __ch;
00354       if (__ch == '(') 
00355     {
00356       __is >> __re_x >> __ch;
00357       if (__ch == ',') 
00358         {
00359           __is >> __im_x >> __ch;
00360           if (__ch == ')') 
00361         __x = complex<_Tp>(__re_x, __im_x);
00362           else
00363         __is.setstate(ios_base::failbit);
00364         }
00365       else if (__ch == ')') 
00366         __x = complex<_Tp>(__re_x, _Tp(0));
00367       else
00368         __is.setstate(ios_base::failbit);
00369     }
00370       else 
00371     {
00372       __is.putback(__ch);
00373       __is >> __re_x;
00374       __x = complex<_Tp>(__re_x, _Tp(0));
00375     }
00376       return __is;
00377     }
00378 
00379   template<typename _Tp, typename _CharT, class _Traits>
00380     basic_ostream<_CharT, _Traits>&
00381     operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
00382     {
00383       basic_ostringstream<_CharT, _Traits> __s;
00384       __s.flags(__os.flags());
00385       __s.imbue(__os.getloc());
00386       __s.precision(__os.precision());
00387       __s << '(' << __x.real() << "," << __x.imag() << ')';
00388       return __os << __s.str();
00389     }
00390 
00391   // Values
00392   template<typename _Tp>
00393     inline _Tp
00394     real(const complex<_Tp>& __z)
00395     { return __z.real(); }
00396     
00397   template<typename _Tp>
00398     inline _Tp
00399     imag(const complex<_Tp>& __z)
00400     { return __z.imag(); }
00401 
00402   template<typename _Tp>
00403     inline _Tp
00404     abs(const complex<_Tp>& __z)
00405     {
00406       _Tp __x = __z.real();
00407       _Tp __y = __z.imag();
00408       const _Tp __s = max(abs(__x), abs(__y));
00409       if (__s == _Tp())  // well ...
00410         return __s;
00411       __x /= __s; 
00412       __y /= __s;
00413       return __s * sqrt(__x * __x + __y * __y);
00414     }
00415 
00416   template<typename _Tp>
00417     inline _Tp
00418     arg(const complex<_Tp>& __z)
00419     { return atan2(__z.imag(), __z.real()); }
00420 
00421   // 26.2.7/5: norm(__z) returns the squared magintude of __z.
00422   //     As defined, norm() is -not- a norm is the common mathematical
00423   //     sens used in numerics.  The helper class _Norm_helper<> tries to
00424   //     distinguish between builtin floating point and the rest, so as
00425   //     to deliver an answer as close as possible to the real value.
00426   template<bool>
00427     struct _Norm_helper
00428     {
00429       template<typename _Tp>
00430         static inline _Tp _S_do_it(const complex<_Tp>& __z)
00431         {
00432           const _Tp __x = __z.real();
00433           const _Tp __y = __z.imag();
00434           return __x * __x + __y * __y;
00435         }
00436     };
00437 
00438   template<>
00439     struct _Norm_helper<true>
00440     {
00441       template<typename _Tp>
00442         static inline _Tp _S_do_it(const complex<_Tp>& __z)
00443         {
00444           _Tp __res = abs(__z);
00445           return __res * __res;
00446         }
00447     };
00448   
00449   template<typename _Tp>
00450     inline _Tp
00451     norm(const complex<_Tp>& __z)
00452     {
00453       return _Norm_helper<__is_floating<_Tp>::_M_type>::_S_do_it(__z);
00454     }
00455 
00456   template<typename _Tp>
00457     inline complex<_Tp>
00458     polar(const _Tp& __rho, const _Tp& __theta)
00459     { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
00460 
00461   template<typename _Tp>
00462     inline complex<_Tp>
00463     conj(const complex<_Tp>& __z)
00464     { return complex<_Tp>(__z.real(), -__z.imag()); }
00465   
00466   // Transcendentals
00467   template<typename _Tp>
00468     inline complex<_Tp>
00469     cos(const complex<_Tp>& __z)
00470     {
00471       const _Tp __x = __z.real();
00472       const _Tp __y = __z.imag();
00473       return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
00474     }
00475 
00476   template<typename _Tp>
00477     inline complex<_Tp>
