// The template and inlines for the -*- C++ -*- complex number classes.
// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
-// 2006, 2007, 2008, 2009, 2010
+// 2006, 2007, 2008, 2009, 2010, 2011
// Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
#include <cmath>
#include <sstream>
-_GLIBCXX_BEGIN_NAMESPACE(std)
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
/**
* @defgroup complex_numbers Complex Numbers
//@{
/// Return true if @a x is equal to @a y.
template<typename _Tp>
- inline bool
+ inline _GLIBCXX_CONSTEXPR bool
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __x.real() == __y.real() && __x.imag() == __y.imag(); }
template<typename _Tp>
- inline bool
+ inline _GLIBCXX_CONSTEXPR bool
operator==(const complex<_Tp>& __x, const _Tp& __y)
{ return __x.real() == __y && __x.imag() == _Tp(); }
template<typename _Tp>
- inline bool
+ inline _GLIBCXX_CONSTEXPR bool
operator==(const _Tp& __x, const complex<_Tp>& __y)
{ return __x == __y.real() && _Tp() == __y.imag(); }
//@}
//@{
/// Return false if @a x is equal to @a y.
template<typename _Tp>
- inline bool
+ inline _GLIBCXX_CONSTEXPR bool
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __x.real() != __y.real() || __x.imag() != __y.imag(); }
template<typename _Tp>
- inline bool
+ inline _GLIBCXX_CONSTEXPR bool
operator!=(const complex<_Tp>& __x, const _Tp& __y)
{ return __x.real() != __y || __x.imag() != _Tp(); }
template<typename _Tp>
- inline bool
+ inline _GLIBCXX_CONSTEXPR bool
operator!=(const _Tp& __x, const complex<_Tp>& __y)
{ return __x != __y.real() || _Tp() != __y.imag(); }
//@}
// Values
#ifdef __GXX_EXPERIMENTAL_CXX0X__
template<typename _Tp>
- inline _Tp
+ inline constexpr _Tp
real(const complex<_Tp>& __z)
{ return __z.real(); }
template<typename _Tp>
- inline _Tp
+ inline constexpr _Tp
imag(const complex<_Tp>& __z)
{ return __z.imag(); }
#else
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
_GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
- : _M_value(__r + __i * 1.0fi) { }
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+ : _M_value{ __r, __i } { }
+#else
+ {
+ __real__ _M_value = __r;
+ __imag__ _M_value = __i;
+ }
+#endif
explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
_GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
- : _M_value(__r + __i * 1.0i) { }
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+ : _M_value{ __r, __i } { }
+#else
+ {
+ __real__ _M_value = __r;
+ __imag__ _M_value = __i;
+ }
+#endif
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
: _M_value(__z.__rep()) { }
_GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
long double __i = 0.0L)
- : _M_value(__r + __i * 1.0Li) { }
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+ : _M_value{ __r, __i } { }
+#else
+ {
+ __real__ _M_value = __r;
+ __imag__ _M_value = __i;
+ }
+#endif
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
: _M_value(__z.__rep()) { }
// @} group complex_numbers
-_GLIBCXX_END_NAMESPACE
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace
-_GLIBCXX_BEGIN_NAMESPACE(__gnu_cxx)
+namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
// See ext/type_traits.h for the primary template.
template<typename _Tp, typename _Up>
typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
};
-_GLIBCXX_END_NAMESPACE
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace
#ifdef __GXX_EXPERIMENTAL_CXX0X__
-# if defined(_GLIBCXX_INCLUDE_AS_TR1)
-# error C++0x header cannot be included from TR1 header
-# endif
-# if defined(_GLIBCXX_INCLUDE_AS_CXX0X)
-# include <tr1_impl/complex>
-# else
-# define _GLIBCXX_INCLUDE_AS_CXX0X
-# define _GLIBCXX_BEGIN_NAMESPACE_TR1
-# define _GLIBCXX_END_NAMESPACE_TR1
-# define _GLIBCXX_TR1
-# include <tr1_impl/complex>
-# undef _GLIBCXX_TR1
-# undef _GLIBCXX_END_NAMESPACE_TR1
-# undef _GLIBCXX_BEGIN_NAMESPACE_TR1
-# undef _GLIBCXX_INCLUDE_AS_CXX0X
-# endif
-
-_GLIBCXX_BEGIN_NAMESPACE(std)
+
+namespace std _GLIBCXX_VISIBILITY(default)
+{
+_GLIBCXX_BEGIN_NAMESPACE_VERSION
+
+ // 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>&);
+ // DR 595.
+ template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ __complex_acos(const std::complex<_Tp>& __z)
+ {
+ const std::complex<_Tp> __t = std::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::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>
+ inline _Tp
+ /// 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].
+ template<typename _Tp>
+ inline typename __gnu_cxx::__promote<_Tp>::__type
+ arg(_Tp __x)
+ {
+ typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
+ return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
+ : __type();
+#else
+ return std::arg(std::complex<__type>(__x));
+#endif
+ }
+
+ 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; }
+
+ 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));
+ }
// Forward declarations.
// DR 781.
conj(_Tp __x)
{ return __x; }
-_GLIBCXX_END_NAMESPACE
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace
-#endif
+#endif // __GXX_EXPERIMENTAL_CXX0X__
-#endif /* _GLIBCXX_COMPLEX */
+#endif /* _GLIBCXX_COMPLEX */
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