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+// TR1 complex -*- C++ -*-
+
+// Copyright (C) 2007, 2008, 2009 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library. This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+// GNU General Public License for more details.
+
+// Under Section 7 of GPL version 3, you are granted additional
+// permissions described in the GCC Runtime Library Exception, version
+// 3.1, as published by the Free Software Foundation.
+
+// You should have received a copy of the GNU General Public License and
+// a copy of the GCC Runtime Library Exception along with this program;
+// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
+// <http://www.gnu.org/licenses/>.
+
+/** @file tr1_impl/complex
+ * This is an internal header file, included by other library headers.
+ * You should not attempt to use it directly.
+ */
+
+namespace std
+{
+_GLIBCXX_BEGIN_NAMESPACE_TR1
+
+ /**
+ * @addtogroup complex_numbers
+ * @{
+ */
+
+ // Forward declarations.
+ template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
+ template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
+ template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
+
+ template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
+ template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
+ template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
+#ifdef _GLIBCXX_INCLUDE_AS_CXX0X
+ // DR 595.
+ template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
+#else
+ template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
+#endif
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ __complex_acos(const std::complex<_Tp>& __z)
+ {
+ const std::complex<_Tp> __t = std::_GLIBCXX_TR1 asin(__z);
+ const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
+ return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX_TR1
+ inline __complex__ float
+ __complex_acos(__complex__ float __z)
+ { return __builtin_cacosf(__z); }
+
+ inline __complex__ double
+ __complex_acos(__complex__ double __z)
+ { return __builtin_cacos(__z); }
+
+ inline __complex__ long double
+ __complex_acos(const __complex__ long double& __z)
+ { return __builtin_cacosl(__z); }
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ acos(const std::complex<_Tp>& __z)
+ { return __complex_acos(__z.__rep()); }
+#else
+ /// acos(__z) [8.1.2].
+ // Effects: Behaves the same as C99 function cacos, defined
+ // in subclause 7.3.5.1.
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ acos(const std::complex<_Tp>& __z)
+ { return __complex_acos(__z); }
+#endif
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ __complex_asin(const std::complex<_Tp>& __z)
+ {
+ std::complex<_Tp> __t(-__z.imag(), __z.real());
+ __t = std::_GLIBCXX_TR1 asinh(__t);
+ return std::complex<_Tp>(__t.imag(), -__t.real());
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX_TR1
+ inline __complex__ float
+ __complex_asin(__complex__ float __z)
+ { return __builtin_casinf(__z); }
+
+ inline __complex__ double
+ __complex_asin(__complex__ double __z)
+ { return __builtin_casin(__z); }
+
+ inline __complex__ long double
+ __complex_asin(const __complex__ long double& __z)
+ { return __builtin_casinl(__z); }
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ asin(const std::complex<_Tp>& __z)
+ { return __complex_asin(__z.__rep()); }
+#else
+ /// asin(__z) [8.1.3].
+ // Effects: Behaves the same as C99 function casin, defined
+ // in subclause 7.3.5.2.
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ asin(const std::complex<_Tp>& __z)
+ { return __complex_asin(__z); }
+#endif
+
+ template<typename _Tp>
+ std::complex<_Tp>
+ __complex_atan(const std::complex<_Tp>& __z)
+ {
+ const _Tp __r2 = __z.real() * __z.real();
+ const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
+
+ _Tp __num = __z.imag() + _Tp(1.0);
+ _Tp __den = __z.imag() - _Tp(1.0);
+
+ __num = __r2 + __num * __num;
+ __den = __r2 + __den * __den;
+
+ return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
+ _Tp(0.25) * log(__num / __den));
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX_TR1
+ inline __complex__ float
+ __complex_atan(__complex__ float __z)
+ { return __builtin_catanf(__z); }
+
+ inline __complex__ double
+ __complex_atan(__complex__ double __z)
+ { return __builtin_catan(__z); }
+
+ inline __complex__ long double
+ __complex_atan(const __complex__ long double& __z)
+ { return __builtin_catanl(__z); }
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ atan(const std::complex<_Tp>& __z)
+ { return __complex_atan(__z.__rep()); }
+#else
+ /// atan(__z) [8.1.4].
+ // Effects: Behaves the same as C99 function catan, defined
+ // in subclause 7.3.5.3.
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ atan(const std::complex<_Tp>& __z)
+ { return __complex_atan(__z); }
+#endif
+
+ template<typename _Tp>
+ std::complex<_Tp>
+ __complex_acosh(const std::complex<_Tp>& __z)
+ {
+ std::complex<_Tp> __t((__z.real() - __z.imag())
+ * (__z.real() + __z.imag()) - _Tp(1.0),
+ _Tp(2.0) * __z.real() * __z.imag());
+ __t = std::sqrt(__t);
+
+ return std::log(__t + __z);
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX_TR1
+ inline __complex__ float
+ __complex_acosh(__complex__ float __z)
+ { return __builtin_cacoshf(__z); }
+
+ inline __complex__ double
+ __complex_acosh(__complex__ double __z)
+ { return __builtin_cacosh(__z); }
+
+ inline __complex__ long double
+ __complex_acosh(const __complex__ long double& __z)
+ { return __builtin_cacoshl(__z); }
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ acosh(const std::complex<_Tp>& __z)
+ { return __complex_acosh(__z.__rep()); }
+#else
+ /// acosh(__z) [8.1.5].
