complex

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00001 // The template and inlines for the -*- C++ -*- complex number classes.
00002 
00003 // Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002
00004 // Free Software Foundation, Inc.
00005 //
00006 // This file is part of the GNU ISO C++ Library.  This library is free
00007 // software; you can redistribute it and/or modify it under the
00008 // terms of the GNU General Public License as published by the
00009 // Free Software Foundation; either version 2, or (at your option)
00010 // any later version.
00011 
00012 // This library is distributed in the hope that it will be useful,
00013 // but WITHOUT ANY WARRANTY; without even the implied warranty of
00014 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00015 // GNU General Public License for more details.
00016 
00017 // You should have received a copy of the GNU General Public License along
00018 // with this library; see the file COPYING.  If not, write to the Free
00019 // Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
00020 // USA.
00021 
00022 // As a special exception, you may use this file as part of a free software
00023 // library without restriction.  Specifically, if other files instantiate
00024 // templates or use macros or inline functions from this file, or you compile
00025 // this file and link it with other files to produce an executable, this
00026 // file does not by itself cause the resulting executable to be covered by
00027 // the GNU General Public License.  This exception does not however
00028 // invalidate any other reasons why the executable file might be covered by
00029 // the GNU General Public License.
00030 
00031 //
00032 // ISO C++ 14882: 26.2  Complex Numbers
00033 // Note: this is not a conforming implementation.
00034 // Initially implemented by Ulrich Drepper <drepper@cygnus.com>
00035 // Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
00036 //
00037 
00038 /** @file complex
00039  *  This is a Standard C++ Library header.  You should @c #include this header
00040  *  in your programs, rather than any of the "st[dl]_*.h" implementation files.
00041  */
00042 
00043 #ifndef _CPP_COMPLEX
00044 #define _CPP_COMPLEX    1
00045 
00046 #pragma GCC system_header
00047 
00048 #include <bits/c++config.h>
00049 #include <bits/cpp_type_traits.h>
00050 #include <cmath>
00051 #include <sstream>
00052 
00053 namespace std
00054 {
00055   // Forward declarations
00056   template<typename _Tp> class complex;
00057   template<> class complex<float>;
00058   template<> class complex<double>;
00059   template<> class complex<long double>;
00060 
00061   template<typename _Tp> _Tp abs(const complex<_Tp>&);
00062   template<typename _Tp> _Tp arg(const complex<_Tp>&);
00063   template<typename _Tp> _Tp norm(const complex<_Tp>&);
00064 
00065   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
00066   template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
00067 
00068   // Transcendentals:
00069   template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
00070   template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
00071   template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
00072   template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
00073   template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
00074   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
00075   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
00076   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, 
00077                        const complex<_Tp>&);
00078   template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
00079   template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
00080   template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
00081   template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
00082   template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
00083   template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
00084     
00085     
00086   // 26.2.2  Primary template class complex
00087   template<typename _Tp>
00088     class complex
00089     {
00090     public:
00091       typedef _Tp value_type;
00092       
00093       complex(const _Tp& = _Tp(), const _Tp & = _Tp());
00094 
00095       // Let's the compiler synthetize the copy constructor   
