# 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, 2003, 2004
    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 _GLIBCXX_COMPLEX
    00044 #define _GLIBCXX_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   ///  Return magnitude of @a z.
    00062   template<typename _Tp> _Tp abs(const complex<_Tp>&);
    00063   ///  Return phase angle of @a z.
    00064   template<typename _Tp> _Tp arg(const complex<_Tp>&);
    00065   ///  Return @a z magnitude squared.
    00066   template<typename _Tp> _Tp norm(const complex<_Tp>&);
    00067
    00068   ///  Return complex conjugate of @a z.
    00069   template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
    00070   ///  Return complex with magnitude @a rho and angle @a theta.
    00071   template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
    00072
    00073   // Transcendentals:
    00074   /// Return complex cosine of @a z.
    00075   template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
    00076   /// Return complex hyperbolic cosine of @a z.
    00077   template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
    00078   /// Return complex base e exponential of @a z.
    00079   template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
    00080   /// Return complex natural logarithm of @a z.
    00081   template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
    00082   /// Return complex base 10 logarithm of @a z.
    00083   template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
    00084   /// Return complex cosine of @a z.
    00085   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
    00086   /// Return @a x to the @a y'th power.
    00087   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
    00088   /// Return @a x to the @a y'th power.
    00089   template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
    00090                                           const complex<_Tp>&);
    00091   /// Return @a x to the @a y'th power.
    00092   template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
    00093   /// Return complex sine of @a z.
    00094   template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
    00095   /// Return complex hyperbolic sine of @a z.
    00096   template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
    00097   /// Return complex square root of @a z.
    00098   template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
    00099   /// Return complex tangent of @a z.
    00100   template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
    00101   /// Return complex hyperbolic tangent of @a z.
    00102   template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
    00103   //@}
    00104
    00105
    00106   // 26.2.2  Primary template class complex
    00107   /**
    00108    *  Template to represent complex numbers.
    00109    *
    00110    *  Specializations for float, double, and long double are part of the
    00111    *  library.  Results with any other type are not guaranteed.
    00112    *
    00113    *  @param  Tp  Type of real and imaginary values.
    00114   */
    00115   template<typename _Tp>
    00116     struct complex
    00117     {
    00118       /// Value typedef.
    00119       typedef _Tp value_type;
    00120
    00121       ///  Default constructor.  First parameter is x, second parameter is y.
    00122       ///  Unspecified parameters default to 0.
    00123       complex(const _Tp& = _Tp(), const _Tp & = _Tp());
    00124
    00125       // Lets the compiler synthesize the copy constructor
    00126       // complex (const complex<_Tp>&);
    00127       ///  Copy constructor.
    00128       template<typename _Up>
    00129         complex(const complex<_Up>&);
    00130
    00131       ///  Return real part of complex number.
    00132       _Tp& real();
    00133       ///  Return real part of complex number.
    00134       const _Tp& real() const;
    00135       ///  Return imaginary part of complex number.
    00136       _Tp& imag();
    00137       ///  Return imaginary part of complex number.
    00138       const _Tp& imag() const;
    00139
    00140       /// Assign this complex number to scalar @a t.
    00141       complex<_Tp>& operator=(const _Tp&);
    00142       /// Add @a t to this complex number.
    00143       complex<_Tp>& operator+=(const _Tp&);
    00144       /// Subtract @a t from this complex number.
    00145       complex<_Tp>& operator-=(const _Tp&);
    00146       /// Multiply this complex number by @a t.
    00147       complex<_Tp>& operator*=(const _Tp&);
    00148       /// Divide this complex number by @a t.
    00149       complex<_Tp>& operator/=(const _Tp&);
    00150
    00151       // Lets the compiler synthesize the
    00152       // copy and assignment operator
    00153       // complex<_Tp>& operator= (const complex<_Tp>&);
    00154       /// Assign this complex number to complex @a z.
    00155       template<typename _Up>
    00156         complex<_Tp>& operator=(const complex<_Up>&);
    00157       /// Add @a z to this complex number.
    00158       template<typename _Up>
    00159         complex<_Tp>& operator+=(const complex<_Up>&);
    00160       /// Subtract @a z from this complex number.
    00161       template<typename _Up>
    00162         complex<_Tp>& operator-=(const complex<_Up>&);
    00163       /// Multiply this complex number by @a z.
    00164       template<typename _Up>
    00165         complex<_Tp>& operator*=(const complex<_Up>&);
    00166       /// Divide this complex number by @a z.
