// The template and inlines for the -*- C++ -*- complex number classes.
-// Copyright (C) 1997-2013 Free Software Foundation, Inc.
+// Copyright (C) 1997-2017 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
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>&);
-#if __cplusplus < 201103L
- // DR 844.
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
-#endif
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
/// Return @a x to the @a y'th power.
- template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
+ 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>&);
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.
{
/// 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.
+ // 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()) { }
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
_GLIBCXX_ABI_TAG_CXX11
- constexpr _Tp
- real() { return _M_real; }
+ constexpr _Tp
+ real() const { return _M_real; }
_GLIBCXX_ABI_TAG_CXX11
- constexpr _Tp
- imag() { return _M_imag; }
+ constexpr _Tp
+ imag() const { return _M_imag; }
#else
/// Return real part of complex number.
- _Tp&
+ _Tp&
real() { return _M_real; }
/// Return real part of complex number.
- const _Tp&
+ const _Tp&
real() const { return _M_real; }
/// Return imaginary part of complex number.
- _Tp&
+ _Tp&
imag() { return _M_imag; }
/// Return imaginary part of complex number.
- const _Tp&
+ const _Tp&
imag() const { return _M_imag; }
#endif
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
- void
+ void
real(_Tp __val) { _M_real = __val; }
- void
+ void
imag(_Tp __val) { _M_imag = __val; }
- /// Assign this complex number to scalar @a t.
+ /// Assign a scalar to this complex number.
complex<_Tp>& operator=(const _Tp&);
-
- /// Add @a t to this complex number.
+
+ /// Add a scalar to this complex number.
// 26.2.5/1
complex<_Tp>&
operator+=(const _Tp& __t)
return *this;
}
- /// Subtract @a t from this complex number.
+ /// Subtract a scalar from this complex number.
// 26.2.5/3
complex<_Tp>&
operator-=(const _Tp& __t)
return *this;
}
- /// Multiply this complex number by @a t.
+ /// Multiply this complex number by a scalar.
complex<_Tp>& operator*=(const _Tp&);
- /// Divide this complex number by @a t.
+ /// Divide this complex number by a scalar.
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.
+ // Let the compiler synthesize the copy assignment operator
+#if __cplusplus >= 201103L
+ complex& operator=(const complex&) = default;
+#endif
+
+ /// Assign another complex number to this one.
template<typename _Up>
complex<_Tp>& operator=(const complex<_Up>&);
- /// Add @a z to this complex number.
+ /// Add another complex number to this one.
template<typename _Up>
complex<_Tp>& operator+=(const complex<_Up>&);
- /// Subtract @a z from this complex number.
+ /// Subtract another complex number from this one.
template<typename _Up>
complex<_Tp>& operator-=(const complex<_Up>&);
- /// Multiply this complex number by @a z.
+ /// Multiply this complex number by another.
template<typename _Up>
complex<_Tp>& operator*=(const complex<_Up>&);
- /// Divide this complex number by @a z.
+ /// Divide this complex number by another.
template<typename _Up>
complex<_Tp>& operator/=(const complex<_Up>&);
- _GLIBCXX_USE_CONSTEXPR complex __rep() const
+ _GLIBCXX_CONSTEXPR complex __rep() const
{ return *this; }
private:
_M_real = __t;
_M_imag = _Tp();
return *this;
- }
+ }
// 26.2.5/5
template<typename _Tp>
_M_real = __r / __n;
return *this;
}
-
+
// Operators:
//@{
/// Return new complex value @a x plus @a y.
__r -= __y;
return __r;
}
-
+
template<typename _Tp>
inline complex<_Tp>
operator-(const complex<_Tp>& __x, const _Tp& __y)
__r /= __y;
return __r;
}
-
+
template<typename _Tp>
inline complex<_Tp>
operator/(const complex<_Tp>& __x, const _Tp& __y)
basic_istream<_CharT, _Traits>&
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
{
- _Tp __re_x, __im_x;
+ bool __fail = true;
_CharT __ch;
- __is >> __ch;
- if (__ch == '(')
+ if (__is >> __ch)
{
- __is >> __re_x >> __ch;
- if (__ch == ',')
+ if (_Traits::eq(__ch, __is.widen('(')))
{
- __is >> __im_x >> __ch;
- if (__ch == ')')
- __x = complex<_Tp>(__re_x, __im_x);
- else
- __is.setstate(ios_base::failbit);
+ _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 if (__ch == ')')
- __x = __re_x;
else
- __is.setstate(ios_base::failbit);
- }
- else
- {
- __is.putback(__ch);
- __is >> __re_x;
- __x = __re_x;
+ {
+ __is.putback(__ch);
+ _Tp __u;
+ if (__is >> __u)
+ {
+ __x = __u;
+ __fail = false;
+ }
+ }
}
+ if (__fail)
+ __is.setstate(ios_base::failbit);
return __is;
}
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)
const _Tp __s = std::max(abs(__x), abs(__y));
if (__s == _Tp()) // well ...
return __s;
- __x /= __s;
+ __x /= __s;
__y /= __s;
return __s * sqrt(__x * __x + __y * __y);
}
template<typename _Tp>
inline _Tp
abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
-#endif
+#endif
// 26.2.7/4: arg(__z): Returns the phase angle of __z.