00096       // complex (const complex<_Tp>&);
00097       template<typename _Up>
00098         complex(const complex<_Up>&);
00099         
00100       _Tp real() const;
00101       _Tp imag() const;
00102 
00103       complex<_Tp>& operator=(const _Tp&);
00104       complex<_Tp>& operator+=(const _Tp&);
00105       complex<_Tp>& operator-=(const _Tp&);
00106       complex<_Tp>& operator*=(const _Tp&);
00107       complex<_Tp>& operator/=(const _Tp&);
00108 
00109       // Let's the compiler synthetize the
00110       // copy and assignment operator
00111       // complex<_Tp>& operator= (const complex<_Tp>&);
00112       template<typename _Up>
00113         complex<_Tp>& operator=(const complex<_Up>&);
00114       template<typename _Up>
00115         complex<_Tp>& operator+=(const complex<_Up>&);
00116       template<typename _Up>
00117         complex<_Tp>& operator-=(const complex<_Up>&);
00118       template<typename _Up>
00119         complex<_Tp>& operator*=(const complex<_Up>&);
00120       template<typename _Up>
00121         complex<_Tp>& operator/=(const complex<_Up>&);
00122 
00123     private:
00124       _Tp _M_real, _M_imag;
00125     };
00126 
00127   template<typename _Tp>
00128     inline _Tp
00129     complex<_Tp>::real() const { return _M_real; }
00130 
00131   template<typename _Tp>
00132     inline _Tp
00133     complex<_Tp>::imag() const { return _M_imag; }
00134 
00135   template<typename _Tp>
00136     inline 
00137     complex<_Tp>::complex(const _Tp& __r, const _Tp& __i)
00138     : _M_real(__r), _M_imag(__i) { }
00139 
00140   template<typename _Tp>
00141     template<typename _Up>
00142     inline 
00143     complex<_Tp>::complex(const complex<_Up>& __z)
00144     : _M_real(__z.real()), _M_imag(__z.imag()) { }
00145         
00146   template<typename _Tp>
00147     complex<_Tp>&
00148     complex<_Tp>::operator=(const _Tp& __t)
00149     {
00150      _M_real = __t;
00151      _M_imag = _Tp();
00152      return *this;
00153     } 
00154 
00155   // 26.2.5/1
00156   template<typename _Tp>
00157     inline complex<_Tp>&
00158     complex<_Tp>::operator+=(const _Tp& __t)
00159     {
00160       _M_real += __t;
00161       return *this;
00162     }
00163 
00164   // 26.2.5/3
00165   template<typename _Tp>
00166     inline complex<_Tp>&
00167     complex<_Tp>::operator-=(const _Tp& __t)
00168     {
00169       _M_real -= __t;
00170       return *this;
00171     }
00172 
00173   // 26.2.5/5
00174   template<typename _Tp>
00175     complex<_Tp>&
00176     complex<_Tp>::operator*=(const _Tp& __t)
00177     {
00178       _M_real *= __t;
00179       _M_imag *= __t;
00180       return *this;
00181     }
00182 
00183   // 26.2.5/7
00184   template<typename _Tp>
00185     complex<_Tp>&
00186     complex<_Tp>::operator/=(const _Tp& __t)
00187     {
00188       _M_real /= __t;
00189       _M_imag /= __t;
00190       return *this;
00191     }
00192 
00193   template<typename _Tp>
00194     template<typename _Up>
00195     complex<_Tp>&
00196     complex<_Tp>::operator=(const complex<_Up>& __z)
00197     {
00198       _M_real = __z.real();
00199       _M_imag = __z.imag();
00200       return *this;
00201     }
00202 
00203   // 26.2.5/9
00204   template<typename _Tp>
00205     template<typename _Up>
00206     complex<_Tp>&
00207     complex<_Tp>::operator+=(const complex<_Up>& __z)
00208     {
00209       _M_real += __z.real();
00210       _M_imag += __z.imag();
00211       return *this;
00212     }
00213 
00214   // 26.2.5/11
00215   template<typename _Tp>
00216     template<typename _Up>
00217     complex<_Tp>&
00218     complex<_Tp>::operator-=(const complex<_Up>& __z)
00219     {
00220       _M_real -= __z.real();
00221       _M_imag -= __z.imag();
00222       return *this;
00223     }
00224 
00225   // 26.2.5/13
00226   // XXX: This is a grammar school implementation.
00227   template<typename _Tp>
00228     template<typename _Up>
00229     complex<_Tp>&
00230     complex<_Tp>::operator*=(const complex<_Up>& __z)
00231     {
00232       const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
00233       _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
00234       _M_real = __r;
00235       return *this;
00236     }
00237 
00238   // 26.2.5/15
00239   // XXX: This is a grammar school implementation.