00478     cosh(const complex<_Tp>& __z)
00479     {
00480       const _Tp __x = __z.real();
00481       const _Tp __y = __z.imag();
00482       return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
00483     }
00484 
00485   template<typename _Tp>
00486     inline complex<_Tp>
00487     exp(const complex<_Tp>& __z)
00488     { return polar(exp(__z.real()), __z.imag()); }
00489 
00490   template<typename _Tp>
00491     inline complex<_Tp>
00492     log(const complex<_Tp>& __z)
00493     { return complex<_Tp>(log(abs(__z)), arg(__z)); }
00494 
00495   template<typename _Tp>
00496     inline complex<_Tp>
00497     log10(const complex<_Tp>& __z)
00498     { return log(__z) / log(_Tp(10.0)); }
00499 
00500   template<typename _Tp>
00501     inline complex<_Tp>
00502     sin(const complex<_Tp>& __z)
00503     {
00504       const _Tp __x = __z.real();
00505       const _Tp __y = __z.imag();
00506       return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 
00507     }
00508 
00509   template<typename _Tp>
00510     inline complex<_Tp>
00511     sinh(const complex<_Tp>& __z)
00512     {
00513       const _Tp __x = __z.real();
00514       const _Tp  __y = __z.imag();
00515       return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
00516     }
00517 
00518   template<typename _Tp>
00519     complex<_Tp>
00520     sqrt(const complex<_Tp>& __z)
00521     {
00522       _Tp __x = __z.real();
00523       _Tp __y = __z.imag();
00524 
00525       if (__x == _Tp())
00526         {
00527           _Tp __t = sqrt(abs(__y) / 2);
00528           return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
00529         }
00530       else
00531         {
00532           _Tp __t = sqrt(2 * (abs(__z) + abs(__x)));
00533           _Tp __u = __t / 2;
00534           return __x > _Tp()
00535             ? complex<_Tp>(__u, __y / __t)
00536             : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
00537         }
00538     }
00539 
00540   template<typename _Tp>
00541     inline complex<_Tp>
00542     tan(const complex<_Tp>& __z)
00543     {
00544       return sin(__z) / cos(__z);
00545     }
00546 
00547   template<typename _Tp>
00548     inline complex<_Tp>
00549     tanh(const complex<_Tp>& __z)
00550     {
00551       return sinh(__z) / cosh(__z);
00552     }
00553 
00554   template<typename _Tp>
00555     inline complex<_Tp>
00556     pow(const complex<_Tp>& __z, int __n)
00557     {
00558       return __pow_helper(__z, __n);
00559     }
00560 
00561   template<typename _Tp>
00562     inline complex<_Tp>
00563     pow(const complex<_Tp>& __x, const _Tp& __y)
00564     {
00565       return exp(__y * log(__x));
00566     }
00567 
00568   template<typename _Tp>
00569     inline complex<_Tp>
00570     pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
00571     {
00572       return exp(__y * log(__x));
00573     }
00574 
00575   template<typename _Tp>
00576     inline complex<_Tp>
00577     pow(const _Tp& __x, const complex<_Tp>& __y)
00578     {
00579       return exp(__y * log(__x));
00580     }
00581 
00582   // 26.2.3  complex specializations
00583   // complex<float> specialization
00584   template<> class complex<float>
00585   {
00586   public:
00587     typedef float value_type;
00588     
00589     complex(float = 0.0f, float = 0.0f);
00590 #ifdef _GLIBCPP_BUGGY_COMPLEX
00591     complex(const complex& __z) : _M_value(__z._M_value) { }
00592 #endif
00593     explicit complex(const complex<double>&);
00594     explicit complex(const complex<long double>&);
00595 
00596     float real() const;
00597     float imag() const;
00598 
00599     complex<float>& operator=(float);
00600     complex<float>& operator+=(float);
00601     complex<float>& operator-=(float);
00602     complex<float>& operator*=(float);
00603     complex<float>& operator/=(float);
00604         
00605     // Let's the compiler synthetize the copy and assignment
00606     // operator.  It always does a pretty good job.