    00167       template<typename _Up>
    00168         complex<_Tp>& operator/=(const complex<_Up>&);
    00169
    00170       const complex& __rep() const;
    00171
    00172     private:
    00173       _Tp _M_real;
    00174       _Tp _M_imag;
    00175     };
    00176
    00177   template<typename _Tp>
    00178     inline _Tp&
    00179     complex<_Tp>::real() { return _M_real; }
    00180
    00181   template<typename _Tp>
    00182     inline const _Tp&
    00183     complex<_Tp>::real() const { return _M_real; }
    00184
    00185   template<typename _Tp>
    00186     inline _Tp&
    00187     complex<_Tp>::imag() { return _M_imag; }
    00188
    00189   template<typename _Tp>
    00190     inline const _Tp&
    00191     complex<_Tp>::imag() const { return _M_imag; }
    00192
    00193   template<typename _Tp>
    00194     inline
    00195     complex<_Tp>::complex(const _Tp& __r, const _Tp& __i)
    00196     : _M_real(__r), _M_imag(__i) { }
    00197
    00198   template<typename _Tp>
    00199     template<typename _Up>
    00200     inline
    00201     complex<_Tp>::complex(const complex<_Up>& __z)
    00202     : _M_real(__z.real()), _M_imag(__z.imag()) { }
    00203
    00204   template<typename _Tp>
    00205     complex<_Tp>&
    00206     complex<_Tp>::operator=(const _Tp& __t)
    00207     {
    00208      _M_real = __t;
    00209      _M_imag = _Tp();
    00210      return *this;
    00211     }
    00212
    00213   // 26.2.5/1
    00214   template<typename _Tp>
    00215     inline complex<_Tp>&
    00216     complex<_Tp>::operator+=(const _Tp& __t)
    00217     {
    00218       _M_real += __t;
    00219       return *this;
    00220     }
    00221
    00222   // 26.2.5/3
    00223   template<typename _Tp>
    00224     inline complex<_Tp>&
    00225     complex<_Tp>::operator-=(const _Tp& __t)
    00226     {
    00227       _M_real -= __t;
    00228       return *this;
    00229     }
    00230
    00231   // 26.2.5/5
    00232   template<typename _Tp>
    00233     complex<_Tp>&
    00234     complex<_Tp>::operator*=(const _Tp& __t)
    00235     {
    00236       _M_real *= __t;
    00237       _M_imag *= __t;
    00238       return *this;
    00239     }
    00240
    00241   // 26.2.5/7
    00242   template<typename _Tp>
    00243     complex<_Tp>&
    00244     complex<_Tp>::operator/=(const _Tp& __t)
    00245     {
    00246       _M_real /= __t;
    00247       _M_imag /= __t;
    00248       return *this;
    00249     }
    00250
    00251   template<typename _Tp>
    00252     template<typename _Up>
    00253     complex<_Tp>&
    00254     complex<_Tp>::operator=(const complex<_Up>& __z)
    00255     {
    00256       _M_real = __z.real();
    00257       _M_imag = __z.imag();
    00258       return *this;
    00259     }
    00260
    00261   // 26.2.5/9
    00262   template<typename _Tp>
    00263     template<typename _Up>
    00264     complex<_Tp>&
    00265     complex<_Tp>::operator+=(const complex<_Up>& __z)
    00266     {
    00267       _M_real += __z.real();
    00268       _M_imag += __z.imag();
    00269       return *this;
    00270     }
    00271
    00272   // 26.2.5/11
    00273   template<typename _Tp>
    00274     template<typename _Up>
    00275     complex<_Tp>&
    00276     complex<_Tp>::operator-=(const complex<_Up>& __z)
    00277     {
    00278       _M_real -= __z.real();
    00279       _M_imag -= __z.imag();
    00280       return *this;
    00281     }
    00282
    00283   // 26.2.5/13
    00284   // XXX: This is a grammar school implementation.
    00285   template<typename _Tp>
    00286     template<typename _Up>
    00287     complex<_Tp>&
    00288     complex<_Tp>::operator*=(const complex<_Up>& __z)
    00289     {
    00290       const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
    00291       _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
    00292       _M_real = __r;
    00293       return *this;
    00294     }
    00295
    00296   // 26.2.5/15
    00297   // XXX: This is a grammar school implementation.
    00298   template<typename _Tp>
    00299     template<typename _Up>
    00300     complex<_Tp>&
    00301     complex<_Tp>::operator/=(const complex<_Up>& __z)
    00302     {
    00303       const _Tp __r =  _M_real * __z.real() + _M_imag * __z.imag();
    00304       const _Tp __n = std::norm(__z);
    00305       _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
    00306       _M_real = __r / __n;
    00307       return *this;
    00308     }
    00309
    00310   template<typename _Tp>
    00311     inline const complex<_Tp>&
    00312     complex<_Tp>::__rep() const { return *this; }
    00313
    00314   // Operators:
    00315   //@{
    00316   ///  Return new complex value @a x plus @a y.
    00317   template<typename _Tp>
    00318     inline complex<_Tp>
    00319     operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
    00320     {
    00321       complex<_Tp> __r = __x;
    00322       __r += __y;
    00323       return __r;
    00324     }
    00325
    00326   template<typename _Tp>
    00327     inline complex<_Tp>
    00328     operator+(const complex<_Tp>& __x, const _Tp& __y)
    00329     {
    00330       complex<_Tp> __r = __x;
    00331       __r.real() += __y;
    00332       return __r;
    00333     }
    00334
    00335   template<typename _Tp>
    00336     inline complex<_Tp>
    00337     operator+(const _Tp& __x, const complex<_Tp>& __y)
    00338     {
    00339       complex<_Tp> __r = __y;
    00340       __r.real() += __x;
    00341       return __r;
    00342     }
    00343   //@}
    00344
    00345   //@{
    00346   ///  Return new complex value @a x minus @a y.
    00347   template<typename _Tp>
    00348     inline complex<_Tp>
    00349     operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
    00350     {
    00351       complex<_Tp> __r = __x;
    00352       __r -= __y;
    00353       return __r;
    00354     }
    00355
    00356   template<typename _Tp>
    00357     inline complex<_Tp>
    00358     operator-(const complex<_Tp>& __x, const _Tp& __y)
    00359     {
    00360       complex<_Tp> __r = __x;
    00361       __r.real() -= __y;
    00362       return __r;
    00363     }
    00364
    00365   template<typename _Tp>
    00366     inline complex<_Tp>
    00367     operator-(const _Tp& __x, const complex<_Tp>& __y)
    00368     {
    00369       complex<_Tp> __r(__x, -__y.imag());
    00370       __r.real() -= __y.real();
    00371       return __r;
    00372     }
    00373   //@}
    00374
    00375   //@{
    00376   ///  Return new complex value @a x times @a y.