00240   template<typename _Tp>
00241     template<typename _Up>
00242     complex<_Tp>&
00243     complex<_Tp>::operator/=(const complex<_Up>& __z)
00244     {
00245       const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
00246       const _Tp __n = norm(__z);
00247       _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
00248       _M_real = __r / __n;
00249       return *this;
00250     }
00251     
00252   // Operators:
00253   template<typename _Tp>
00254     inline complex<_Tp>
00255     operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
00256     { return complex<_Tp> (__x) += __y; }
00257 
00258   template<typename _Tp>
00259     inline complex<_Tp>
00260     operator+(const complex<_Tp>& __x, const _Tp& __y)
00261     { return complex<_Tp> (__x) += __y; }
00262 
00263   template<typename _Tp>
00264     inline complex<_Tp>
00265     operator+(const _Tp& __x, const complex<_Tp>& __y)
00266     { return complex<_Tp> (__y) += __x; }
00267 
00268   template<typename _Tp>
00269     inline complex<_Tp>
00270     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
00271     { return complex<_Tp> (__x) -= __y; }
00272     
00273   template<typename _Tp>
00274     inline complex<_Tp>
00275     operator-(const complex<_Tp>& __x, const _Tp& __y)
00276     { return complex<_Tp> (__x) -= __y; }
00277 
00278   template<typename _Tp>
00279     inline complex<_Tp>
00280     operator-(const _Tp& __x, const complex<_Tp>& __y)
00281     { return complex<_Tp> (__x) -= __y; }
00282 
00283   template<typename _Tp>
00284     inline complex<_Tp>
00285     operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
00286     { return complex<_Tp> (__x) *= __y; }
00287 
00288   template<typename _Tp>
00289     inline complex<_Tp>
00290     operator*(const complex<_Tp>& __x, const _Tp& __y)
00291     { return complex<_Tp> (__x) *= __y; }
00292 
00293   template<typename _Tp>
00294     inline complex<_Tp>
00295     operator*(const _Tp& __x, const complex<_Tp>& __y)
00296     { return complex<_Tp> (__y) *= __x; }
00297 
00298   template<typename _Tp>
00299     inline complex<_Tp>
00300     operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
00301     { return complex<_Tp> (__x) /= __y; }
00302     
00303   template<typename _Tp>
00304     inline complex<_Tp>
00305     operator/(const complex<_Tp>& __x, const _Tp& __y)
00306     { return complex<_Tp> (__x) /= __y; }
00307 
00308   template<typename _Tp>
00309     inline complex<_Tp>
00310     operator/(const _Tp& __x, const complex<_Tp>& __y)
00311     { return complex<_Tp> (__x) /= __y; }
00312 
00313   template<typename _Tp>
00314     inline complex<_Tp>
00315     operator+(const complex<_Tp>& __x)
00316     { return __x; }
00317 
00318   template<typename _Tp>
00319     inline complex<_Tp>
00320     operator-(const complex<_Tp>& __x)
00321     {  return complex<_Tp>(-__x.real(), -__x.imag()); }
00322 
00323   template<typename _Tp>
00324     inline bool
00325     operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
00326     { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
00327 
00328   template<typename _Tp>
00329     inline bool
00330     operator==(const complex<_Tp>& __x, const _Tp& __y)
00331     { return __x.real() == __y && __x.imag() == _Tp(); }
00332 
00333   template<typename _Tp>
00334     inline bool
00335     operator==(const _Tp& __x, const complex<_Tp>& __y)
00336     { return __x == __y.real() && _Tp() == __y.imag(); }
00337 
00338   template<typename _Tp>
00339     inline bool
00340     operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
00341     { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
00342 
00343   template<typename _Tp>
00344     inline bool
00345     operator!=(const complex<_Tp>& __x, const _Tp& __y)
00346     { return __x.real() != __y || __x.imag() != _Tp(); }
00347 
00348   template<typename _Tp>
00349     inline bool
00350     operator!=(const _Tp& __x, const complex<_Tp>& __y)
00351     { return __x != __y.real() || _Tp() != __y.imag(); }
00352 
00353   template<typename _Tp, typename _CharT, class _Traits>
00354     basic_istream<_CharT, _Traits>&
00355     operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
00356     {
00357       _Tp __re_x, __im_x;
00358       _CharT __ch;
00359       __is >> __ch;
00360       if (__ch == '(') 
00361     {
00362       __is >> __re_x >> __ch;
00363       if (__ch == ',') 
00364         {
00365           __is >> __im_x >> __ch;
00366           if (__ch == ')') 
00367         __x = complex<_Tp>(__re_x, __im_x);
00368           else
00369         __is.setstate(ios_base::failbit);
00370         }
00371       else if (__ch == ')') 
00372         __x = complex<_Tp>(__re_x, _Tp(0));
00373       else
00374         __is.setstate(ios_base::failbit);
00375     }
00376       else 
00377     {
00378       __is.putback(__ch);
00379       __is >> __re_x;
00380       __x = complex<_Tp>(__re_x, _Tp(0));
00381     }
00382       return __is;
00383     }
00384 
00385   template<typename _Tp, typename _CharT, class _Traits>
00386     basic_ostream<_CharT, _Traits>&
00387     operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
00388     {
00389       basic_ostringstream<_CharT, _Traits> __s;
00390       __s.flags(__os.flags());
00391       __s.imbue(__os.getloc());
00392       __s.precision(__os.precision());
00393       __s << '(' << __x.real() << ',' << __x.imag() << ')';
00394       return __os << __s.str();
00395     }
00396 
00397   // Values
00398   template<typename _Tp>
00399     inline _Tp
00400     real(const complex<_Tp>& __z)
00401     { return __z.real(); }
00402     
00403   template<typename _Tp>
00404     inline _Tp
00405     imag(const complex<_Tp>& __z)
00406     { return __z.imag(); }
00407 
00408   template<typename _Tp>
00409     inline _Tp
00410     abs(const complex<_Tp>& __z)
00411     {
00412       _Tp __x = __z.real();
00413       _Tp __y = __z.imag();
00414       const _Tp __s = max(abs(__x), abs(__y));
00415       if (__s == _Tp())  // well ...
