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- // The template and inlines for the -*- C++ -*- complex number classes.
- // Copyright (C) 1997-2022 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
- #if __cplusplus > 201703L
- # define __cpp_lib_constexpr_complex 201711L
- #endif
- 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 _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&);
- /// Return complex conjugate of @a z.
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR 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>
- class complex
- {
- public:
- /// 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) { }
- // Let the compiler synthesize the copy constructor
- #if __cplusplus >= 201103L
- constexpr complex(const complex&) = default;
- #endif
- /// Converting 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() const { return _M_real; }
- _GLIBCXX_ABI_TAG_CXX11
- 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.
- _GLIBCXX20_CONSTEXPR void
- real(_Tp __val) { _M_real = __val; }
- _GLIBCXX20_CONSTEXPR void
- imag(_Tp __val) { _M_imag = __val; }
- /// Assign a scalar to this complex number.
- _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&);
- /// Add a scalar to this complex number.
- // 26.2.5/1
- _GLIBCXX20_CONSTEXPR complex<_Tp>&
- operator+=(const _Tp& __t)
- {
- _M_real += __t;
- return *this;
- }
- /// Subtract a scalar from this complex number.
- // 26.2.5/3
- _GLIBCXX20_CONSTEXPR complex<_Tp>&
- operator-=(const _Tp& __t)
- {
- _M_real -= __t;
- return *this;
- }
- /// Multiply this complex number by a scalar.
- _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&);
- /// Divide this complex number by a scalar.
- _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&);
- // Let the compiler synthesize the copy assignment operator
- #if __cplusplus >= 201103L
- _GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default;
- #endif
- /// Assign another complex number to this one.
- template<typename _Up>
- _GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&);
- /// Add another complex number to this one.
- template<typename _Up>
- _GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&);
- /// Subtract another complex number from this one.
- template<typename _Up>
- _GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&);
- /// Multiply this complex number by another.
- template<typename _Up>
- _GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&);
- /// Divide this complex number by another.
- template<typename _Up>
- _GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&);
- _GLIBCXX_CONSTEXPR complex __rep() const
- { return *this; }
- private:
- _Tp _M_real;
- _Tp _M_imag;
- };
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex<_Tp>&
- complex<_Tp>::operator=(const _Tp& __t)
- {
- _M_real = __t;
- _M_imag = _Tp();
- return *this;
- }
- // 26.2.5/5
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex<_Tp>&
- complex<_Tp>::operator*=(const _Tp& __t)
- {
- _M_real *= __t;
- _M_imag *= __t;
- return *this;
- }
- // 26.2.5/7
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex<_Tp>&
- complex<_Tp>::operator/=(const _Tp& __t)
- {
- _M_real /= __t;
- _M_imag /= __t;
- return *this;
- }
- template<typename _Tp>
- template<typename _Up>
- _GLIBCXX20_CONSTEXPR 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>
- _GLIBCXX20_CONSTEXPR 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>
- _GLIBCXX20_CONSTEXPR 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>
- _GLIBCXX20_CONSTEXPR 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>
- _GLIBCXX20_CONSTEXPR 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 _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
- {
- complex<_Tp> __r = __x;
- __r += __y;
- return __r;
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator+(const complex<_Tp>& __x, const _Tp& __y)
- {
- complex<_Tp> __r = __x;
- __r += __y;
- return __r;
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR 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 _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
- {
- complex<_Tp> __r = __x;
- __r -= __y;
- return __r;
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator-(const complex<_Tp>& __x, const _Tp& __y)
- {
- complex<_Tp> __r = __x;
- __r -= __y;
- return __r;
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator-(const _Tp& __x, const complex<_Tp>& __y)
- {
- complex<_Tp> __r = -__y;
- __r += __x;
- return __r;
- }
- ///@}
- ///@{
- /// Return new complex value @a x times @a y.
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
- {
- complex<_Tp> __r = __x;
- __r *= __y;
- return __r;
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator*(const complex<_Tp>& __x, const _Tp& __y)
- {
- complex<_Tp> __r = __x;
- __r *= __y;
- return __r;
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR 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 _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
- {
- complex<_Tp> __r = __x;
- __r /= __y;
- return __r;
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator/(const complex<_Tp>& __x, const _Tp& __y)
- {
- complex<_Tp> __r = __x;
- __r /= __y;
- return __r;
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR 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 _GLIBCXX20_CONSTEXPR complex<_Tp>
- operator+(const complex<_Tp>& __x)
- { return __x; }
- /// Return complex negation of @a x.