    00377   template<typename _Tp>
    00378     inline complex<_Tp>
    00379     operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
    00380     {
    00381       complex<_Tp> __r = __x;
    00382       __r *= __y;
    00383       return __r;
    00384     }
    00385
    00386   template<typename _Tp>
    00387     inline complex<_Tp>
    00388     operator*(const complex<_Tp>& __x, const _Tp& __y)
    00389     {
    00390       complex<_Tp> __r = __x;
    00391       __r *= __y;
    00392       return __r;
    00393     }
    00394
    00395   template<typename _Tp>
    00396     inline complex<_Tp>
    00397     operator*(const _Tp& __x, const complex<_Tp>& __y)
    00398     {
    00399       complex<_Tp> __r = __y;
    00400       __r *= __x;
    00401       return __r;
    00402     }
    00403   //@}
    00404
    00405   //@{
    00406   ///  Return new complex value @a x divided by @a y.
    00407   template<typename _Tp>
    00408     inline complex<_Tp>
    00409     operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
    00410     {
    00411       complex<_Tp> __r = __x;
    00412       __r /= __y;
    00413       return __r;
    00414     }
    00415
    00416   template<typename _Tp>
    00417     inline complex<_Tp>
    00418     operator/(const complex<_Tp>& __x, const _Tp& __y)
    00419     {
    00420       complex<_Tp> __r = __x;
    00421       __r /= __y;
    00422       return __r;
    00423     }
    00424
    00425   template<typename _Tp>
    00426     inline complex<_Tp>
    00427     operator/(const _Tp& __x, const complex<_Tp>& __y)
    00428     {
    00429       complex<_Tp> __r = __x;
    00430       __r /= __y;
    00431       return __r;
    00432     }
    00433   //@}
    00434
    00435   ///  Return @a x.
    00436   template<typename _Tp>
    00437     inline complex<_Tp>
    00438     operator+(const complex<_Tp>& __x)
    00439     { return __x; }
    00440
    00441   ///  Return complex negation of @a x.
    00442   template<typename _Tp>
    00443     inline complex<_Tp>
    00444     operator-(const complex<_Tp>& __x)
    00445     {  return complex<_Tp>(-__x.real(), -__x.imag()); }
    00446
    00447   //@{
    00448   ///  Return true if @a x is equal to @a y.
    00449   template<typename _Tp>
    00450     inline bool
    00451     operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
    00452     { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
    00453
    00454   template<typename _Tp>
    00455     inline bool
    00456     operator==(const complex<_Tp>& __x, const _Tp& __y)
    00457     { return __x.real() == __y && __x.imag() == _Tp(); }
    00458
    00459   template<typename _Tp>
    00460     inline bool
    00461     operator==(const _Tp& __x, const complex<_Tp>& __y)
    00462     { return __x == __y.real() && _Tp() == __y.imag(); }
    00463   //@}
    00464
    00465   //@{
    00466   ///  Return false if @a x is equal to @a y.
    00467   template<typename _Tp>
    00468     inline bool
    00469     operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
    00470     { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
    00471
    00472   template<typename _Tp>
    00473     inline bool
    00474     operator!=(const complex<_Tp>& __x, const _Tp& __y)
    00475     { return __x.real() != __y || __x.imag() != _Tp(); }
    00476
    00477   template<typename _Tp>
    00478     inline bool
    00479     operator!=(const _Tp& __x, const complex<_Tp>& __y)
    00480     { return __x != __y.real() || _Tp() != __y.imag(); }
    00481   //@}
    00482
    00483   ///  Extraction operator for complex values.
    00484   template<typename _Tp, typename _CharT, class _Traits>
    00485     basic_istream<_CharT, _Traits>&
    00486     operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
    00487     {
    00488       _Tp __re_x, __im_x;
    00489       _CharT __ch;
    00490       __is >> __ch;
    00491       if (__ch == '(')
    00492     {
    00493       __is >> __re_x >> __ch;
    00494       if (__ch == ',')
    00495         {
    00496           __is >> __im_x >> __ch;
    00497           if (__ch == ')')
    00498         __x = complex<_Tp>(__re_x, __im_x);
    00499           else
    00500         __is.setstate(ios_base::failbit);
    00501         }
    00502       else if (__ch == ')')
    00503         __x = __re_x;
    00504       else
    00505         __is.setstate(ios_base::failbit);
    00506     }
    00507       else
    00508     {
    00509       __is.putback(__ch);
    00510       __is >> __re_x;
    00511       __x = __re_x;
    00512     }
    00513       return __is;
    00514     }
    00515
    00516   ///  Insertion operator for complex values.
    00517   template<typename _Tp, typename _CharT, class _Traits>
    00518     basic_ostream<_CharT, _Traits>&
    00519     operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
    00520     {
    00521       basic_ostringstream<_CharT, _Traits> __s;
    00522       __s.flags(__os.flags());
    00523       __s.imbue(__os.getloc());
    00524       __s.precision(__os.precision());
    00525       __s << '(' << __x.real() << ',' << __x.imag() << ')';
    00526       return __os << __s.str();
    00527     }
    00528
    00529   // Values
    00530   template<typename _Tp>
    00531     inline _Tp&
    00532     real(complex<_Tp>& __z)
    00533     { return __z.real(); }
    00534
    00535   template<typename _Tp>
    00536     inline const _Tp&
    00537     real(const complex<_Tp>& __z)
    00538     { return __z.real(); }
    00539
    00540   template<typename _Tp>
    00541     inline _Tp&
    00542     imag(complex<_Tp>& __z)
    00543     { return __z.imag(); }
    00544
    00545   template<typename _Tp>
    00546     inline const _Tp&
    00547     imag(const complex<_Tp>& __z)
    00548     { return __z.imag(); }
    00549
    00550   // 26.2.7/3 abs(__z):  Returns the magnitude of __z.