00607     // complex& operator= (const complex&);
00608     template<typename _Tp>
00609       complex<float>&operator=(const complex<_Tp>&);
00610     template<typename _Tp>
00611       complex<float>& operator+=(const complex<_Tp>&);
00612     template<class _Tp>
00613       complex<float>& operator-=(const complex<_Tp>&);
00614     template<class _Tp>
00615       complex<float>& operator*=(const complex<_Tp>&);
00616     template<class _Tp>
00617       complex<float>&operator/=(const complex<_Tp>&);
00618 
00619   private:
00620     typedef __complex__ float _ComplexT;
00621     _ComplexT _M_value;
00622 
00623     complex(_ComplexT __z) : _M_value(__z) { }
00624         
00625     friend class complex<double>;
00626     friend class complex<long double>;
00627   };
00628 
00629   inline float
00630   complex<float>::real() const
00631   { return __real__ _M_value; }
00632 
00633   inline float
00634   complex<float>::imag() const
00635   { return __imag__ _M_value; }
00636 
00637   inline
00638   complex<float>::complex(float r, float i)
00639   {
00640     __real__ _M_value = r;
00641     __imag__ _M_value = i;
00642   }
00643 
00644   inline complex<float>&
00645   complex<float>::operator=(float __f)
00646   {
00647     __real__ _M_value = __f;
00648     __imag__ _M_value = 0.0f;
00649     return *this;
00650   }
00651 
00652   inline complex<float>&
00653   complex<float>::operator+=(float __f)
00654   {
00655     __real__ _M_value += __f;
00656     return *this;
00657   }
00658 
00659   inline complex<float>&
00660   complex<float>::operator-=(float __f)
00661   {
00662     __real__ _M_value -= __f;
00663     return *this;
00664   }
00665 
00666   inline complex<float>&
00667   complex<float>::operator*=(float __f)
00668   {
00669     _M_value *= __f;
00670     return *this;
00671   }
00672 
00673   inline complex<float>&
00674   complex<float>::operator/=(float __f)
00675   {
00676     _M_value /= __f;
00677     return *this;
00678   }
00679 
00680   template<typename _Tp>
00681   inline complex<float>&
00682   complex<float>::operator=(const complex<_Tp>& __z)
00683   {
00684     __real__ _M_value = __z.real();
00685     __imag__ _M_value = __z.imag();
00686     return *this;
00687   }
00688 
00689   template<typename _Tp>
00690   inline complex<float>&
00691   complex<float>::operator+=(const complex<_Tp>& __z)
00692   {
00693     __real__ _M_value += __z.real();
00694     __imag__ _M_value += __z.imag();
00695     return *this;
00696   }
00697     
00698   template<typename _Tp>
00699     inline complex<float>&
00700     complex<float>::operator-=(const complex<_Tp>& __z)
00701     {
00702      __real__ _M_value -= __z.real();
00703      __imag__ _M_value -= __z.imag();
00704      return *this;
00705     } 
00706 
00707   template<typename _Tp>
00708     inline complex<float>&
00709     complex<float>::operator*=(const complex<_Tp>& __z)
00710     {
00711       _ComplexT __t;
00712       __real__ __t = __z.real();
00713       __imag__ __t = __z.imag();
00714       _M_value *= __t;
00715       return *this;
00716     }
00717 
00718   template<typename _Tp>
00719     inline complex<float>&
00720     complex<float>::operator/=(const complex<_Tp>& __z)
00721     {
00722       _ComplexT __t;
00723       __real__ __t = __z.real();
00724       __imag__ __t = __z.imag();
00725       _M_value /= __t;
00726       return *this;
00727     }
00728 
00729   // 26.2.3  complex specializations
00730   // complex<double> specialization
00731   template<> class complex<double>
00732   {
00733   public:
00734     typedef double value_type;
00735 
00736     complex(double  =0.0, double =0.0);
00737 #ifdef _GLIBCPP_BUGGY_COMPLEX
00738     complex(const complex& __z) : _M_value(__z._M_value) { }
00739 #endif
00740     complex(const complex<float>&);
00741     explicit complex(const complex<long double>&);
00742         
00743     double real() const;
00744     double imag() const;
00745         
00746     complex<double>& operator=(double);
00747     complex<double>& operator+=(double);
00748     complex<double>& operator-=(double);
00749     complex<double>& operator*=(double);
00750     complex<double>& operator/=(double);
00751 
00752     // The compiler will synthetize this, efficiently.