00416         return __s;
00417       __x /= __s; 
00418       __y /= __s;
00419       return __s * sqrt(__x * __x + __y * __y);
00420     }
00421 
00422   template<typename _Tp>
00423     inline _Tp
00424     arg(const complex<_Tp>& __z)
00425     { return atan2(__z.imag(), __z.real()); }
00426 
00427   // 26.2.7/5: norm(__z) returns the squared magintude of __z.
00428   //     As defined, norm() is -not- a norm is the common mathematical
00429   //     sens used in numerics.  The helper class _Norm_helper<> tries to
00430   //     distinguish between builtin floating point and the rest, so as
00431   //     to deliver an answer as close as possible to the real value.
00432   template<bool>
00433     struct _Norm_helper
00434     {
00435       template<typename _Tp>
00436         static inline _Tp _S_do_it(const complex<_Tp>& __z)
00437         {
00438           const _Tp __x = __z.real();
00439           const _Tp __y = __z.imag();
00440           return __x * __x + __y * __y;
00441         }
00442     };
00443 
00444   template<>
00445     struct _Norm_helper<true>
00446     {
00447       template<typename _Tp>
00448         static inline _Tp _S_do_it(const complex<_Tp>& __z)
00449         {
00450           _Tp __res = abs(__z);
00451           return __res * __res;
00452         }
00453     };
00454   
00455   template<typename _Tp>
00456     inline _Tp
00457     norm(const complex<_Tp>& __z)
00458     {
00459       return _Norm_helper<__is_floating<_Tp>::_M_type && !_GLIBCPP_FAST_MATH>::_S_do_it(__z);
00460     }
00461 
00462   template<typename _Tp>
00463     inline complex<_Tp>
00464     polar(const _Tp& __rho, const _Tp& __theta)
00465     { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
00466 
00467   template<typename _Tp>
00468     inline complex<_Tp>
00469     conj(const complex<_Tp>& __z)
00470     { return complex<_Tp>(__z.real(), -__z.imag()); }
00471   
00472   // Transcendentals
00473   template<typename _Tp>
00474     inline complex<_Tp>
00475     cos(const complex<_Tp>& __z)
00476     {
00477       const _Tp __x = __z.real();
00478       const _Tp __y = __z.imag();
00479       return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
00480     }
00481 
00482   template<typename _Tp>
00483     inline complex<_Tp>
00484     cosh(const complex<_Tp>& __z)
00485     {
00486       const _Tp __x = __z.real();
00487       const _Tp __y = __z.imag();
00488       return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
00489     }
00490 
00491   template<typename _Tp>
00492     inline complex<_Tp>
00493     exp(const complex<_Tp>& __z)
00494     { return polar(exp(__z.real()), __z.imag()); }
00495 
00496   template<typename _Tp>
00497     inline complex<_Tp>
00498     log(const complex<_Tp>& __z)
00499     { return complex<_Tp>(log(abs(__z)), arg(__z)); }
00500 
00501   template<typename _Tp>
00502     inline complex<_Tp>
00503     log10(const complex<_Tp>& __z)
00504     { return log(__z) / log(_Tp(10.0)); }
00505 
00506   template<typename _Tp>
00507     inline complex<_Tp>
00508     sin(const complex<_Tp>& __z)
00509     {
00510       const _Tp __x = __z.real();
00511       const _Tp __y = __z.imag();
00512       return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); 
