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Diffstat (limited to 'libstdc++-v3/include/std/complex')
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diff --git a/libstdc++-v3/include/std/complex b/libstdc++-v3/include/std/complex new file mode 100644 index 000000000..da3c469f8 --- /dev/null +++ b/libstdc++-v3/include/std/complex @@ -0,0 +1,1933 @@ +// 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, 2011 +// 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 include/complex + * This is a Standard C++ Library header. + */ + +// +// ISO C++ 14882: 26.2 Complex Numbers +// Note: this is not a conforming implementation. +// Initially implemented by Ulrich Drepper <drepper@cygnus.com> +// Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr> +// + +#ifndef _GLIBCXX_COMPLEX +#define _GLIBCXX_COMPLEX 1 + +#pragma GCC system_header + +#include <bits/c++config.h> +#include <bits/cpp_type_traits.h> +#include <ext/type_traits.h> +#include <cmath> +#include <sstream> + +namespace std _GLIBCXX_VISIBILITY(default) +{ +_GLIBCXX_BEGIN_NAMESPACE_VERSION + + /** + * @defgroup complex_numbers Complex Numbers + * @ingroup numerics + * + * Classes and functions for complex numbers. + * @{ + */ + + // Forward declarations. + template<typename _Tp> class complex; + template<> class complex<float>; + template<> class complex<double>; + template<> class complex<long double>; + + /// Return magnitude of @a z. + template<typename _Tp> _Tp abs(const complex<_Tp>&); + /// Return phase angle of @a z. + template<typename _Tp> _Tp arg(const complex<_Tp>&); + /// Return @a z magnitude squared. + template<typename _Tp> _Tp norm(const complex<_Tp>&); + + /// Return complex conjugate of @a z. + template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); + /// Return complex with magnitude @a rho and angle @a theta. + template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); + + // Transcendentals: + /// Return complex cosine of @a z. + template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); + /// Return complex hyperbolic cosine of @a z. + template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); + /// Return complex base e exponential of @a z. + template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); + /// Return complex natural logarithm of @a z. + template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); + /// Return complex base 10 logarithm of @a z. + template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); +#ifndef __GXX_EXPERIMENTAL_CXX0X__ + // DR 844. + /// Return @a x to the @a y'th power. + template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); +#endif + /// Return @a x to the @a y'th power. + template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); + /// Return @a x to the @a y'th power. + template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, + const complex<_Tp>&); + /// Return @a x to the @a y'th power. + template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); + /// Return complex sine of @a z. + template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); + /// Return complex hyperbolic sine of @a z. + template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); + /// Return complex square root of @a z. + template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); + /// Return complex tangent of @a z. + template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); + /// Return complex hyperbolic tangent of @a z. + template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); + + + // 26.2.2 Primary template class complex + /** + * Template to represent complex numbers. + * + * Specializations for float, double, and long double are part of the + * library. Results with any other type are not guaranteed. + * + * @param Tp Type of real and imaginary values. + */ + template<typename _Tp> + struct complex + { + /// Value typedef. + typedef _Tp value_type; + + /// Default constructor. First parameter is x, second parameter is y. + /// Unspecified parameters default to 0. + _GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp()) + : _M_real(__r), _M_imag(__i) { } + + // Lets the compiler synthesize the copy constructor + // complex (const complex<_Tp>&); + /// Copy constructor. + template<typename _Up> + _GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z) + : _M_real(__z.real()), _M_imag(__z.imag()) { } + +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 387. std::complex over-encapsulated. + constexpr _Tp + real() const { return _M_real; } + + constexpr _Tp + imag() const { return _M_imag; } +#else + /// Return real part of complex number. + _Tp& + real() { return _M_real; } + + /// Return real part of complex number. + const _Tp& + real() const { return _M_real; } + + /// Return imaginary part of complex number. + _Tp& + imag() { return _M_imag; } + + /// Return imaginary part of complex number. + const _Tp& + imag() const { return _M_imag; } +#endif + + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 387. std::complex over-encapsulated. + void + real(_Tp __val) { _M_real = __val; } + + void + imag(_Tp __val) { _M_imag = __val; } + + /// Assign this complex number to scalar @a t. + complex<_Tp>& operator=(const _Tp&); + + /// Add @a t to this complex number. + // 26.2.5/1 + complex<_Tp>& + operator+=(const _Tp& __t) + { + _M_real += __t; + return *this; + } + + /// Subtract @a t from this complex number. + // 26.2.5/3 + complex<_Tp>& + operator-=(const _Tp& __t) + { + _M_real -= __t; + return *this; + } + + /// Multiply this complex number by @a t. + complex<_Tp>& operator*=(const _Tp&); + /// Divide this complex number by @a t. + complex<_Tp>& operator/=(const _Tp&); + + // Lets the compiler synthesize the + // copy and assignment operator + // complex<_Tp>& operator= (const complex<_Tp>&); + /// Assign this complex number to complex @a z. + template<typename _Up> + complex<_Tp>& operator=(const complex<_Up>&); + /// Add @a z to this complex number. + template<typename _Up> + complex<_Tp>& operator+=(const complex<_Up>&); + /// Subtract @a z from this complex number. + template<typename _Up> + complex<_Tp>& operator-=(const complex<_Up>&); + /// Multiply this complex number by @a z. + template<typename _Up> + complex<_Tp>& operator*=(const complex<_Up>&); + /// Divide this complex number by @a z. + template<typename _Up> + complex<_Tp>& operator/=(const complex<_Up>&); + + _GLIBCXX_USE_CONSTEXPR complex __rep() const + { return *this; } + + private: + _Tp _M_real; + _Tp _M_imag; + }; + + template<typename _Tp> + complex<_Tp>& + complex<_Tp>::operator=(const _Tp& __t) + { + _M_real = __t; + _M_imag = _Tp(); + return *this; + } + + // 26.2.5/5 + template<typename _Tp> + complex<_Tp>& + complex<_Tp>::operator*=(const _Tp& __t) + { + _M_real *= __t; + _M_imag *= __t; + return *this; + } + + // 26.2.5/7 + template<typename _Tp> + complex<_Tp>& + complex<_Tp>::operator/=(const _Tp& __t) + { + _M_real /= __t; + _M_imag /= __t; + return *this; + } + + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator=(const complex<_Up>& __z) + { + _M_real = __z.real(); + _M_imag = __z.imag(); + return *this; + } + + // 26.2.5/9 + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator+=(const complex<_Up>& __z) + { + _M_real += __z.real(); + _M_imag += __z.imag(); + return *this; + } + + // 26.2.5/11 + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator-=(const complex<_Up>& __z) + { + _M_real -= __z.real(); + _M_imag -= __z.imag(); + return *this; + } + + // 26.2.5/13 + // XXX: This is a grammar school implementation. + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator*=(const complex<_Up>& __z) + { + const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); + _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); + _M_real = __r; + return *this; + } + + // 26.2.5/15 + // XXX: This is a grammar school implementation. + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator/=(const complex<_Up>& __z) + { + const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); + const _Tp __n = std::norm(__z); + _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; + _M_real = __r / __n; + return *this; + } + + // Operators: + //@{ + /// Return new complex value @a x plus @a y. + template<typename _Tp> + inline complex<_Tp> + operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r += __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator+(const complex<_Tp>& __x, const _Tp& __y) + { + complex<_Tp> __r = __x; + __r += __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator+(const _Tp& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __y; + __r += __x; + return __r; + } + //@} + + //@{ + /// Return new complex value @a x minus @a y. + template<typename _Tp> + inline complex<_Tp> + operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r -= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator-(const complex<_Tp>& __x, const _Tp& __y) + { + complex<_Tp> __r = __x; + __r -= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator-(const _Tp& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r(__x, -__y.imag()); + __r -= __y.real(); + return __r; + } + //@} + + //@{ + /// Return new complex value @a x times @a y. + template<typename _Tp> + inline complex<_Tp> + operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r *= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator*(const complex<_Tp>& __x, const _Tp& __y) + { + complex<_Tp> __r = __x; + __r *= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator*(const _Tp& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __y; + __r *= __x; + return __r; + } + //@} + + //@{ + /// Return new complex value @a x divided by @a y. + template<typename _Tp> + inline complex<_Tp> + operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r /= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator/(const complex<_Tp>& __x, const _Tp& __y) + { + complex<_Tp> __r = __x; + __r /= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator/(const _Tp& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r /= __y; + return __r; + } + //@} + + /// Return @a x. + template<typename _Tp> + inline complex<_Tp> + operator+(const complex<_Tp>& __x) + { return __x; } + + /// Return complex negation of @a x. + template<typename _Tp> + inline complex<_Tp> + operator-(const complex<_Tp>& __x) + { return complex<_Tp>(-__x.real(), -__x.imag()); } + + //@{ + /// Return true if @a x is equal to @a y. + template<typename _Tp> + 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 _GLIBCXX_CONSTEXPR bool + operator==(const complex<_Tp>& __x, const _Tp& __y) + { return __x.real() == __y && __x.imag() == _Tp(); } + + template<typename _Tp> + 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 _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 _GLIBCXX_CONSTEXPR bool + operator!=(const complex<_Tp>& __x, const _Tp& __y) + { return __x.real() != __y || __x.imag() != _Tp(); } + + template<typename _Tp> + inline _GLIBCXX_CONSTEXPR bool + operator!=(const _Tp& __x, const complex<_Tp>& __y) + { return __x != __y.real() || _Tp() != __y.imag(); } + //@} + + /// Extraction operator for complex values. + template<typename _Tp, typename _CharT, class _Traits> + basic_istream<_CharT, _Traits>& + operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) + { + _Tp __re_x, __im_x; + _CharT __ch; + __is >> __ch; + if (__ch == '(') + { + __is >> __re_x >> __ch; + if (__ch == ',') + { + __is >> __im_x >> __ch; + if (__ch == ')') + __x = complex<_Tp>(__re_x, __im_x); + else + __is.setstate(ios_base::failbit); + } + else if (__ch == ')') + __x = __re_x; + else + __is.setstate(ios_base::failbit); + } + else + { + __is.putback(__ch); + __is >> __re_x; + __x = __re_x; + } + return __is; + } + + /// Insertion operator for complex values. + template<typename _Tp, typename _CharT, class _Traits> + basic_ostream<_CharT, _Traits>& + operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) + { + basic_ostringstream<_CharT, _Traits> __s; + __s.flags(__os.flags()); + __s.imbue(__os.getloc()); + __s.precision(__os.precision()); + __s << '(' << __x.real() << ',' << __x.imag() << ')'; + return __os << __s.str(); + } + + // Values +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + template<typename _Tp> + inline constexpr _Tp + real(const complex<_Tp>& __z) + { return __z.real(); } + + template<typename _Tp> + inline constexpr _Tp + imag(const complex<_Tp>& __z) + { return __z.imag(); } +#else + template<typename _Tp> + inline _Tp& + real(complex<_Tp>& __z) + { return __z.real(); } + + template<typename _Tp> + inline const _Tp& + real(const complex<_Tp>& __z) + { return __z.real(); } + + template<typename _Tp> + inline _Tp& + imag(complex<_Tp>& __z) + { return __z.imag(); } + + template<typename _Tp> + inline const _Tp& + imag(const complex<_Tp>& __z) + { return __z.imag(); } +#endif + + // 26.2.7/3 abs(__z): Returns the magnitude of __z. + template<typename _Tp> + inline _Tp + __complex_abs(const complex<_Tp>& __z) + { + _Tp __x = __z.real(); + _Tp __y = __z.imag(); + const _Tp __s = std::max(abs(__x), abs(__y)); + if (__s == _Tp()) // well ... + return __s; + __x /= __s; + __y /= __s; + return __s * sqrt(__x * __x + __y * __y); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline float + __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } + + inline double + __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } + + inline long double + __complex_abs(const __complex__ long double& __z) + { return __builtin_cabsl(__z); } + + template<typename _Tp> + inline _Tp + abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } +#else + template<typename _Tp> + inline _Tp + abs(const complex<_Tp>& __z) { return __complex_abs(__z); } +#endif + + + // 26.2.7/4: arg(__z): Returns the phase angle of __z. + template<typename _Tp> + inline _Tp + __complex_arg(const complex<_Tp>& __z) + { return atan2(__z.imag(), __z.real()); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline float + __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } + + inline double + __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } + + inline long double + __complex_arg(const __complex__ long double& __z) + { return __builtin_cargl(__z); } + + template<typename _Tp> + inline _Tp + arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } +#else + template<typename _Tp> + inline _Tp + arg(const complex<_Tp>& __z) { return __complex_arg(__z); } +#endif + + // 26.2.7/5: norm(__z) returns the squared magnitude of __z. + // As defined, norm() is -not- a norm is the common mathematical + // sens used in numerics. The helper class _Norm_helper<> tries to + // distinguish between builtin floating point and the rest, so as + // to deliver an answer as close as possible to the real value. + template<bool> + struct _Norm_helper + { + template<typename _Tp> + static inline _Tp _S_do_it(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return __x * __x + __y * __y; + } + }; + + template<> + struct _Norm_helper<true> + { + template<typename _Tp> + static inline _Tp _S_do_it(const complex<_Tp>& __z) + { + _Tp __res = std::abs(__z); + return __res * __res; + } + }; + + template<typename _Tp> + inline _Tp + norm(const complex<_Tp>& __z) + { + return _Norm_helper<__is_floating<_Tp>::__value + && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); + } + + template<typename _Tp> + inline complex<_Tp> + polar(const _Tp& __rho, const _Tp& __theta) + { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } + + template<typename _Tp> + inline complex<_Tp> + conj(const complex<_Tp>& __z) + { return complex<_Tp>(__z.real(), -__z.imag()); } + + // Transcendentals + + // 26.2.8/1 cos(__z): Returns the cosine of __z. + template<typename _Tp> + inline complex<_Tp> + __complex_cos(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } + + inline __complex__ double + __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } + + inline __complex__ long double + __complex_cos(const __complex__ long double& __z) + { return __builtin_ccosl(__z); } + + template<typename _Tp> + inline complex<_Tp> + cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + cos(const complex<_Tp>& __z) { return __complex_cos(__z); } +#endif + + // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. + template<typename _Tp> + inline complex<_Tp> + __complex_cosh(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } + + inline __complex__ double + __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } + + inline __complex__ long double + __complex_cosh(const __complex__ long double& __z) + { return __builtin_ccoshl(__z); } + + template<typename _Tp> + inline complex<_Tp> + cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } +#endif + + // 26.2.8/3 exp(__z): Returns the complex base e exponential of x + template<typename _Tp> + inline complex<_Tp> + __complex_exp(const complex<_Tp>& __z) + { return std::polar(exp(__z.real()), __z.imag()); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } + + inline __complex__ double + __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } + + inline __complex__ long double + __complex_exp(const __complex__ long double& __z) + { return __builtin_cexpl(__z); } + + template<typename _Tp> + inline complex<_Tp> + exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + exp(const complex<_Tp>& __z) { return __complex_exp(__z); } +#endif + + // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. + // The branch cut is along the negative axis. + template<typename _Tp> + inline complex<_Tp> + __complex_log(const complex<_Tp>& __z) + { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } + + inline __complex__ double + __complex_log(__complex__ double __z) { return __builtin_clog(__z); } + + inline __complex__ long double + __complex_log(const __complex__ long double& __z) + { return __builtin_clogl(__z); } + + template<typename _Tp> + inline complex<_Tp> + log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + log(const complex<_Tp>& __z) { return __complex_log(__z); } +#endif + + template<typename _Tp> + inline complex<_Tp> + log10(const complex<_Tp>& __z) + { return std::log(__z) / log(_Tp(10.0)); } + + // 26.2.8/10 sin(__z): Returns the sine of __z. + template<typename _Tp> + inline complex<_Tp> + __complex_sin(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } + + inline __complex__ double + __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } + + inline __complex__ long double + __complex_sin(const __complex__ long double& __z) + { return __builtin_csinl(__z); } + + template<typename _Tp> + inline complex<_Tp> + sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + sin(const complex<_Tp>& __z) { return __complex_sin(__z); } +#endif + + // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. + template<typename _Tp> + inline complex<_Tp> + __complex_sinh(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } + + inline __complex__ double + __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } + + inline __complex__ long double + __complex_sinh(const __complex__ long double& __z) + { return __builtin_csinhl(__z); } + + template<typename _Tp> + inline complex<_Tp> + sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } +#endif + + // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. + // The branch cut is on the negative axis. + template<typename _Tp> + complex<_Tp> + __complex_sqrt(const complex<_Tp>& __z) + { + _Tp __x = __z.real(); + _Tp __y = __z.imag(); + + if (__x == _Tp()) + { + _Tp __t = sqrt(abs(__y) / 2); + return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); + } + else + { + _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); + _Tp __u = __t / 2; + return __x > _Tp() + ? complex<_Tp>(__u, __y / __t) + : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); + } + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } + + inline __complex__ double + __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } + + inline __complex__ long double + __complex_sqrt(const __complex__ long double& __z) + { return __builtin_csqrtl(__z); } + + template<typename _Tp> + inline complex<_Tp> + sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } +#endif + + // 26.2.8/14 tan(__z): Return the complex tangent of __z. + + template<typename _Tp> + inline complex<_Tp> + __complex_tan(const complex<_Tp>& __z) + { return std::sin(__z) / std::cos(__z); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } + + inline __complex__ double + __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } + + inline __complex__ long double + __complex_tan(const __complex__ long double& __z) + { return __builtin_ctanl(__z); } + + template<typename _Tp> + inline complex<_Tp> + tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + tan(const complex<_Tp>& __z) { return __complex_tan(__z); } +#endif + + + // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. + + template<typename _Tp> + inline complex<_Tp> + __complex_tanh(const complex<_Tp>& __z) + { return std::sinh(__z) / std::cosh(__z); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } + + inline __complex__ double + __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } + + inline __complex__ long double + __complex_tanh(const __complex__ long double& __z) + { return __builtin_ctanhl(__z); } + + template<typename _Tp> + inline complex<_Tp> + tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } +#endif + + + // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x + // raised to the __y-th power. The branch + // cut is on the negative axis. +#ifndef __GXX_EXPERIMENTAL_CXX0X__ + template<typename _Tp> + complex<_Tp> + __complex_pow_unsigned(complex<_Tp> __x, unsigned __n) + { + complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); + + while (__n >>= 1) + { + __x *= __x; + if (__n % 2) + __y *= __x; + } + + return __y; + } + + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 844. complex pow return type is ambiguous. + template<typename _Tp> + inline complex<_Tp> + pow(const complex<_Tp>& __z, int __n) + { + return __n < 0 + ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -__n) + : std::__complex_pow_unsigned(__z, __n); + } +#endif + + template<typename _Tp> + complex<_Tp> + pow(const complex<_Tp>& __x, const _Tp& __y) + { +#ifndef _GLIBCXX_USE_C99_COMPLEX + if (__x == _Tp()) + return _Tp(); +#endif + if (__x.imag() == _Tp() && __x.real() > _Tp()) + return pow(__x.real(), __y); + + complex<_Tp> __t = std::log(__x); + return std::polar(exp(__y * __t.real()), __y * __t.imag()); + } + + template<typename _Tp> + inline complex<_Tp> + __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) + { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_pow(__complex__ float __x, __complex__ float __y) + { return __builtin_cpowf(__x, __y); } + + inline __complex__ double + __complex_pow(__complex__ double __x, __complex__ double __y) + { return __builtin_cpow(__x, __y); } + + inline __complex__ long double + __complex_pow(const __complex__ long double& __x, + const __complex__ long double& __y) + { return __builtin_cpowl(__x, __y); } + + template<typename _Tp> + inline complex<_Tp> + pow(const complex<_Tp>& __x, const complex<_Tp>& __y) + { return __complex_pow(__x.__rep(), __y.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + pow(const complex<_Tp>& __x, const complex<_Tp>& __y) + { return __complex_pow(__x, __y); } +#endif + + template<typename _Tp> + inline complex<_Tp> + pow(const _Tp& __x, const complex<_Tp>& __y) + { + return __x > _Tp() ? std::polar(pow(__x, __y.real()), + __y.imag() * log(__x)) + : std::pow(complex<_Tp>(__x), __y); + } + + // 26.2.3 complex specializations + // complex<float> specialization + template<> + struct complex<float> + { + typedef float value_type; + typedef __complex__ float _ComplexT; + + _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } + + _GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + // The list-initialization extension to __complex__ types is + // not available in GCC 4.6. Thus libstdc++/48760 cannot be + // fixed in C++0x mode, unfortunately. + : _M_value(__r + __i * 1.0fi) { } +#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>&); + +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 387. std::complex over-encapsulated. + constexpr float + real() const { return __real__ _M_value; } + + constexpr float + imag() const { return __imag__ _M_value; } +#else + float& + real() { return __real__ _M_value; } + + const float& + real() const { return __real__ _M_value; } + + float& + imag() { return __imag__ _M_value; } + + const float& + imag() const { return __imag__ _M_value; } +#endif + + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 387. std::complex over-encapsulated. + void + real(float __val) { __real__ _M_value = __val; } + + void + imag(float __val) { __imag__ _M_value = __val; } + + complex& + operator=(float __f) + { + _M_value = __f; + return *this; + } + + complex& + operator+=(float __f) + { + _M_value += __f; + return *this; + } + + complex& + operator-=(float __f) + { + _M_value -= __f; + return *this; + } + + complex& + operator*=(float __f) + { + _M_value *= __f; + return *this; + } + + complex& + operator/=(float __f) + { + _M_value /= __f; + return *this; + } + + // Let the compiler synthesize the copy and assignment + // operator. It always does a pretty good job. + // complex& operator=(const complex&); + + template<typename _Tp> + complex& + operator=(const complex<_Tp>& __z) + { + __real__ _M_value = __z.real(); + __imag__ _M_value = __z.imag(); + return *this; + } + + template<typename _Tp> + complex& + operator+=(const complex<_Tp>& __z) + { + __real__ _M_value += __z.real(); + __imag__ _M_value += __z.imag(); + return *this; + } + + template<class _Tp> + complex& + operator-=(const complex<_Tp>& __z) + { + __real__ _M_value -= __z.real(); + __imag__ _M_value -= __z.imag(); + return *this; + } + + template<class _Tp> + complex& + operator*=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value *= __t; + return *this; + } + + template<class _Tp> + complex& + operator/=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value /= __t; + return *this; + } + + _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } + + private: + _ComplexT _M_value; + }; + + // 26.2.3 complex specializations + // complex<double> specialization + template<> + struct complex<double> + { + typedef double value_type; + typedef __complex__ double _ComplexT; + + _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } + + _GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + // The list-initialization extension to __complex__ types is + // not available in GCC 4.6. Thus libstdc++/48760 cannot be + // fixed in C++0x mode, unfortunately. + : _M_value(__r + __i * 1.0i) { } +#else + { + __real__ _M_value = __r; + __imag__ _M_value = __i; + } +#endif + + _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) + : _M_value(__z.