    00551   template<typename _Tp>
    00552     inline _Tp
    00553     __complex_abs(const complex<_Tp>& __z)
    00554     {
    00555       _Tp __x = __z.real();
    00556       _Tp __y = __z.imag();
    00557       const _Tp __s = std::max(abs(__x), abs(__y));
    00558       if (__s == _Tp())  // well ...
    00559         return __s;
    00560       __x /= __s;
    00561       __y /= __s;
    00562           return __s * sqrt(__x * __x + __y * __y);
    00563     }
    00564
    00565   inline float
    00566   __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
    00567
    00568   inline double
    00569   __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
    00570
    00571   inline long double
    00572   __complex_abs(const __complex__ long double& __z)
    00573   {
    00574     return __builtin_cabsl(__z);
    00575   }
    00576
    00577   template<typename _Tp>
    00578     inline _Tp
    00579     abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
    00580
    00581
    00582   // 26.2.7/4: arg(__z): Returns the phase angle of __z.
    00583   template<typename _Tp>
    00584     inline _Tp
    00585     __complex_arg(const complex<_Tp>& __z)
    00586     {
    00587       return  atan2(__z.imag(), __z.real());
    00588     }
    00589
    00590   inline float
    00591   __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
    00592
    00593   inline double
    00594   __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
    00595
    00596   inline long double
    00597   __complex_arg(const __complex__ long double& __z)
    00598   { return __builtin_cargl(__z); }
    00599
    00600   template<typename _Tp>
    00601     inline _Tp
    00602     arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
    00603
    00604   // 26.2.7/5: norm(__z) returns the squared magintude of __z.
    00605   //     As defined, norm() is -not- a norm is the common mathematical
    00606   //     sens used in numerics.  The helper class _Norm_helper<> tries to
    00607   //     distinguish between builtin floating point and the rest, so as
    00608   //     to deliver an answer as close as possible to the real value.
    00609   template<bool>
    00610     struct _Norm_helper
    00611     {
    00612       template<typename _Tp>
    00613         static inline _Tp _S_do_it(const complex<_Tp>& __z)
    00614         {
    00615           const _Tp __x = __z.real();
    00616           const _Tp __y = __z.imag();
    00617           return __x * __x + __y * __y;
    00618         }
    00619     };
    00620
    00621   template<>
    00622     struct _Norm_helper<true>
    00623     {
    00624       template<typename _Tp>
    00625         static inline _Tp _S_do_it(const complex<_Tp>& __z)
    00626         {
    00627           _Tp __res = std::abs(__z);
    00628           return __res * __res;
    00629         }
    00630     };
    00631
    00632   template<typename _Tp>
    00633     inline _Tp
    00634     norm(const complex<_Tp>& __z)
    00635     {
    00636       return _Norm_helper<__is_floating<_Tp>::_M_type && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
    00637     }
    00638
    00639   template<typename _Tp>
    00640     inline complex<_Tp>
    00641     polar(const _Tp& __rho, const _Tp& __theta)
    00642     { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
    00643
    00644   template<typename _Tp>
    00645     inline complex<_Tp>
    00646     conj(const complex<_Tp>& __z)
    00647     { return complex<_Tp>(__z.real(), -__z.imag()); }
    00648
    00649   // Transcendentals
    00650
    00651   // 26.2.8/1 cos(__z):  Returns the cosine of __z.
    00652   template<typename _Tp>
    00653     inline complex<_Tp>
    00654     __complex_cos(const complex<_Tp>& __z)
    00655     {
    00656       const _Tp __x = __z.real();
    00657       const _Tp __y = __z.imag();
    00658       return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
    00659     }
    00660
    00661   inline __complex__ float
    00662   __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
    00663
    00664   inline __complex__ double
    00665   __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
    00666
    00667   inline __complex__ long double
    00668   __complex_cos(const __complex__ long double& __z)
    00669   { return __builtin_ccosl(__z); }
    00670
    00671   template<typename _Tp>
    00672     inline complex<_Tp>
    00673     cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
    00674
    00675   // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
    00676   template<typename _Tp>
    00677     inline complex<_Tp>
    00678     __complex_cosh(const complex<_Tp>& __z)
    00679       {
    00680         const _Tp __x = __z.real();
    00681         const _Tp __y = __z.imag();
    00682         return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
    00683       }
    00684
    00685   inline __complex__ float
    00686   __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
    00687
    00688   inline __complex__ double
    00689   __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
    00690
    00691   inline __complex__ long double
    00692   __complex_cosh(const __complex__ long double& __z)
    00693   { return __builtin_ccoshl(__z); }
    00694
    00695   template<typename _Tp>
    00696     inline complex<_Tp>
    00697     cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
    00698
    00699   // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
    00700   template<typename _Tp>
    00701     inline complex<_Tp>
    00702     __complex_exp(const complex<_Tp>& __z)
    00703     { return std::polar(exp(__z.real()), __z.imag()); }
    00704
    00705   inline __complex__ float
    00706   __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
    00707
    00708   inline __complex__ double
    00709   __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
    00710
    00711   inline __complex__ long double
    00712     __complex_exp(const __complex__ long double& __z)
    00713     { return __builtin_cexpl(__z); }
    00714
    00715   template<typename _Tp>
    00716     inline complex<_Tp>
    00717     exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
    00718
    00719   // 26.2.8/5 log(__z): Reurns the natural complex logaritm of __z.
    00720   //                    The branch cut is along the negative axis.
    00721   template<typename _Tp>
    00722     inline complex<_Tp>
    00723     __complex_log(const complex<_Tp>& __z)
    00724     { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
    00725
    00726   /*
    00727   inline __complex__ float
    00728   __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
    00729
    00730   inline __complex__ double
    00731   __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
    00732
    00733   inline __complex__ long double
    00734   __complex_log(const __complex__ long double& __z)
    00735   { return __builtin_clogl(__z); } */
    00736
    00737   // FIXME: Currently wer don't use built-ins for log() because of some
    00738   //        obscure user name-space issues.  So, we use the generic version
    00739   //        which is why we don't use __z.__rep() in the call below.