00753     // complex& operator= (const complex&);
00754     template<typename _Tp>
00755       complex<double>& operator=(const complex<_Tp>&);
00756     template<typename _Tp>
00757       complex<double>& operator+=(const complex<_Tp>&);
00758     template<typename _Tp>
00759       complex<double>& operator-=(const complex<_Tp>&);
00760     template<typename _Tp>
00761       complex<double>& operator*=(const complex<_Tp>&);
00762     template<typename _Tp>
00763       complex<double>& operator/=(const complex<_Tp>&);
00764 
00765   private:
00766     typedef __complex__ double _ComplexT;
00767     _ComplexT _M_value;
00768 
00769     complex(_ComplexT __z) : _M_value(__z) { }
00770         
00771     friend class complex<float>;
00772     friend class complex<long double>;
00773   };
00774 
00775   inline double
00776   complex<double>::real() const
00777   { return __real__ _M_value; }
00778 
00779   inline double
00780   complex<double>::imag() const
00781   { return __imag__ _M_value; }
00782 
00783   inline
00784   complex<double>::complex(double __r, double __i)
00785   {
00786     __real__ _M_value = __r;
00787     __imag__ _M_value = __i;
00788   }
00789 
00790   inline complex<double>&
00791   complex<double>::operator=(double __d)
00792   {
00793     __real__ _M_value = __d;
00794     __imag__ _M_value = 0.0;
00795     return *this;
00796   }
00797 
00798   inline complex<double>&
00799   complex<double>::operator+=(double __d)
00800   {
00801     __real__ _M_value += __d;
00802     return *this;
00803   }
00804 
00805   inline complex<double>&
00806   complex<double>::operator-=(double __d)
00807   {
00808     __real__ _M_value -= __d;
00809     return *this;
00810   }
00811 
00812   inline complex<double>&
00813   complex<double>::operator*=(double __d)
00814   {
00815     _M_value *= __d;
00816     return *this;
00817   }
00818 
00819   inline complex<double>&
00820   complex<double>::operator/=(double __d)
00821   {
00822     _M_value /= __d;
00823     return *this;
00824   }
00825 
00826   template<typename _Tp>
00827     inline complex<double>&
00828     complex<double>::operator=(const complex<_Tp>& __z)
00829     {
00830       __real__ _M_value = __z.real();
00831       __imag__ _M_value = __z.imag();
00832       return *this;
00833     }
00834     
00835   template<typename _Tp>
00836     inline complex<double>&
00837     complex<double>::operator+=(const complex<_Tp>& __z)
00838     {
00839       __real__ _M_value += __z.real();
00840       __imag__ _M_value += __z.imag();
00841       return *this;
00842     }
00843 
00844   template<typename _Tp>
00845     inline complex<double>&
00846     complex<double>::operator-=(const complex<_Tp>& __z)
00847     {
00848       __real__ _M_value -= __z.real();
00849       __imag__ _M_value -= __z.imag();
00850       return *this;
00851     }
00852 
00853   template<typename _Tp>
00854     inline complex<double>&
00855     complex<double>::operator*=(const complex<_Tp>& __z)
00856     {
00857       _ComplexT __t;
00858       __real__ __t = __z.real();
00859       __imag__ __t = __z.imag();
00860       _M_value *= __t;
00861       return *this;
00862     }
00863 
00864   template<typename _Tp>
00865     inline complex<double>&
00866     complex<double>::operator/=(const complex<_Tp>& __z)
00867     {
00868       _ComplexT __t;
00869       __real__ __t = __z.real();
00870       __imag__ __t = __z.imag();
00871       _M_value /= __t;
00872       return *this;
00873     }
00874 
00875   // 26.2.3  complex specializations
00876   // complex<long double> specialization
00877   template<> class complex<long double>
00878   {
00879   public:
00880     typedef long double value_type;
00881 
00882     complex(long double = 0.0L, long double = 0.0L);
00883 #ifdef _GLIBCPP_BUGGY_COMPLEX
00884     complex(const complex& __z) : _M_value(__z._M_value) { }
00885 #endif
00886     complex(const complex<float>&);
00887     complex(const complex<double>&);
00888 
00889     long double real() const;
00890     long double imag() const;
00891 
00892     complex<long double>& operator= (long double);
00893     complex<long double>& operator+= (long double);
00894     complex<long double>& operator-= (long double);
00895     complex<long double>& operator*= (long double);
00896     complex<long double>& operator/= (long double);
00897 
00898     // The compiler knows how to do this efficiently
00899     // complex& operator= (const complex&);
00900     template<typename _Tp>
00901       complex<long double>& operator=(const complex<_Tp>&);
00902     template<typename _Tp>
00903       complex<long double>& operator+=(const complex<_Tp>&);