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR 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(); }
- #if !(__cpp_impl_three_way_comparison >= 201907L)
- 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(); }
- #endif
- ///@}
- /// 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)
- {
- bool __fail = true;
- _CharT __ch;
- if (__is >> __ch)
- {
- if (_Traits::eq(__ch, __is.widen('(')))
- {
- _Tp __u;
- if (__is >> __u >> __ch)
- {
- const _CharT __rparen = __is.widen(')');
- if (_Traits::eq(__ch, __rparen))
- {
- __x = __u;
- __fail = false;
- }
- else if (_Traits::eq(__ch, __is.widen(',')))
- {
- _Tp __v;
- if (__is >> __v >> __ch)
- {
- if (_Traits::eq(__ch, __rparen))
- {
- __x = complex<_Tp>(__u, __v);
- __fail = false;
- }
- else
- __is.putback(__ch);
- }
- }
- else
- __is.putback(__ch);
- }
- }
- else
- {
- __is.putback(__ch);
- _Tp __u;
- if (__is >> __u)
- {
- __x = __u;
- __fail = false;
- }
- }
- }
- if (__fail)
- __is.setstate(ios_base::failbit);
- 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
- // sense 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 _GLIBCXX20_CONSTEXPR _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 _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
- {
- //_Tp __res = std::abs(__z);
- //return __res * __res;
- const _Tp __x = __z.real();
- const _Tp __y = __z.imag();
- return __x * __x + __y * __y;
- }
- };
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR _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)
- {
- __glibcxx_assert( __rho >= 0 );
- return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR 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<_Tp>(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)
- {
- #if ! _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<_Tp>(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<_Tp>(pow(__x, __y.real()),
- __y.imag() * log(__x))
- : std::pow(complex<_Tp>(__x), __y);
- }
- /// 26.2.3 complex specializations
- /// complex<float> specialization
- template<>
- class complex<float>
- {
- public:
- 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.
- _GLIBCXX20_CONSTEXPR void
- real(float __val) { __real__ _M_value = __val; }
- _GLIBCXX20_CONSTEXPR void
- imag(float __val) { __imag__ _M_value = __val; }
- _GLIBCXX20_CONSTEXPR complex&
- operator=(float __f)
- {
- _M_value = __f;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator+=(float __f)
- {
- _M_value += __f;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator-=(float __f)
- {
- _M_value -= __f;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator*=(float __f)
- {
- _M_value *= __f;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR 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.
- #if __cplusplus >= 201103L
- _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
- #endif
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator=(const complex<_Tp>& __z)
- {
- __real__ _M_value = __z.real();
- __imag__ _M_value = __z.imag();
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator+=(const complex<_Tp>& __z)
- {
- _M_value += __z.__rep();
- return *this;
- }
- template<class _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator-=(const complex<_Tp>& __z)
- {
- _M_value -= __z.__rep();
- return *this;
- }
- template<class _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator*=(const complex<_Tp>& __z)
- {
- const _ComplexT __t = __z.__rep();
- _M_value *= __t;
- return *this;
- }
- template<class _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator/=(const complex<_Tp>& __z)
- {
- const _ComplexT __t = __z.__rep();
- _M_value /= __t;
- return *this;
- }
- _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
- private:
- _ComplexT _M_value;
- };
- /// 26.2.3 complex specializations
- /// complex<double> specialization
- template<>
- class complex<double>
- {
- public:
- 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.
- _GLIBCXX20_CONSTEXPR void
- real(double __val) { __real__ _M_value = __val; }
- _GLIBCXX20_CONSTEXPR void
- imag(double __val) { __imag__ _M_value = __val; }
- _GLIBCXX20_CONSTEXPR complex&
- operator=(double __d)
- {
- _M_value = __d;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator+=(double __d)
- {
- _M_value += __d;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator-=(double __d)
- {
- _M_value -= __d;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator*=(double __d)
- {
- _M_value *= __d;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator/=(double __d)
- {
- _M_value /= __d;
- return *this;
- }
- // The compiler will synthesize this, efficiently.
- #if __cplusplus >= 201103L
- _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
- #endif
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator=(const complex<_Tp>& __z)
- {
- _M_value = __z.__rep();
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator+=(const complex<_Tp>& __z)
- {
- _M_value += __z.__rep();
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator-=(const complex<_Tp>& __z)
- {
- _M_value -= __z.__rep();
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator*=(const complex<_Tp>& __z)
- {
- const _ComplexT __t = __z.__rep();
- _M_value *= __t;
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator/=(const complex<_Tp>& __z)
- {
- const _ComplexT __t = __z.__rep();
- _M_value /= __t;
- return *this;
- }
- _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
- private:
- _ComplexT _M_value;
- };
- /// 26.2.3 complex specializations
- /// complex<long double> specialization
- template<>
- class complex<long double>
- {
- public:
- 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.