__rep()) { } + + explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); + +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 387. std::complex over-encapsulated. + constexpr double + real() const { return __real__ _M_value; } + + constexpr double + imag() const { return __imag__ _M_value; } +#else + double& + real() { return __real__ _M_value; } + + const double& + real() const { return __real__ _M_value; } + + double& + imag() { return __imag__ _M_value; } + + const double& + imag() const { return __imag__ _M_value; } +#endif + + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 387. std::complex over-encapsulated. + void + real(double __val) { __real__ _M_value = __val; } + + void + imag(double __val) { __imag__ _M_value = __val; } + + complex& + operator=(double __d) + { + _M_value = __d; + return *this; + } + + complex& + operator+=(double __d) + { + _M_value += __d; + return *this; + } + + complex& + operator-=(double __d) + { + _M_value -= __d; + return *this; + } + + complex& + operator*=(double __d) + { + _M_value *= __d; + return *this; + } + + complex& + operator/=(double __d) + { + _M_value /= __d; + return *this; + } + + // The compiler will synthesize this, efficiently. + // complex& operator=(const complex&); + + template<typename _Tp> + complex& + operator=(const complex<_Tp>& __z) + { + __real__ _M_value = __z.real(); + __imag__ _M_value = __z.imag(); + return *this; + } + + template<typename _Tp> + complex& + operator+=(const complex<_Tp>& __z) + { + __real__ _M_value += __z.real(); + __imag__ _M_value += __z.imag(); + return *this; + } + + template<typename _Tp> + complex& + operator-=(const complex<_Tp>& __z) + { + __real__ _M_value -= __z.real(); + __imag__ _M_value -= __z.imag(); + return *this; + } + + template<typename _Tp> + complex& + operator*=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value *= __t; + return *this; + } + + template<typename _Tp> + complex& + operator/=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value /= __t; + return *this; + } + + _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } + + private: + _ComplexT _M_value; + }; + + // 26.2.3 complex specializations + // complex<long double> specialization + template<> + struct complex<long double> + { + typedef long double value_type; + typedef __complex__ long double _ComplexT; + + _GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } + + _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, + long double __i = 0.0L) +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + // The list-initialization extension to __complex__ types is + // not available in GCC 4.6. Thus libstdc++/48760 cannot be + // fixed in C++0x mode, unfortunately. + : _M_value(__r + __i * 1.0Li) { } +#else + { + __real__ _M_value = __r; + __imag__ _M_value = __i; + } +#endif + + _GLIBCXX_CONSTEXPR complex(const complex<float>& __z) + : _M_value(__z.__rep()) { } + + _GLIBCXX_CONSTEXPR complex(const complex<double>& __z) + : _M_value(__z.__rep()) { } + +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 387. std::complex over-encapsulated. + constexpr long double + real() const { return __real__ _M_value; } + + constexpr long double + imag() const { return __imag__ _M_value; } +#else + long double& + real() { return __real__ _M_value; } + + const long double& + real() const { return __real__ _M_value; } + + long double& + imag() { return __imag__ _M_value; } + + const long double& + imag() const { return __imag__ _M_value; } +#endif + + // _GLIBCXX_RESOLVE_LIB_DEFECTS + // DR 387. std::complex over-encapsulated. + void + real(long double __val) { __real__ _M_value = __val; } + + void + imag(long double __val) { __imag__ _M_value = __val; } + + complex& + operator=(long double __r) + { + _M_value = __r; + return *this; + } + + complex& + operator+=(long double __r) + { + _M_value += __r; + return *this; + } + + complex& + operator-=(long double __r) + { + _M_value -= __r; + return *this; + } + + complex& + operator*=(long double __r) + { + _M_value *= __r; + return *this; + } + + complex& + operator/=(long double __r) + { + _M_value /= __r; + return *this; + } + + // The compiler knows how to do this efficiently + // complex& operator=(const complex&); + + template<typename _Tp> + complex& + operator=(const complex<_Tp>& __z) + { + __real__ _M_value = __z.real(); + __imag__ _M_value = __z.imag(); + return *this; + } + + template<typename _Tp> + complex& + operator+=(const complex<_Tp>& __z) + { + __real__ _M_value += __z.real(); + __imag__ _M_value += __z.imag(); + return *this; + } + + template<typename _Tp> + complex& + operator-=(const