+ // Effects: Behaves the same as C99 function cacosh, defined
+ // in subclause 7.3.6.1.
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ acosh(const std::complex<_Tp>& __z)
+ { return __complex_acosh(__z); }
+#endif
+
+ template<typename _Tp>
+ std::complex<_Tp>
+ __complex_asinh(const std::complex<_Tp>& __z)
+ {
+ std::complex<_Tp> __t((__z.real() - __z.imag())
+ * (__z.real() + __z.imag()) + _Tp(1.0),
+ _Tp(2.0) * __z.real() * __z.imag());
+ __t = std::sqrt(__t);
+
+ return std::log(__t + __z);
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX_TR1
+ inline __complex__ float
+ __complex_asinh(__complex__ float __z)
+ { return __builtin_casinhf(__z); }
+
+ inline __complex__ double
+ __complex_asinh(__complex__ double __z)
+ { return __builtin_casinh(__z); }
+
+ inline __complex__ long double
+ __complex_asinh(const __complex__ long double& __z)
+ { return __builtin_casinhl(__z); }
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ asinh(const std::complex<_Tp>& __z)
+ { return __complex_asinh(__z.__rep()); }
+#else
+ /// asinh(__z) [8.1.6].
+ // Effects: Behaves the same as C99 function casin, defined
+ // in subclause 7.3.6.2.
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ asinh(const std::complex<_Tp>& __z)
+ { return __complex_asinh(__z); }
+#endif
+
+ template<typename _Tp>
+ std::complex<_Tp>
+ __complex_atanh(const std::complex<_Tp>& __z)
+ {
+ const _Tp __i2 = __z.imag() * __z.imag();
+ const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
+
+ _Tp __num = _Tp(1.0) + __z.real();
+ _Tp __den = _Tp(1.0) - __z.real();
+
+ __num = __i2 + __num * __num;
+ __den = __i2 + __den * __den;
+
+ return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
+ _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX_TR1
+ inline __complex__ float
+ __complex_atanh(__complex__ float __z)
+ { return __builtin_catanhf(__z); }
+
+ inline __complex__ double
+ __complex_atanh(__complex__ double __z)
+ { return __builtin_catanh(__z); }
+
+ inline __complex__ long double
+ __complex_atanh(const __complex__ long double& __z)
+ { return __builtin_catanhl(__z); }
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ atanh(const std::complex<_Tp>& __z)
+ { return __complex_atanh(__z.__rep()); }
+#else
+ /// atanh(__z) [8.1.7].
+ // Effects: Behaves the same as C99 function catanh, defined
+ // in subclause 7.3.6.3.
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ atanh(const std::complex<_Tp>& __z)
+ { return __complex_atanh(__z); }
+#endif
+
+ template<typename _Tp>
+#ifdef _GLIBCXX_INCLUDE_AS_CXX0X
+ inline _Tp
+#else
+ inline std::complex<_Tp>
+#endif
+ /// fabs(__z) [8.1.8].
+ // Effects: Behaves the same as C99 function cabs, defined
+ // in subclause 7.3.8.1.
+ fabs(const std::complex<_Tp>& __z)
+ { return std::abs(__z); }
+
+ /// Additional overloads [8.1.9].
+#if (defined(_GLIBCXX_INCLUDE_AS_CXX0X) \
+ || (defined(_GLIBCXX_INCLUDE_AS_TR1) \
+ && !defined(__GXX_EXPERIMENTAL_CXX0X__)))
+
+ template<typename _Tp>
+ inline typename __gnu_cxx::__promote<_Tp>::__type
+ arg(_Tp __x)
+ {
+ typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+ return std::arg(std::complex<__type>(__x));
+ }
+
+ template<typename _Tp>
+ inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
+ conj(_Tp __x)
+ { return __x; }
+
+ template<typename _Tp>
+ inline typename __gnu_cxx::__promote<_Tp>::__type
+ imag(_Tp)
+ { return _Tp(); }
+
+ template<typename _Tp>
+ inline typename __gnu_cxx::__promote<_Tp>::__type
+ norm(_Tp __x)
+ {
+ typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+ return __type(__x) * __type(__x);
+ }
+
+ template<typename _Tp>
+ inline typename __gnu_cxx::__promote<_Tp>::__type
+ real(_Tp __x)
+ { return __x; }
+
+#endif
+
+ template<typename _Tp, typename _Up>
+ inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
+ pow(const std::complex<_Tp>& __x, const _Up& __y)
+ {
+ typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+ return std::pow(std::complex<__type>(__x), __type(__y));
+ }
+
+ template<typename _Tp, typename _Up>
+ inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
+ pow(const _Tp& __x, const std::complex<_Up>& __y)
+ {
+ typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+ return std::pow(__type(__x), std::complex<__type>(__y));
+ }
+
+ template<typename _Tp, typename _Up>
+ inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
+ pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
+ {
+ typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
+ return std::pow(std::complex<__type>(__x),
+ std::complex<__type>(__y));
+ }
+
+ // @} group complex_numbers
+
+_GLIBCXX_END_NAMESPACE_TR1
+}
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