00513     }
00514 
00515   template<typename _Tp>
00516     inline complex<_Tp>
00517     sinh(const complex<_Tp>& __z)
00518     {
00519       const _Tp __x = __z.real();
00520       const _Tp  __y = __z.imag();
00521       return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
00522     }
00523 
00524   template<typename _Tp>
00525     complex<_Tp>
00526     sqrt(const complex<_Tp>& __z)
00527     {
00528       _Tp __x = __z.real();
00529       _Tp __y = __z.imag();
00530 
00531       if (__x == _Tp())
00532         {
00533           _Tp __t = sqrt(abs(__y) / 2);
00534           return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
00535         }
00536       else
00537         {
00538           _Tp __t = sqrt(2 * (abs(__z) + abs(__x)));
00539           _Tp __u = __t / 2;
00540           return __x > _Tp()
00541             ? complex<_Tp>(__u, __y / __t)
00542             : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
00543         }
00544     }
00545 
00546   template<typename _Tp>
00547     inline complex<_Tp>
00548     tan(const complex<_Tp>& __z)
00549     {
00550       return sin(__z) / cos(__z);
00551     }
00552 
00553   template<typename _Tp>
00554     inline complex<_Tp>
00555     tanh(const complex<_Tp>& __z)
00556     {
00557       return sinh(__z) / cosh(__z);
00558     }
00559 
00560   template<typename _Tp>
00561     inline complex<_Tp>
00562     pow(const complex<_Tp>& __z, int __n)
00563     {
00564       return __pow_helper(__z, __n);
00565     }
00566 
00567   template<typename _Tp>
00568     complex<_Tp>
00569     pow(const complex<_Tp>& __x, const _Tp& __y)
00570     {
00571       if (__x.imag() == _Tp())
00572         return pow(__x.real(), __y);
00573 
00574       complex<_Tp> __t = log(__x);
00575       return polar(exp(__y * __t.real()), __y * __t.imag());
00576     }
00577 
00578   template<typename _Tp>
00579     inline complex<_Tp>
00580     pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
00581     {
00582       return __x == _Tp() ? _Tp() : exp(__y * log(__x));
00583     }
00584 
00585   template<typename _Tp>
00586     inline complex<_Tp>
00587     pow(const _Tp& __x, const complex<_Tp>& __y)
00588     {
00589       return __x == _Tp()
00590         ? _Tp()
00591         : polar(pow(__x, __y.real()), __y.imag() * log(__x));
00592     }
00593 
00594   // 26.2.3  complex specializations
00595   // complex<float> specialization
00596   template<> class complex<float>
00597   {
00598   public:
00599     typedef float value_type;
00600     
00601     complex(float = 0.0f, float = 0.0f);
00602 #ifdef _GLIBCPP_BUGGY_COMPLEX
00603     complex(const complex& __z) : _M_value(__z._M_value) { }
00604 #endif
00605     explicit complex(const complex<double>&);
00606     explicit complex(const complex<long double>&);
00607 
00608     float real() const;
00609     float imag() const;
00610 
00611     complex<float>& operator=(float);
00612     complex<float>& operator+=(float);
00613     complex<float>& operator-=(float);
00614     complex<float>& operator*=(float);
00615     complex<float>& operator/=(float);
00616         
00617     // Let's the compiler synthetize the copy and assignment
00618     // operator.  It always does a pretty good job.