    00740   template<typename _Tp>
    00741     inline complex<_Tp>
    00742     log(const complex<_Tp>& __z) { return __complex_log(__z); }
    00743
    00744   template<typename _Tp>
    00745     inline complex<_Tp>
    00746     log10(const complex<_Tp>& __z)
    00747     { return std::log(__z) / log(_Tp(10.0)); }
    00748
    00749   // 26.2.8/10 sin(__z): Returns the sine of __z.
    00750   template<typename _Tp>
    00751     inline complex<_Tp>
    00752     __complex_sin(const complex<_Tp>& __z)
    00753     {
    00754       const _Tp __x = __z.real();
    00755       const _Tp __y = __z.imag();
    00756       return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
    00757     }
    00758
    00759   inline __complex__ float
    00760   __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
    00761
    00762   inline __complex__ double
    00763   __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
    00764
    00765   inline __complex__ long double
    00766   __complex_sin(const __complex__ long double& __z)
    00767   { return __builtin_csinl(__z); }
    00768
    00769   template<typename _Tp>
    00770     inline complex<_Tp>
    00771     sin(const complex<_Tp>& __z) { __complex_sin(__z.__rep()); }
    00772
    00773   // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
    00774   template<typename _Tp>
    00775     inline complex<_Tp>
    00776     __complex_sinh(const complex<_Tp>& __z)
    00777     {
    00778       const _Tp __x = __z.real();
    00779       const _Tp  __y = __z.imag();
    00780       return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
    00781     }
    00782
    00783   inline __complex__ float
    00784   __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
    00785
    00786   inline __complex__ double
    00787   __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
    00788
    00789   inline __complex__ long double
    00790   __complex_sinh(const __complex__ long double& __z)
    00791   { return __builtin_csinhl(__z); }
    00792
    00793   template<typename _Tp>
    00794     inline complex<_Tp>
    00795     sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
    00796
    00797   // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
    00798   //                     The branch cut is on the negative axis.
    00799   template<typename _Tp>
    00800     complex<_Tp>
    00801     __complex_sqrt(const complex<_Tp>& __z)
    00802     {
    00803       _Tp __x = __z.real();
    00804       _Tp __y = __z.imag();
    00805
    00806       if (__x == _Tp())
    00807         {
    00808           _Tp __t = sqrt(abs(__y) / 2);
    00809           return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
    00810         }
    00811       else
    00812         {
    00813           _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
    00814           _Tp __u = __t / 2;
    00815           return __x > _Tp()
    00816             ? complex<_Tp>(__u, __y / __t)
    00817             : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
    00818         }
    00819     }
    00820
    00821   inline __complex__ float
    00822   __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
    00823
    00824   inline __complex__ double
    00825   __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
    00826
    00827   inline __complex__ long double
    00828   __complex_sqrt(const __complex__ long double& __z)
    00829   { return __builtin_csqrtl(__z); }
    00830
    00831   template<typename _Tp>
    00832     inline complex<_Tp>
    00833     sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
    00834
    00835   // 26.2.8/14 tan(__z):  Return the complex tangent of __z.
    00836
    00837   template<typename _Tp>
    00838     inline complex<_Tp>
    00839     __complex_tan(const complex<_Tp>& __z)
    00840     { return std::sin(__z) / std::cos(__z); }
    00841
    00842   inline __complex__ float
    00843   __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
    00844
    00845   inline __complex__ double
    00846   __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
    00847
    00848   inline __complex__ long double
    00849   __complex_tan(const __complex__ long double& __z)
    00850   { return __builtin_ctanl(__z); }
    00851
    00852   template<typename _Tp>
    00853     inline complex<_Tp>
    00854     tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
    00855
    00856   // 26.2.8/15 tanh(__z):  Returns the hyperbolic tangent of __z.
    00857
    00858   template<typename _Tp>
    00859     inline complex<_Tp>
    00860     __complex_tanh(const complex<_Tp>& __z)
    00861     { return std::sinh(__z) / std::cosh(__z); }
    00862
    00863   inline __complex__ float
    00864   __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
    00865
    00866   inline __complex__ double
    00867   __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
    00868
    00869   inline __complex__ long double
    00870   __complex_tanh(const __complex__ long double& __z)
    00871   { return __builtin_ctanhl(__z); }
    00872
    00873   template<typename _Tp>
    00874     inline complex<_Tp>
    00875     tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
    00876
    00877   // 26.2.8/9  pow(__x, __y): Returns the complex power base of __x
    00878   //                          raised to the __y-th power.  The branch
    00879   //                          cut is on the negative axis.
