| // The template and inlines for the -*- C++ -*- complex number classes. |
| |
| // Copyright (C) 1997-2014 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> |
| |
| // Get rid of a macro possibly defined in <complex.h> |
| #undef complex |
| |
| 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>&); |
| /// Return @a x to the @a y'th power. |
| template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); |
| /// 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()) { } |
| |
| #if __cplusplus >= 201103L |
| // _GLIBCXX_RESOLVE_LIB_DEFECTS |
| // DR 387. std::complex over-encapsulated. |
| _GLIBCXX_ABI_TAG_CXX11 |
| constexpr _Tp |
| real() { return _M_real; } |
| |
| _GLIBCXX_ABI_TAG_CXX11 |
| constexpr _Tp |
| imag() { 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 |
| #if __cplusplus >= 201103L |
| template<typename _Tp> |
| constexpr _Tp |
| real(const complex<_Tp>& __z) |
| { return __z.real(); } |
| |
| template<typename _Tp> |
| 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. |
| 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; |
| } |
| |
| // In C++11 mode we used to implement the resolution of |
| // DR 844. complex pow return type is ambiguous. |
| // thus the following overload was disabled in that mode. However, doing |
| // that causes all sorts of issues, see, for example: |
| // http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html |
| // and also PR57974. |
| template<typename _Tp> |
| inline complex<_Tp> |
| pow(const complex<_Tp>& __z, int __n) |
| { |
| return __n < 0 |
| ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) |
| : std::__complex_pow_unsigned(__z, __n); |
| } |
| |
| 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) |
| #if __cplusplus >= 201103L |
| : _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>&); |
| |
| #if __cplusplus >= 201103L |
| // _GLIBCXX_RESOLVE_LIB_DEFECTS |
| // DR 387. std::complex over-encapsulated. |
| __attribute ((__abi_tag__ ("cxx11"))) |
| constexpr float |
| real() const { return __real__ _M_value; } |
| |
| __attribute ((__abi_tag__ ("cxx11"))) |
| 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) |
| #if __cplusplus >= 201103L |
| : _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()) { } |
| |
| explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&); |
| |
| #if __cplusplus >= 201103L |
| // _GLIBCXX_RESOLVE_LIB_DEFECTS |
| // DR 387. std::complex over-encapsulated. |
| __attribute ((__abi_tag__ ("cxx11"))) |
| constexpr double |
| real() const { return __real__ _M_value; } |
| |
| __attribute ((__abi_tag__ ("cxx11"))) |
| 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) |
| #if __cplusplus >= 201103L |
| : _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(const complex<double>& __z) |
| : _M_value(__z.__rep()) { } |
| |
| #if __cplusplus >= 201103L |
| // _GLIBCXX_RESOLVE_LIB_DEFECTS |
| // DR 387. std::complex over-encapsulated. |
| __attribute ((__abi_tag__ ("cxx11"))) |
| constexpr long double |
| real() const { return __real__ _M_value; } |
| |
| __attribute ((__abi_tag__ ("cxx11"))) |
| 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 |
| |
| #if __cplusplus >= 201103L |
| |
| 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; } |
| |
| #if __cplusplus > 201103L |
| |
| inline namespace literals { |
| inline namespace complex_literals { |
| |
| constexpr std::complex<float> |
| operator""if(long double __num) |
| { return std::complex<float>{0.0F, static_cast<float>(__num)}; } |
| |
| constexpr std::complex<float> |
| operator""if(unsigned long long __num) |
| { return std::complex<float>{0.0F, static_cast<float>(__num)}; } |
| |
| constexpr std::complex<double> |
| operator""i(long double __num) |
| { return std::complex<double>{0.0, static_cast<double>(__num)}; } |
| |
| constexpr std::complex<double> |
| operator""i(unsigned long long __num) |
| { return std::complex<double>{0.0, static_cast<double>(__num)}; } |
| |
| constexpr std::complex<long double> |
| operator""il(long double __num) |
| { return std::complex<long double>{0.0L, __num}; } |
| |
| constexpr std::complex<long double> |
| operator""il(unsigned long long __num) |
| { return std::complex<long double>{0.0L, static_cast<long double>(__num)}; } |
| |
| } // inline namespace complex_literals |
| } // inline namespace literals |
| |
| #endif // C++14 |
| |
| _GLIBCXX_END_NAMESPACE_VERSION |
| } // namespace |
| |
| #endif // C++11 |
| |
| #endif /* _GLIBCXX_COMPLEX */ |