00619     // complex& operator= (const complex&);
00620     template<typename _Tp>
00621       complex<float>&operator=(const complex<_Tp>&);
00622     template<typename _Tp>
00623       complex<float>& operator+=(const complex<_Tp>&);
00624     template<class _Tp>
00625       complex<float>& operator-=(const complex<_Tp>&);
00626     template<class _Tp>
00627       complex<float>& operator*=(const complex<_Tp>&);
00628     template<class _Tp>
00629       complex<float>&operator/=(const complex<_Tp>&);
00630 
00631   private:
00632     typedef __complex__ float _ComplexT;
00633     _ComplexT _M_value;
00634 
00635     complex(_ComplexT __z) : _M_value(__z) { }
00636         
00637     friend class complex<double>;
00638     friend class complex<long double>;
00639   };
00640 
00641   inline float
00642   complex<float>::real() const
00643   { return __real__ _M_value; }
00644 
00645   inline float
00646   complex<float>::imag() const
00647   { return __imag__ _M_value; }
00648 
00649   inline
00650   complex<float>::complex(float r, float i)
00651   {
00652     __real__ _M_value = r;
00653     __imag__ _M_value = i;
00654   }
00655 
00656   inline complex<float>&
00657   complex<float>::operator=(float __f)
00658   {
00659     __real__ _M_value = __f;
00660     __imag__ _M_value = 0.0f;
00661     return *this;
00662   }
00663 
00664   inline complex<float>&
00665   complex<float>::operator+=(float __f)
00666   {
00667     __real__ _M_value += __f;
00668     return *this;
00669   }
00670 
00671   inline complex<float>&
00672   complex<float>::operator-=(float __f)
00673   {
00674     __real__ _M_value -= __f;
00675     return *this;
00676   }
00677 
00678   inline complex<float>&
00679   complex<float>::operator*=(float __f)
00680   {
00681     _M_value *= __f;
00682     return *this;
00683   }
00684 
00685   inline complex<float>&
00686   complex<float>::operator/=(float __f)
00687   {
00688     _M_value /= __f;
00689     return *this;
00690   }
00691 
00692   template<typename _Tp>
00693   inline complex<float>&
00694   complex<float>::operator=(const complex<_Tp>& __z)
00695   {
00696     __real__ _M_value = __z.real();
00697     __imag__ _M_value = __z.imag();
00698     return *this;
00699   }
00700 
00701   template<typename _Tp>
00702   inline complex<float>&
00703   complex<float>::operator+=(const complex<_Tp>& __z)
00704   {
00705     __real__ _M_value += __z.real();
00706     __imag__ _M_value += __z.imag();
00707     return *this;
00708   }
00709     
00710   template<typename _Tp>
00711     inline complex<float>&
00712     complex<float>::operator-=(const complex<_Tp>& __z)
00713     {
00714      __real__ _M_value -= __z.real();
00715      __imag__ _M_value -= __z.imag();
00716      return *this;
00717     } 
00718 
00719   template<typename _Tp>
00720     inline complex<float>&
00721     complex<float>::operator*=(const complex<_Tp>& __z)
00722     {
00723       _ComplexT __t;
00724       __real__ __t = __z.real();
00725       __imag__ __t = __z.imag();
00726       _M_value *= __t;
00727       return *this;
00728     }
00729 
00730   template<typename _Tp>
00731     inline complex<float>&
00732     complex<float>::operator/=(const complex<_Tp>& __z)
00733     {
00734       _ComplexT __t;
00735       __real__ __t = __z.real();
00736       __imag__ __t = __z.imag();
00737       _M_value /= __t;
00738       return *this;
00739     }
00740 
00741   // 26.2.3  complex specializations
00742   // complex<double> specialization
00743   template<> class complex<double>
00744   {
00745   public:
00746     typedef double value_type;
00747 
00748     complex(double  =0.0, double =0.0);
00749 #ifdef _GLIBCPP_BUGGY_COMPLEX
00750     complex(const complex& __z) : _M_value(__z._M_value) { }
00751 #endif
00752     complex(const complex<float>&);
00753     explicit complex(const complex<long double>&);
00754         
00755     double real() const;
00756     double imag() const;
00757         
00758     complex<double>& operator=(double);
00759     complex<double>& operator+=(double);
00760     complex<double>& operator-=(double);
00761     complex<double>& operator*=(double);
00762     complex<double>& operator/=(double);
00763 
00764     // The compiler will synthetize this, efficiently.