    00880   template<typename _Tp>
    00881     inline complex<_Tp>
    00882     pow(const complex<_Tp>& __z, int __n)
    00883     {
    00884       return std::__pow_helper(__z, __n);
    00885     }
    00886
    00887   template<typename _Tp>
    00888     complex<_Tp>
    00889     pow(const complex<_Tp>& __x, const _Tp& __y)
    00890     {
    00891       if (__x.imag() == _Tp() && __x.real() > _Tp())
    00892         return pow(__x.real(), __y);
    00893
    00894       complex<_Tp> __t = std::log(__x);
    00895       return std::polar(exp(__y * __t.real()), __y * __t.imag());
    00896     }
    00897
    00898   template<typename _Tp>
    00899     inline complex<_Tp>
    00900     __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
    00901     { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
    00902
    00903   inline __complex__ float
    00904   __complex_pow(__complex__ float __x, __complex__ float __y)
    00905   { return __builtin_cpowf(__x, __y); }
    00906
    00907   inline __complex__ double
    00908   __complex_pow(__complex__ double __x, __complex__ double __y)
    00909   { return __builtin_cpow(__x, __y); }
    00910
    00911   inline __complex__ long double
    00912   __complex_pow(__complex__ long double& __x, __complex__ long double& __y)
    00913   { return __builtin_cpowl(__x, __y); }
    00914
    00915   template<typename _Tp>
    00916     inline complex<_Tp>
    00917     pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
    00918     { return __complex_pow(__x, __y); }
    00919
    00920   template<typename _Tp>
    00921     inline complex<_Tp>
    00922     pow(const _Tp& __x, const complex<_Tp>& __y)
    00923     {
    00924       return __x > _Tp() ? std::polar(pow(__x, __y.real()),
    00925                       __y.imag() * log(__x))
    00926                      : std::pow(complex<_Tp>(__x, _Tp()), __y);
    00927     }
    00928
    00929   // 26.2.3  complex specializations
    00930   // complex<float> specialization
    00931   template<>
    00932     struct complex<float>
    00933     {
    00934       typedef float value_type;
    00935       typedef __complex__ float _ComplexT;
    00936
    00937       complex(_ComplexT __z) : _M_value(__z) { }
    00938
    00939       complex(float = 0.0f, float = 0.0f);
    00940 #ifdef _GLIBCXX_BUGGY_COMPLEX
    00941       complex(const complex& __z) : _M_value(__z._M_value) { }
    00942 #endif
    00943       explicit complex(const complex<double>&);
    00944       explicit complex(const complex<long double>&);
    00945
    00946       float& real();
    00947       const float& real() const;
    00948       float& imag();
    00949       const float& imag() const;
    00950
    00951       complex<float>& operator=(float);
    00952       complex<float>& operator+=(float);
    00953       complex<float>& operator-=(float);
    00954       complex<float>& operator*=(float);
    00955       complex<float>& operator/=(float);
    00956
    00957       // Let's the compiler synthetize the copy and assignment
    00958       // operator.  It always does a pretty good job.
    00959       // complex& operator= (const complex&);
    00960       template<typename _Tp>
    00961         complex<float>&operator=(const complex<_Tp>&);
    00962       template<typename _Tp>
    00963         complex<float>& operator+=(const complex<_Tp>&);
    00964       template<class _Tp>
    00965         complex<float>& operator-=(const complex<_Tp>&);
    00966       template<class _Tp>
    00967         complex<float>& operator*=(const complex<_Tp>&);
    00968       template<class _Tp>
    00969         complex<float>&operator/=(const complex<_Tp>&);
    00970
    00971       const _ComplexT& __rep() const { return _M_value; }
    00972
    00973     private:
    00974       _ComplexT _M_value;
    00975     };
    00976
    00977   inline float&
    00978   complex<float>::real()
    00979   { return __real__ _M_value; }
    00980
    00981   inline const float&
    00982   complex<float>::real() const
    00983   { return __real__ _M_value; }
    00984
    00985   inline float&
    00986   complex<float>::imag()
    00987   { return __imag__ _M_value; }
    00988
    00989   inline const float&
    00990   complex<float>::imag() const
    00991   { return __imag__ _M_value; }
    00992
    00993   inline
    00994   complex<float>::complex(float r, float i)
    00995   {
    00996     __real__ _M_value = r;
    00997     __imag__ _M_value = i;
    00998   }
    00999
    01000   inline complex<float>&
    01001   complex<float>::operator=(float __f)
    01002   {
    01003     __real__ _M_value = __f;
    01004     __imag__ _M_value = 0.0f;
    01005     return *this;
    01006   }
    01007
    01008   inline complex<float>&
    01009   complex<float>::operator+=(float __f)
    01010   {
    01011     __real__ _M_value += __f;
    01012     return *this;
    01013   }
    01014
    01015   inline complex<float>&
    01016   complex<float>::operator-=(float __f)
    01017   {
    01018     __real__ _M_value -= __f;
    01019     return *this;
    01020   }
    01021
    01022   inline complex<float>&
    01023   complex<float>::operator*=(float __f)
    01024   {
    01025     _M_value *= __f;
    01026     return *this;
    01027   }
    01028
    01029   inline complex<float>&
    01030   complex<float>::operator/=(float __f)
    01031   {
    01032     _M_value /= __f;
    01033     return *this;
    01034   }
    01035
    01036   template<typename _Tp>
    01037   inline complex<float>&
    01038   complex<float>::operator=(const complex<_Tp>& __z)
    01039   {
    01040     __real__ _M_value = __z.real();
    01041     __imag__ _M_value = __z.imag();
    01042     return *this;
    01043   }
    01044
    01045   template<typename _Tp>
    01046   inline complex<float>&
    01047   complex<float>::operator+=(const complex<_Tp>& __z)
    01048   {
    01049     __real__ _M_value += __z.real();
    01050     __imag__ _M_value += __z.imag();
    01051     return *this;
    01052   }
    01053
    01054   template<typename _Tp>
    01055     inline complex<float>&
    01056     complex<float>::operator-=(const complex<_Tp>& __z)
    01057     {
    01058      __real__ _M_value -= __z.real();
    01059      __imag__ _M_value -= __z.imag();
    01060      return *this;
    01061     }
    01062
    01063   template<typename _Tp>
    01064     inline complex<float>&
    01065     complex<float>::operator*=(const complex<_Tp>& __z)
    01066     {
    01067       _ComplexT __t;
    01068       __real__ __t = __z.real();
    01069       __imag__ __t = __z.imag();
    01070       _M_value *= __t;
    01071       return *this;
    01072     }
    01073
    01074   template<typename _Tp>
    01075     inline complex<float>&
    01076     complex<float>::operator/=(const complex<_Tp>& __z)
    01077     {
    01078       _ComplexT __t;
    01079       __real__ __t = __z.real();
    01080       __imag__ __t = __z.imag();
    01081       _M_value /= __t;
    01082       return *this;
    01083     }
    01084
    01085   // 26.2.3  complex specializations
    01086   // complex<double> specialization
    01087   template<>
    01088     struct complex<double>
    01089     {
    01090       typedef double value_type;
    01091       typedef __complex__ double _ComplexT;
    01092
    01093       complex(_ComplexT __z) : _M_value(__z) { }
    01094
    01095       complex(double  = 0.0, double = 0.0);
    01096 #ifdef _GLIBCXX_BUGGY_COMPLEX
    01097       complex(const complex& __z) : _M_value(__z._M_value) { }
    01098 #endif
    01099       complex(const complex<float>&);
    01100       explicit complex(const complex<long double>&);
    01101
    01102       double& real();
    01103       const double& real() const;
    01104       double& imag();
    01105       const double& imag() const;
    01106
    01107       complex<double>& operator=(double);
    01108       complex<double>& operator+=(double);
    01109       complex<double>& operator-=(double);
    01110       complex<double>& operator*=(double);
    01111       complex<double>& operator/=(double);
    01112
    01113       // The compiler will synthetize this, efficiently.