complex<_Tp>& __z) + { + __real__ _M_value -= __z.real(); + __imag__ _M_value -= __z.imag(); + return *this; + } + + template<typename _Tp> + complex& + operator*=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value *= __t; + return *this; + } + + template<typename _Tp> + complex& + operator/=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value /= __t; + return *this; + } + + _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; } + + private: + _ComplexT _M_value; + }; + + // These bits have to be at the end of this file, so that the + // specializations have all been defined. + inline _GLIBCXX_CONSTEXPR + complex<float>::complex(const complex<double>& __z) + : _M_value(__z.__rep()) { } + + inline _GLIBCXX_CONSTEXPR + complex<float>::complex(const complex<long double>& __z) + : _M_value(__z.__rep()) { } + + inline _GLIBCXX_CONSTEXPR + complex<double>::complex(const complex<long double>& __z) + : _M_value(__z.__rep()) { } + + // Inhibit implicit instantiations for required instantiations, + // which are defined via explicit instantiations elsewhere. + // NB: This syntax is a GNU extension. +#if _GLIBCXX_EXTERN_TEMPLATE + extern template istream& operator>>(istream&, complex<float>&); + extern template ostream& operator<<(ostream&, const complex<float>&); + extern template istream& operator>>(istream&, complex<double>&); + extern template ostream& operator<<(ostream&, const complex<double>&); + extern template istream& operator>>(istream&, complex<long double>&); + extern template ostream& operator<<(ostream&, const complex<long double>&); + +#ifdef _GLIBCXX_USE_WCHAR_T + extern template wistream& operator>>(wistream&, complex<float>&); + extern template wostream& operator<<(wostream&, const complex<float>&); + extern template wistream& operator>>(wistream&, complex<double>&); + extern template wostream& operator<<(wostream&, const complex<double>&); + extern template wistream& operator>>(wistream&, complex<long double>&); + extern template wostream& operator<<(wostream&, const complex<long double>&); +#endif +#endif + + // @} group complex_numbers + +_GLIBCXX_END_NAMESPACE_VERSION +} // namespace + +namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) +{ +_GLIBCXX_BEGIN_NAMESPACE_VERSION + + // See ext/type_traits.h for the primary template. + template<typename _Tp, typename _Up> + struct __promote_2<std::complex<_Tp>, _Up> + { + public: + typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; + }; + + template<typename _Tp, typename _Up> + struct __promote_2<_Tp, std::complex<_Up> > + { + public: + typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; + }; + + template<typename _Tp, typename _Up> + struct __promote_2<std::complex<_Tp>, std::complex<_Up> > + { + public: + typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type; + }; + +_GLIBCXX_END_NAMESPACE_VERSION +} // namespace + +#ifdef __GXX_EXPERIMENTAL_CXX0X__ + +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) + { + // Kahan's formula. + return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) + + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); + } + +#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. + template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&); + + template<typename _Tp> + std::complex<_Tp> + __complex_proj(const std::complex<_Tp>& __z) + { + const _Tp __den = (__z.real() * __z.real() + + __z.imag() * __z.imag() + _Tp(1.0)); + + return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, + (_Tp(2.0) * __z.imag()) / __den); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_proj(__complex__ float __z) + { return __builtin_cprojf(__z); } + + inline __complex__ double + __complex_proj(__complex__ double __z) + { return __builtin_cproj(__z); } + + inline __complex__ long double + __complex_proj(const __complex__ long double& __z) + { return __builtin_cprojl(__z); } + + template<typename _Tp> + inline std::complex<_Tp> + proj(const std::complex<_Tp>& __z) + { return __complex_proj(__z.__rep()); } +#else + template<typename _Tp> + inline std::complex<_Tp> + proj(const std::complex<_Tp>& __z) + { return __complex_proj(__z); } +#endif + + // DR 1137. + template<typename _Tp> + inline typename __gnu_cxx::__promote<_Tp>::__type + proj(_Tp __x) + { return __x; } + + template<typename _Tp> + inline typename __gnu_cxx::__promote<_Tp>::__type + conj(_Tp __x) + { return __x; } + +_GLIBCXX_END_NAMESPACE_VERSION +} // namespace + +#endif // __GXX_EXPERIMENTAL_CXX0X__ + +#endif /* _GLIBCXX_COMPLEX */ |