00765     // complex& operator= (const complex&);
00766     template<typename _Tp>
00767       complex<double>& operator=(const complex<_Tp>&);
00768     template<typename _Tp>
00769       complex<double>& operator+=(const complex<_Tp>&);
00770     template<typename _Tp>
00771       complex<double>& operator-=(const complex<_Tp>&);
00772     template<typename _Tp>
00773       complex<double>& operator*=(const complex<_Tp>&);
00774     template<typename _Tp>
00775       complex<double>& operator/=(const complex<_Tp>&);
00776 
00777   private:
00778     typedef __complex__ double _ComplexT;
00779     _ComplexT _M_value;
00780 
00781     complex(_ComplexT __z) : _M_value(__z) { }
00782         
00783     friend class complex<float>;
00784     friend class complex<long double>;
00785   };
00786 
00787   inline double
00788   complex<double>::real() const
00789   { return __real__ _M_value; }
00790 
00791   inline double
00792   complex<double>::imag() const
00793   { return __imag__ _M_value; }
00794 
00795   inline
00796   complex<double>::complex(double __r, double __i)
00797   {
00798     __real__ _M_value = __r;
00799     __imag__ _M_value = __i;
00800   }
00801 
00802   inline complex<double>&
00803   complex<double>::operator=(double __d)
00804   {
00805     __real__ _M_value = __d;
00806     __imag__ _M_value = 0.0;
00807     return *this;
00808   }
00809 
00810   inline complex<double>&
00811   complex<double>::operator+=(double __d)
00812   {
00813     __real__ _M_value += __d;
00814     return *this;
00815   }
00816 
00817   inline complex<double>&
00818   complex<double>::operator-=(double __d)
00819   {
00820     __real__ _M_value -= __d;
00821     return *this;
00822   }
00823 
00824   inline complex<double>&
00825   complex<double>::operator*=(double __d)
00826   {
00827     _M_value *= __d;
00828     return *this;
00829   }
00830 
00831   inline complex<double>&
00832   complex<double>::operator/=(double __d)
00833   {
00834     _M_value /= __d;
00835     return *this;
00836   }
00837 
00838   template<typename _Tp>
00839     inline complex<double>&
00840     complex<double>::operator=(const complex<_Tp>& __z)
00841     {
00842       __real__ _M_value = __z.real();
00843       __imag__ _M_value = __z.imag();
00844       return *this;
00845     }
00846     
00847   template<typename _Tp>
00848     inline complex<double>&
00849     complex<double>::operator+=(const complex<_Tp>& __z)
00850     {
00851       __real__ _M_value += __z.real();
00852       __imag__ _M_value += __z.imag();
00853       return *this;
00854     }
00855 
00856   template<typename _Tp>
00857     inline complex<double>&
00858     complex<double>::operator-=(const complex<_Tp>& __z)
00859     {
00860       __real__ _M_value -= __z.real();
00861       __imag__ _M_value -= __z.imag();
00862       return *this;
00863     }
00864 
00865   template<typename _Tp>
00866     inline complex<double>&
00867     complex<double>::operator*=(const complex<_Tp>& __z)
00868     {
00869       _ComplexT __t;
00870       __real__ __t = __z.real();
00871       __imag__ __t = __z.imag();
00872       _M_value *= __t;
00873       return *this;
00874     }
00875 
00876   template<typename _Tp>
00877     inline complex<double>&
00878     complex<double>::operator/=(const complex<_Tp>& __z)
00879     {
00880       _ComplexT __t;
00881       __real__ __t = __z.real();
00882       __imag__ __t = __z.imag();
00883       _M_value /= __t;
00884       return *this;
00885     }
00886 
00887   // 26.2.3  complex specializations
00888   // complex<long double> specialization
00889   template<> class complex<long double>
00890   {
00891   public:
00892     typedef long double value_type;
00893 
00894     complex(long double = 0.0L, long double = 0.0L);
00895 #ifdef _GLIBCPP_BUGGY_COMPLEX
00896     complex(const complex& __z) : _M_value(__z._M_value) { }
00897 #endif
00898     complex(const complex<float>&);
00899     complex(const complex<double>&);
00900 
00901     long double real() const;
00902     long double imag() const;
00903 
00904     complex<long double>& operator= (long double);
00905     complex<long double>& operator+= (long double);
00906     complex<long double>& operator-= (long double);
00907     complex<long double>& operator*= (long double);
00908     complex<long double>& operator/= (long double);
00909 
00910     // The compiler knows how to do this efficiently
00911     // complex& operator= (const complex&);
00912     template<typename _Tp>
00913       complex<long double>& operator=(const complex<_Tp>&);
00914     template<typename _Tp>
00915       complex<long double>& operator+=(const complex<_Tp>&);