    01114       // complex& operator= (const complex&);
    01115       template<typename _Tp>
    01116         complex<double>& operator=(const complex<_Tp>&);
    01117       template<typename _Tp>
    01118         complex<double>& operator+=(const complex<_Tp>&);
    01119       template<typename _Tp>
    01120         complex<double>& operator-=(const complex<_Tp>&);
    01121       template<typename _Tp>
    01122         complex<double>& operator*=(const complex<_Tp>&);
    01123       template<typename _Tp>
    01124         complex<double>& operator/=(const complex<_Tp>&);
    01125
    01126       const _ComplexT& __rep() const { return _M_value; }
    01127
    01128     private:
    01129       _ComplexT _M_value;
    01130     };
    01131
    01132   inline double&
    01133   complex<double>::real()
    01134   { return __real__ _M_value; }
    01135
    01136   inline const double&
    01137   complex<double>::real() const
    01138   { return __real__ _M_value; }
    01139
    01140   inline double&
    01141   complex<double>::imag()
    01142   { return __imag__ _M_value; }
    01143
    01144   inline const double&
    01145   complex<double>::imag() const
    01146   { return __imag__ _M_value; }
    01147
    01148   inline
    01149   complex<double>::complex(double __r, double __i)
    01150   {
    01151     __real__ _M_value = __r;
    01152     __imag__ _M_value = __i;
    01153   }
    01154
    01155   inline complex<double>&
    01156   complex<double>::operator=(double __d)
    01157   {
    01158     __real__ _M_value = __d;
    01159     __imag__ _M_value = 0.0;
    01160     return *this;
    01161   }
    01162
    01163   inline complex<double>&
    01164   complex<double>::operator+=(double __d)
    01165   {
    01166     __real__ _M_value += __d;
    01167     return *this;
    01168   }
    01169
    01170   inline complex<double>&
    01171   complex<double>::operator-=(double __d)
    01172   {
    01173     __real__ _M_value -= __d;
    01174     return *this;
    01175   }
    01176
    01177   inline complex<double>&
    01178   complex<double>::operator*=(double __d)
    01179   {
    01180     _M_value *= __d;
    01181     return *this;
    01182   }
    01183
    01184   inline complex<double>&
    01185   complex<double>::operator/=(double __d)
    01186   {
    01187     _M_value /= __d;
    01188     return *this;
    01189   }
    01190
    01191   template<typename _Tp>
    01192     inline complex<double>&
    01193     complex<double>::operator=(const complex<_Tp>& __z)
    01194     {
    01195       __real__ _M_value = __z.real();
    01196       __imag__ _M_value = __z.imag();
    01197       return *this;
    01198     }
    01199
    01200   template<typename _Tp>
    01201     inline complex<double>&
    01202     complex<double>::operator+=(const complex<_Tp>& __z)
    01203     {
    01204       __real__ _M_value += __z.real();
    01205       __imag__ _M_value += __z.imag();
    01206       return *this;
    01207     }
    01208
    01209   template<typename _Tp>
    01210     inline complex<double>&
    01211     complex<double>::operator-=(const complex<_Tp>& __z)
    01212     {
    01213       __real__ _M_value -= __z.real();
    01214       __imag__ _M_value -= __z.imag();
    01215       return *this;
    01216     }
    01217
    01218   template<typename _Tp>
    01219     inline complex<double>&
    01220     complex<double>::operator*=(const complex<_Tp>& __z)
    01221     {
    01222       _ComplexT __t;
    01223       __real__ __t = __z.real();
    01224       __imag__ __t = __z.imag();
    01225       _M_value *= __t;
    01226       return *this;
    01227     }
    01228
    01229   template<typename _Tp>
    01230     inline complex<double>&
    01231     complex<double>::operator/=(const complex<_Tp>& __z)
    01232     {
    01233       _ComplexT __t;
    01234       __real__ __t = __z.real();
    01235       __imag__ __t = __z.imag();
    01236       _M_value /= __t;
    01237       return *this;
    01238     }
    01239
    01240   // 26.2.3  complex specializations
    01241   // complex<long double> specialization
    01242   template<>
    01243     struct complex<long double>
    01244     {
    01245       typedef long double value_type;
    01246       typedef __complex__ long double _ComplexT;
    01247
    01248       complex(_ComplexT __z) : _M_value(__z) { }
    01249
    01250       complex(long double = 0.0L, long double = 0.0L);
    01251 #ifdef _GLIBCXX_BUGGY_COMPLEX
    01252       complex(const complex& __z) : _M_value(__z._M_value) { }
    01253 #endif
    01254       complex(const complex<float>&);
    01255       complex(const complex<double>&);
    01256
    01257       long double& real();
    01258       const long double& real() const;
    01259       long double& imag();
    01260       const long double& imag() const;
    01261
    01262       complex<long double>& operator= (long double);
    01263       complex<long double>& operator+= (long double);
    01264       complex<long double>& operator-= (long double);
    01265       complex<long double>& operator*= (long double);
    01266       complex<long double>& operator/= (long double);
    01267
    01268       // The compiler knows how to do this efficiently
    01269       // complex& operator= (const complex&);
