# impl/complex

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    00001 // TR1 complex -*- C++ -*-
    00002
    00003 // Copyright (C) 2007 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, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
    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 /** @file tr1_impl/complex
    00031  *  This is an internal header file, included by other library headers.
    00032  *  You should not attempt to use it directly.
    00033  */
    00034
    00035 namespace std
    00036 {
    00037 _GLIBCXX_BEGIN_NAMESPACE_TR1
    00038
    00039   // Forward declarations.
    00040   template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
    00041   template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
    00042   template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
    00043
    00044   template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
    00045   template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
    00046   template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
    00047 #ifdef _GLIBCXX_INCLUDE_AS_CXX0X
    00048   // DR 595.
    00049   template<typename _Tp> _Tp               fabs(const std::complex<_Tp>&);
    00050 #else
    00051   template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
    00052 #endif
    00053
    00054   /// acos(__z) [8.1.2].
    00055   //  Effects:  Behaves the same as C99 function cacos, defined
    00056   //            in subclause 7.3.5.1.
    00057   template<typename _Tp>
    00058     inline std::complex<_Tp>
    00059     __complex_acos(const std::complex<_Tp>& __z)
    00060     {
    00061       const std::complex<_Tp> __t = std::_GLIBCXX_TR1 asin(__z);
    00062       const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
    00063       return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
    00064     }
    00065
    00066 #if _GLIBCXX_USE_C99_COMPLEX_TR1
    00067   inline __complex__ float
    00068   __complex_acos(__complex__ float __z)
    00069   { return __builtin_cacosf(__z); }
    00070
    00071   inline __complex__ double
    00072   __complex_acos(__complex__ double __z)
    00073   { return __builtin_cacos(__z); }
    00074
    00075   inline __complex__ long double
    00076   __complex_acos(const __complex__ long double& __z)
    00077   { return __builtin_cacosl(__z); }
    00078
    00079   template<typename _Tp>
    00080     inline std::complex<_Tp>
    00081     acos(const std::complex<_Tp>& __z)
    00082     { return __complex_acos(__z.__rep()); }
    00083 #else
    00084   template<typename _Tp>
    00085     inline std::complex<_Tp>
    00086     acos(const std::complex<_Tp>& __z)
    00087     { return __complex_acos(__z); }
    00088 #endif
    00089
    00090   /// asin(__z) [8.1.3].
    00091   //  Effects:  Behaves the same as C99 function casin, defined
    00092   //            in subclause 7.3.5.2.
    00093   template<typename _Tp>
    00094     inline std::complex<_Tp>
    00095     __complex_asin(const std::complex<_Tp>& __z)
    00096     {
    00097       std::complex<_Tp> __t(-__z.imag(), __z.real());
    00098       __t = std::_GLIBCXX_TR1 asinh(__t);
    00099       return std::complex<_Tp>(__t.imag(), -__t.real());
    00100     }
    00101
    00102 #if _GLIBCXX_USE_C99_COMPLEX_TR1
    00103   inline __complex__ float
    00104   __complex_asin(__complex__ float __z)
    00105   { return __builtin_casinf(__z); }
    00106
    00107   inline __complex__ double
    00108   __complex_asin(__complex__ double __z)
    00109   { return __builtin_casin(__z); }
    00110
    00111   inline __complex__ long double
    00112   __complex_asin(const __complex__ long double& __z)
    00113   { return __builtin_casinl(__z); }
    00114
    00115   template<typename _Tp>
    00116     inline std::complex<_Tp>
    00117     asin(const std::complex<_Tp>& __z)
    00118     { return __complex_asin(__z.__rep()); }
    00119 #else
    00120   template<typename _Tp>
    00121     inline std::complex<_Tp>
    00122     asin(const std::complex<_Tp>& __z)
    00123     { return __complex_asin(__z); }
    00124 #endif
    00125
    00126   /// atan(__z) [8.1.4].
    00127   //  Effects:  Behaves the same as C99 function catan, defined
    00128   //            in subclause 7.3.5.3.