00916     template<typename _Tp>
00917       complex<long double>& operator-=(const complex<_Tp>&);
00918     template<typename _Tp>
00919       complex<long double>& operator*=(const complex<_Tp>&);
00920     template<typename _Tp>
00921       complex<long double>& operator/=(const complex<_Tp>&);
00922 
00923   private:
00924     typedef __complex__ long double _ComplexT;
00925     _ComplexT _M_value;
00926 
00927     complex(_ComplexT __z) : _M_value(__z) { }
00928 
00929     friend class complex<float>;
00930     friend class complex<double>;
00931   };
00932 
00933   inline
00934   complex<long double>::complex(long double __r, long double __i)
00935   {
00936     __real__ _M_value = __r;
00937     __imag__ _M_value = __i;
00938   }
00939 
00940   inline long double
00941   complex<long double>::real() const
00942   { return __real__ _M_value; }
00943 
00944   inline long double
00945   complex<long double>::imag() const
00946   { return __imag__ _M_value; }
00947 
00948   inline complex<long double>&   
00949   complex<long double>::operator=(long double __r)
00950   {
00951     __real__ _M_value = __r;
00952     __imag__ _M_value = 0.0L;
00953     return *this;
00954   }
00955 
00956   inline complex<long double>&
00957   complex<long double>::operator+=(long double __r)
00958   {
00959     __real__ _M_value += __r;
00960     return *this;
00961   }
00962 
00963   inline complex<long double>&
00964   complex<long double>::operator-=(long double __r)
00965   {
00966     __real__ _M_value -= __r;
00967     return *this;
00968   }
00969 
00970   inline complex<long double>&
00971   complex<long double>::operator*=(long double __r)
00972   {
00973     _M_value *= __r;
00974     return *this;
00975   }
00976 
00977   inline complex<long double>&
00978   complex<long double>::operator/=(long double __r)
00979   {
00980     _M_value /= __r;
00981     return *this;
00982   }
00983 
00984   template<typename _Tp>
00985     inline complex<long double>&
00986     complex<long double>::operator=(const complex<_Tp>& __z)
00987     {
00988       __real__ _M_value = __z.real();
00989       __imag__ _M_value = __z.imag();
00990       return *this;
00991     }
00992 
00993   template<typename _Tp>
00994     inline complex<long double>&
00995     complex<long double>::operator+=(const complex<_Tp>& __z)
00996     {
00997       __real__ _M_value += __z.real();
00998       __imag__ _M_value += __z.imag();
00999       return *this;
01000     }
01001 
01002   template<typename _Tp>
01003     inline complex<long double>&
01004     complex<long double>::operator-=(const complex<_Tp>& __z)
01005     {
01006       __real__ _M_value -= __z.real();
01007       __imag__ _M_value -= __z.imag();
01008       return *this;
01009     }
01010     
01011   template<typename _Tp>
01012     inline complex<long double>&
01013     complex<long double>::operator*=(const complex<_Tp>& __z)
01014     {
01015       _ComplexT __t;
01016       __real__ __t = __z.real();
01017       __imag__ __t = __z.imag();
01018       _M_value *= __t;
01019       return *this;
01020     }
01021 
01022   template<typename _Tp>
01023     inline complex<long double>&
01024     complex<long double>::operator/=(const complex<_Tp>& __z)
01025     {
01026       _ComplexT __t;
01027       __real__ __t = __z.real();
01028       __imag__ __t = __z.imag();
01029       _M_value /= __t;
01030       return *this;
01031     }
01032 
01033   // These bits have to be at the end of this file, so that the
01034   // specializations have all been defined.
01035   // ??? No, they have to be there because of compiler limitation at
01036   // inlining.  It suffices that class specializations be defined.
01037   inline
01038   complex<float>::complex(const complex<double>& __z)
01039   : _M_value(_ComplexT(__z._M_value)) { }
01040 
01041   inline
01042   complex<float>::complex(const complex<long double>& __z)
01043   : _M_value(_ComplexT(__z._M_value)) { }
01044 
01045   inline
01046   complex<double>::complex(const complex<float>& __z) 
01047   : _M_value(_ComplexT(__z._M_value)) { }
01048 
01049   inline
01050   complex<double>::complex(const complex<long double>& __z)
01051   {
01052     __real__ _M_value = __z.real();
01053     __imag__ _M_value = __z.imag();
01054   }
01055 
01056   inline
01057   complex<long double>::complex(const complex<float>& __z)
01058   : _M_value(_ComplexT(__z._M_value)) { }
01059 
01060   inline
01061   complex<long double>::complex(const complex<double>& __z)
01062   : _M_value(_ComplexT(__z._M_value)) { }
01063 } // namespace std
01064 
01065 #endif  /* _CPP_COMPLEX */

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