00904     template<typename _Tp>
00905       complex<long double>& operator-=(const complex<_Tp>&);
00906     template<typename _Tp>
00907       complex<long double>& operator*=(const complex<_Tp>&);
00908     template<typename _Tp>
00909       complex<long double>& operator/=(const complex<_Tp>&);
00910 
00911   private:
00912     typedef __complex__ long double _ComplexT;
00913     _ComplexT _M_value;
00914 
00915     complex(_ComplexT __z) : _M_value(__z) { }
00916 
00917     friend class complex<float>;
00918     friend class complex<double>;
00919   };
00920 
00921   inline
00922   complex<long double>::complex(long double __r, long double __i)
00923   {
00924     __real__ _M_value = __r;
00925     __imag__ _M_value = __i;
00926   }
00927 
00928   inline long double
00929   complex<long double>::real() const
00930   { return __real__ _M_value; }
00931 
00932   inline long double
00933   complex<long double>::imag() const
00934   { return __imag__ _M_value; }
00935 
00936   inline complex<long double>&   
00937   complex<long double>::operator=(long double __r)
00938   {
00939     __real__ _M_value = __r;
00940     __imag__ _M_value = 0.0L;
00941     return *this;
00942   }
00943 
00944   inline complex<long double>&
00945   complex<long double>::operator+=(long double __r)
00946   {
00947     __real__ _M_value += __r;
00948     return *this;
00949   }
00950 
00951   inline complex<long double>&
00952   complex<long double>::operator-=(long double __r)
00953   {
00954     __real__ _M_value -= __r;
00955     return *this;
00956   }
00957 
00958   inline complex<long double>&
00959   complex<long double>::operator*=(long double __r)
00960   {
00961     _M_value *= __r;
00962     return *this;
00963   }
00964 
00965   inline complex<long double>&
00966   complex<long double>::operator/=(long double __r)
00967   {
00968     _M_value /= __r;
00969     return *this;
00970   }
00971 
00972   template<typename _Tp>
00973     inline complex<long double>&
00974     complex<long double>::operator=(const complex<_Tp>& __z)
00975     {
00976       __real__ _M_value = __z.real();
00977       __imag__ _M_value = __z.imag();
00978       return *this;
00979     }
00980 
00981   template<typename _Tp>
00982     inline complex<long double>&
00983     complex<long double>::operator+=(const complex<_Tp>& __z)
00984     {
00985       __real__ _M_value += __z.real();
00986       __imag__ _M_value += __z.imag();
00987       return *this;
00988     }
00989 
00990   template<typename _Tp>
00991     inline complex<long double>&
00992     complex<long double>::operator-=(const complex<_Tp>& __z)
00993     {
00994       __real__ _M_value -= __z.real();
00995       __imag__ _M_value -= __z.imag();
00996       return *this;
00997     }
00998     
00999   template<typename _Tp>
01000     inline complex<long double>&
01001     complex<long double>::operator*=(const complex<_Tp>& __z)
01002     {
01003       _ComplexT __t;
01004       __real__ __t = __z.real();
01005       __imag__ __t = __z.imag();
01006       _M_value *= __t;
01007       return *this;
01008     }
01009 
01010   template<typename _Tp>
01011     inline complex<long double>&
01012     complex<long double>::operator/=(const complex<_Tp>& __z)
01013     {
01014       _ComplexT __t;
01015       __real__ __t = __z.real();
01016       __imag__ __t = __z.imag();
01017       _M_value /= __t;
01018       return *this;
01019     }
01020 
01021   // These bits have to be at the end of this file, so that the
01022   // specializations have all been defined.
01023   // ??? No, they have to be there because of compiler limitation at
01024   // inlining.  It suffices that class specializations be defined.
01025   inline
01026   complex<float>::complex(const complex<double>& __z)
01027   : _M_value(_ComplexT(__z._M_value)) { }
01028 
01029   inline
01030   complex<float>::complex(const complex<long double>& __z)
01031   : _M_value(_ComplexT(__z._M_value)) { }
01032 
01033   inline
01034   complex<double>::complex(const complex<float>& __z) 
01035   : _M_value(_ComplexT(__z._M_value)) { }
01036 
01037   inline
01038   complex<double>::complex(const complex<long double>& __z)
01039   {
01040     __real__ _M_value = __z.real();
01041     __imag__ _M_value = __z.imag();
01042   }
01043 
01044   inline
01045   complex<long double>::complex(const complex<float>& __z)
01046   : _M_value(_ComplexT(__z._M_value)) { }
01047 
01048   inline
01049   complex<long double>::complex(const complex<double>& __z)
01050   : _M_value(_ComplexT(__z._M_value)) { }
01051 } // namespace std
01052 
01053 #endif  /* _CPP_COMPLEX */