- _GLIBCXX20_CONSTEXPR void
- real(long double __val) { __real__ _M_value = __val; }
- _GLIBCXX20_CONSTEXPR void
- imag(long double __val) { __imag__ _M_value = __val; }
- _GLIBCXX20_CONSTEXPR complex&
- operator=(long double __r)
- {
- _M_value = __r;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator+=(long double __r)
- {
- _M_value += __r;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator-=(long double __r)
- {
- _M_value -= __r;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator*=(long double __r)
- {
- _M_value *= __r;
- return *this;
- }
- _GLIBCXX20_CONSTEXPR complex&
- operator/=(long double __r)
- {
- _M_value /= __r;
- return *this;
- }
- // The compiler knows how to do this efficiently
- #if __cplusplus >= 201103L
- _GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
- #endif
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator=(const complex<_Tp>& __z)
- {
- _M_value = __z.__rep();
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator+=(const complex<_Tp>& __z)
- {
- _M_value += __z.__rep();
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator-=(const complex<_Tp>& __z)
- {
- _M_value -= __z.__rep();
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator*=(const complex<_Tp>& __z)
- {
- const _ComplexT __t = __z.__rep();
- _M_value *= __t;
- return *this;
- }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR complex&
- operator/=(const complex<_Tp>& __z)
- {
- const _ComplexT __t = __z.__rep();
- _M_value /= __t;
- return *this;
- }
- _GLIBCXX_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
- #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 (_GLIBCXX11_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>
- _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
- imag(_Tp)
- { return _Tp(); }
- template<typename _Tp>
- _GLIBCXX20_CONSTEXPR 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>
- _GLIBCXX_CONSTEXPR 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>&);
- // Generic implementation of std::proj, does not work for infinities.
- template<typename _Tp>
- inline std::complex<_Tp>
- __complex_proj(const std::complex<_Tp>& __z)
- { return __z; }
- #if _GLIBCXX_USE_C99_COMPLEX
- inline complex<float>
- __complex_proj(const complex<float>& __z)
- { return __builtin_cprojf(__z.__rep()); }
- inline complex<double>
- __complex_proj(const complex<double>& __z)
- { return __builtin_cproj(__z.__rep()); }
- inline complex<long double>
- __complex_proj(const complex<long double>& __z)
- { return __builtin_cprojl(__z.__rep()); }
- #elif defined _GLIBCXX_USE_C99_MATH_TR1
- inline complex<float>
- __complex_proj(const complex<float>& __z)
- {
- if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
- return complex<float>(__builtin_inff(),
- __builtin_copysignf(0.0f, __z.imag()));
- return __z;
- }
- inline complex<double>
- __complex_proj(const complex<double>& __z)
- {
- if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
- return complex<double>(__builtin_inf(),
- __builtin_copysign(0.0, __z.imag()));
- return __z;
- }
- inline complex<long double>
- __complex_proj(const complex<long double>& __z)
- {
- if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
- return complex<long double>(__builtin_infl(),
- __builtin_copysignl(0.0l, __z.imag()));
- return __z;
- }
- #endif
- template<typename _Tp>
- inline std::complex<_Tp>
- proj(const std::complex<_Tp>& __z)
- { return __complex_proj(__z); }
- // Overload for scalars
- template<typename _Tp>
- inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
- proj(_Tp __x)
- {
- typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
- return std::proj(std::complex<__type>(__x));
- }
- template<typename _Tp>
- inline _GLIBCXX20_CONSTEXPR
- std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
- conj(_Tp __x)
- {
- typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
- return std::complex<__type>(__x, -__type());
- }
- #if __cplusplus > 201103L
- inline namespace literals {
- inline namespace complex_literals {
- #pragma GCC diagnostic push
- #pragma GCC diagnostic ignored "-Wliteral-suffix"
- #define __cpp_lib_complex_udls 201309L
- 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)}; }
- #pragma GCC diagnostic pop
- } // inline namespace complex_literals
- } // inline namespace literals
- #endif // C++14
- _GLIBCXX_END_NAMESPACE_VERSION
- } // namespace
- #endif // C++11
- #endif /* _GLIBCXX_COMPLEX */
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