    01270       template<typename _Tp>
    01271         complex<long double>& operator=(const complex<_Tp>&);
    01272       template<typename _Tp>
    01273         complex<long double>& operator+=(const complex<_Tp>&);
    01274       template<typename _Tp>
    01275         complex<long double>& operator-=(const complex<_Tp>&);
    01276       template<typename _Tp>
    01277         complex<long double>& operator*=(const complex<_Tp>&);
    01278       template<typename _Tp>
    01279         complex<long double>& operator/=(const complex<_Tp>&);
    01280
    01281       const _ComplexT& __rep() const { return _M_value; }
    01282
    01283     private:
    01284       _ComplexT _M_value;
    01285     };
    01286
    01287   inline
    01288   complex<long double>::complex(long double __r, long double __i)
    01289   {
    01290     __real__ _M_value = __r;
    01291     __imag__ _M_value = __i;
    01292   }
    01293
    01294   inline long double&
    01295   complex<long double>::real()
    01296   { return __real__ _M_value; }
    01297
    01298   inline const long double&
    01299   complex<long double>::real() const
    01300   { return __real__ _M_value; }
    01301
    01302   inline long double&
    01303   complex<long double>::imag()
    01304   { return __imag__ _M_value; }
    01305
    01306   inline const long double&
    01307   complex<long double>::imag() const
    01308   { return __imag__ _M_value; }
    01309
    01310   inline complex<long double>&
    01311   complex<long double>::operator=(long double __r)
    01312   {
    01313     __real__ _M_value = __r;
    01314     __imag__ _M_value = 0.0L;
    01315     return *this;
    01316   }
    01317
    01318   inline complex<long double>&
    01319   complex<long double>::operator+=(long double __r)
    01320   {
    01321     __real__ _M_value += __r;
    01322     return *this;
    01323   }
    01324
    01325   inline complex<long double>&
    01326   complex<long double>::operator-=(long double __r)
    01327   {
    01328     __real__ _M_value -= __r;
    01329     return *this;
    01330   }
    01331
    01332   inline complex<long double>&
    01333   complex<long double>::operator*=(long double __r)
    01334   {
    01335     _M_value *= __r;
    01336     return *this;
    01337   }
    01338
    01339   inline complex<long double>&
    01340   complex<long double>::operator/=(long double __r)
    01341   {
    01342     _M_value /= __r;
    01343     return *this;
    01344   }
    01345
    01346   template<typename _Tp>
    01347     inline complex<long double>&
    01348     complex<long double>::operator=(const complex<_Tp>& __z)
    01349     {
    01350       __real__ _M_value = __z.real();
    01351       __imag__ _M_value = __z.imag();
    01352       return *this;
    01353     }
    01354
    01355   template<typename _Tp>
    01356     inline complex<long double>&
    01357     complex<long double>::operator+=(const complex<_Tp>& __z)
    01358     {
    01359       __real__ _M_value += __z.real();
    01360       __imag__ _M_value += __z.imag();
    01361       return *this;
    01362     }
    01363
    01364   template<typename _Tp>
    01365     inline complex<long double>&
    01366     complex<long double>::operator-=(const complex<_Tp>& __z)
    01367     {
    01368       __real__ _M_value -= __z.real();
    01369       __imag__ _M_value -= __z.imag();
    01370       return *this;
    01371     }
    01372
    01373   template<typename _Tp>
    01374     inline complex<long double>&
    01375     complex<long double>::operator*=(const complex<_Tp>& __z)
    01376     {
    01377       _ComplexT __t;
    01378       __real__ __t = __z.real();
    01379       __imag__ __t = __z.imag();
    01380       _M_value *= __t;
    01381       return *this;
    01382     }
    01383
    01384   template<typename _Tp>
    01385     inline complex<long double>&
    01386     complex<long double>::operator/=(const complex<_Tp>& __z)
    01387     {
    01388       _ComplexT __t;
    01389       __real__ __t = __z.real();
    01390       __imag__ __t = __z.imag();
    01391       _M_value /= __t;
    01392       return *this;
    01393     }
    01394
    01395   // These bits have to be at the end of this file, so that the
    01396   // specializations have all been defined.
    01397   // ??? No, they have to be there because of compiler limitation at
    01398   // inlining.  It suffices that class specializations be defined.
    01399   inline
    01400   complex<float>::complex(const complex<double>& __z)
    01401   : _M_value(__z.__rep()) { }
    01402
    01403   inline
    01404   complex<float>::complex(const complex<long double>& __z)
    01405   : _M_value(__z.__rep()) { }
    01406
    01407   inline
    01408   complex<double>::complex(const complex<float>& __z)
    01409   : _M_value(__z.__rep()) { }
    01410
    01411   inline
    01412   complex<double>::complex(const complex<long double>& __z)
    01413     : _M_value(__z.__rep()) { }
    01414
    01415   inline
    01416   complex<long double>::complex(const complex<float>& __z)
    01417   : _M_value(__z.__rep()) { }
    01418
    01419   inline
    01420   complex<long double>::complex(const complex<double>& __z)
    01421   : _M_value(__z.__rep()) { }
    01422 } // namespace std
    01423
    01424 #endif  /* _GLIBCXX_COMPLEX */