    00129   template<typename _Tp>
    00130     std::complex<_Tp>
    00131     __complex_atan(const std::complex<_Tp>& __z)
    00132     {
    00133       const _Tp __r2 = __z.real() * __z.real();
    00134       const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
    00135
    00136       _Tp __num = __z.imag() + _Tp(1.0);
    00137       _Tp __den = __z.imag() - _Tp(1.0);
    00138
    00139       __num = __r2 + __num * __num;
    00140       __den = __r2 + __den * __den;
    00141
    00142       return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
    00143                    _Tp(0.25) * log(__num / __den));
    00144     }
    00145
    00146 #if _GLIBCXX_USE_C99_COMPLEX_TR1
    00147   inline __complex__ float
    00148   __complex_atan(__complex__ float __z)
    00149   { return __builtin_catanf(__z); }
    00150
    00151   inline __complex__ double
    00152   __complex_atan(__complex__ double __z)
    00153   { return __builtin_catan(__z); }
    00154
    00155   inline __complex__ long double
    00156   __complex_atan(const __complex__ long double& __z)
    00157   { return __builtin_catanl(__z); }
    00158
    00159   template<typename _Tp>
    00160     inline std::complex<_Tp>
    00161     atan(const std::complex<_Tp>& __z)
    00162     { return __complex_atan(__z.__rep()); }
    00163 #else
    00164   template<typename _Tp>
    00165     inline std::complex<_Tp>
    00166     atan(const std::complex<_Tp>& __z)
    00167     { return __complex_atan(__z); }
    00168 #endif
    00169
    00170   /// acosh(__z) [8.1.5].
    00171   //  Effects:  Behaves the same as C99 function cacosh, defined
    00172   //            in subclause 7.3.6.1.
    00173   template<typename _Tp>
    00174     std::complex<_Tp>
    00175     __complex_acosh(const std::complex<_Tp>& __z)
    00176     {
    00177       std::complex<_Tp> __t((__z.real() - __z.imag())
    00178                 * (__z.real() + __z.imag()) - _Tp(1.0),
    00179                 _Tp(2.0) * __z.real() * __z.imag());
    00180       __t = std::sqrt(__t);
    00181
    00182       return std::log(__t + __z);
    00183     }
    00184
    00185 #if _GLIBCXX_USE_C99_COMPLEX_TR1
    00186   inline __complex__ float
    00187   __complex_acosh(__complex__ float __z)
    00188   { return __builtin_cacoshf(__z); }
    00189
    00190   inline __complex__ double
    00191   __complex_acosh(__complex__ double __z)
    00192   { return __builtin_cacosh(__z); }
    00193
    00194   inline __complex__ long double
    00195   __complex_acosh(const __complex__ long double& __z)
    00196   { return __builtin_cacoshl(__z); }
    00197
    00198   template<typename _Tp>
    00199     inline std::complex<_Tp>
    00200     acosh(const std::complex<_Tp>& __z)
    00201     { return __complex_acosh(__z.__rep()); }
    00202 #else
    00203   template<typename _Tp>
    00204     inline std::complex<_Tp>
    00205     acosh(const std::complex<_Tp>& __z)
    00206     { return __complex_acosh(__z); }
    00207 #endif
    00208
    00209   /// asinh(__z) [8.1.6].
    00210   //  Effects:  Behaves the same as C99 function casin, defined
    00211   //            in subclause 7.3.6.2.
    00212   template<typename _Tp>
    00213     std::complex<_Tp>
    00214     __complex_asinh(const std::complex<_Tp>& __z)
    00215     {
    00216       std::complex<_Tp> __t((__z.real() - __z.imag())
    00217                 * (__z.real() + __z.imag()) + _Tp(1.0),
    00218                 _Tp(2.0) * __z.real() * __z.imag());
    00219       __t = std::sqrt(__t);
    00220
    00221       return std::log(__t + __z);
    00222     }
    00223
    00224 #if _GLIBCXX_USE_C99_COMPLEX_TR1
    00225   inline __complex__ float
    00226   __complex_asinh(__complex__ float __z)
    00227   { return __builtin_casinhf(__z); }
    00228
    00229   inline __complex__ double
    00230   __complex_asinh(__complex__ double __z)
    00231   { return __builtin_casinh(__z); }
    00232
    00233   inline __complex__ long double
    00234   __complex_asinh(const __complex__ long double& __z)
    00235   { return __builtin_casinhl(__z); }
    00236
    00237   template<typename _Tp>
    00238     inline std::complex<_Tp>
    00239     asinh(const std::complex<_Tp>& __z)
    00240     { return __complex_asinh(__z.__rep()); }
    00241 #else
    00242   template<typename _Tp>
    00243     inline std::complex<_Tp>
    00244     asinh(const std::complex<_Tp>& __z)
    00245     { return __complex_asinh(__z); }
    00246 #endif
    00247
    00248   /// atanh(__z) [8.1.7].
    00249   //  Effects:  Behaves the same as C99 function catanh, defined
    00250   //            in subclause 7.3.6.3.
    00251   template<typename _Tp>
    00252     std::complex<_Tp>
    00253     __complex_atanh(const std::complex<_Tp>& __z)
    00254     {
    00255       const _Tp __i2 = __z.imag() * __z.imag();
    00256       const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
    00257
    00258       _Tp __num = _Tp(1.0) + __z.real();
    00259       _Tp __den = _Tp(1.0) - __z.real();
    00260
    00261       __num = __i2 + __num * __num;
    00262       __den = __i2 + __den * __den;
    00263
    00264       return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
    00265                    _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
    00266     }
    00267
    00268 #if _GLIBCXX_USE_C99_COMPLEX_TR1
    00269   inline __complex__ float
    00270   __complex_atanh(__complex__ float __z)
    00271   { return __builtin_catanhf(__z); }
    00272
    00273   inline __complex__ double
    00274   __complex_atanh(__complex__ double __z)
    00275   { return __builtin_catanh(__z); }
    00276
    00277   inline __complex__ long double
    00278   __complex_atanh(const __complex__ long double& __z)
    00279   { return __builtin_catanhl(__z); }
    00280
    00281   template<typename _Tp>
    00282     inline std::complex<_Tp>
    00283     atanh(const std::complex<_Tp>& __z)
    00284     { return __complex_atanh(__z.__rep()); }
    00285 #else
    00286   template<typename _Tp>
    00287     inline std::complex<_Tp>
    00288     atanh(const std::complex<_Tp>& __z)
    00289     { return __complex_atanh(__z); }
    00290 #endif
    00291
    00292   /// fabs(__z) [8.1.8].
    00293   //  Effects:  Behaves the same as C99 function cabs, defined
    00294   //            in subclause 7.3.8.1.
    00295   template<typename _Tp>
    00296 #ifdef _GLIBCXX_INCLUDE_AS_CXX0X
    00297     inline _Tp
    00298 #else
    00299     inline std::complex<_Tp>
    00300 #endif
    00301     fabs(const std::complex<_Tp>& __z)
    00302     { return std::abs(__z); }
    00303
    00304
    00305 #if (defined(_GLIBCXX_INCLUDE_AS_CXX0X) \
    00306      || (defined(_GLIBCXX_INCLUDE_AS_TR1) \
    00307      && !defined(__GXX_EXPERIMENTAL_CXX0X__)))
    00308
    00309   /// Additional overloads [8.1.9].
    00310   template<typename _Tp>
    00311     inline typename __gnu_cxx::__promote<_Tp>::__type
    00312     arg(_Tp __x)
    00313     {
    00314       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
    00315       return std::arg(std::complex<__type>(__x));
    00316     }
    00317
    00318   template<typename _Tp>
    00319     inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
    00320     conj(_Tp __x)
    00321     { return __x; }
    00322
    00323   template<typename _Tp>
    00324     inline typename __gnu_cxx::__promote<_Tp>::__type
    00325     imag(_Tp)
    00326     { return _Tp(); }
    00327
    00328   template<typename _Tp>
    00329     inline typename __gnu_cxx::__promote<_Tp>::__type
    00330     norm(_Tp __x)
    00331     {
    00332       typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
    00333       return __type(__x) * __type(__x);
    00334     }
    00335
    00336   template<typename _Tp, typename _Up>
    00337     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    00338     polar(const _Tp& __rho, const _Up& __theta)
    00339     {
    00340       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
    00341       return std::polar(__type(__rho), __type(__theta));
    00342     }
    00343
    00344   template<typename _Tp, typename _Up>
    00345     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    00346     pow(const std::complex<_Tp>& __x, const _Up& __y)
    00347     {
    00348       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
    00349       return std::pow(std::complex<__type>(__x), __type(__y));
    00350     }
    00351
    00352   template<typename _Tp, typename _Up>
    00353     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    00354     pow(const _Tp& __x, const std::complex<_Up>& __y)
    00355     {
    00356       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
    00357       return std::pow(__type(__x), std::complex<__type>(__y));
    00358     }
    00359
    00360   template<typename _Tp, typename _Up>
    00361     inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    00362     pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
    00363     {
    00364       typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
    00365       return std::pow(std::complex<__type>(__x),
    00366               std::complex<__type>(__y));
    00367     }
    00368
    00369   template<typename _Tp>
    00370     inline typename __gnu_cxx::__promote<_Tp>::__type
    00371     real(_Tp __x)
    00372     { return __x; }
    00373
    00374 #endif
    00375
    00376 _GLIBCXX_END_NAMESPACE_TR1
    00377 }