// 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
+ // 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>
return __res * __res;
}
};
-
+
template<typename _Tp>
inline _Tp
norm(const complex<_Tp>& __z)
{
- return _Norm_helper<__is_floating<_Tp>::__value
+ 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)); }
+ {
+ __glibcxx_assert( __rho >= 0 );
+ 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_exp(const complex<_Tp>& __z)
- { return std::polar(exp(__z.real()), __z.imag()); }
+ { return std::polar<_Tp>(exp(__z.real()), __z.imag()); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
- return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
+ return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
- __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
+ __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
inline __complex__ double
- __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
+ __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
inline __complex__ long double
__complex_sinh(const __complex__ long double& __z)
- { return __builtin_csinhl(__z); }
+ { return __builtin_csinhl(__z); }
template<typename _Tp>
inline complex<_Tp>
#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)
// 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
-
+
template<typename _Tp>
inline complex<_Tp>
__complex_tanh(const complex<_Tp>& __z)
// 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.
-#if __cplusplus < 201103L
template<typename _Tp>
complex<_Tp>
__complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
return __y;
}
- // _GLIBCXX_RESOLVE_LIB_DEFECTS
+ // 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)
? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
: std::__complex_pow_unsigned(__z, __n);
}
-#endif
template<typename _Tp>
complex<_Tp>
pow(const complex<_Tp>& __x, const _Tp& __y)
{
-#ifndef _GLIBCXX_USE_C99_COMPLEX
+#if ! _GLIBCXX_USE_C99_COMPLEX
if (__x == _Tp())
return _Tp();
#endif
return pow(__x.real(), __y);
complex<_Tp> __t = std::log(__x);
- return std::polar(exp(__y * __t.real()), __y * __t.imag());
+ return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
}
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))
+ return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
+ __y.imag() * log(__x))
: std::pow(complex<_Tp>(__x), __y);
}
#endif
explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
- explicit _GLIBCXX_CONSTEXPR complex(const complex<long 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
+ constexpr float
real() const { return __real__ _M_value; }
__attribute ((__abi_tag__ ("cxx11")))
- constexpr float
+ constexpr float
imag() const { return __imag__ _M_value; }
#else
- float&
+ float&
real() { return __real__ _M_value; }
- const float&
- real() const { return __real__ _M_value; }
+ const float&
+ real() const { return __real__ _M_value; }
- float&
+ float&
imag() { return __imag__ _M_value; }
- const float&
+ const float&
imag() const { return __imag__ _M_value; }
#endif
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
- void
+ void
real(float __val) { __real__ _M_value = __val; }
- void
+ void
imag(float __val) { __imag__ _M_value = __val; }
complex&
return *this;
}
- _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
+ _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
private:
_ComplexT _M_value;
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
: _M_value(__z.__rep()) { }
- explicit _GLIBCXX_CONSTEXPR complex(const complex<long 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 double
+ constexpr double
real() const { return __real__ _M_value; }
__attribute ((__abi_tag__ ("cxx11")))
- constexpr double
+ constexpr double
imag() const { return __imag__ _M_value; }
#else
- double&
+ double&
real() { return __real__ _M_value; }
- const double&
+ const double&
real() const { return __real__ _M_value; }
- double&
+ double&
imag() { return __imag__ _M_value; }
- const double&
+ const double&
imag() const { return __imag__ _M_value; }
#endif
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
- void
+ void
real(double __val) { __real__ _M_value = __val; }
- void
+ void
imag(double __val) { __imag__ _M_value = __val; }
complex&
_M_value += __d;
return *this;
}
-
+
complex&
operator-=(double __d)
{
return *this;
}
- _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
+ _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
private:
_ComplexT _M_value;
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
- _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
+ _GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
long double __i = 0.0L)
#if __cplusplus >= 201103L
: _M_value{ __r, __i } { }
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
__attribute ((__abi_tag__ ("cxx11")))
- constexpr long double
+ constexpr long double
real() const { return __real__ _M_value; }
__attribute ((__abi_tag__ ("cxx11")))
- constexpr long double
+ constexpr long double
imag() const { return __imag__ _M_value; }
#else
- long double&
+ long double&
real() { return __real__ _M_value; }
- const long double&
+ const long double&
real() const { return __real__ _M_value; }
- long double&
+ long double&
imag() { return __imag__ _M_value; }
- const long double&
+ const long double&
imag() const { return __imag__ _M_value; }
#endif
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
- void
+ void
real(long double __val) { __real__ _M_value = __val; }
- void
+ void
imag(long double __val) { __imag__ _M_value = __val; }
complex&
return *this;
}
- _GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
+ _GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
private:
_ComplexT _M_value;
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> >
{
asin(const std::complex<_Tp>& __z)
{ return __complex_asin(__z); }
#endif
-
+
template<typename _Tp>
std::complex<_Tp>
__complex_atan(const std::complex<_Tp>& __z)
arg(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
-#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
+#if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
: __type();
#else
}
template<typename _Tp>
- inline typename __gnu_cxx::__promote<_Tp>::__type
+ _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
imag(_Tp)
{ return _Tp(); }
}
template<typename _Tp>
- inline typename __gnu_cxx::__promote<_Tp>::__type
+ _GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
real(_Tp __x)
{ return __x; }
{ return __complex_proj(__z); }
#endif
- // DR 1137.
template<typename _Tp>
- inline typename __gnu_cxx::__promote<_Tp>::__type
+ inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
proj(_Tp __x)
- { return __x; }
+ {
+ typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
+ return std::proj(std::complex<__type>(__x));
+ }
template<typename _Tp>
- inline typename __gnu_cxx::__promote<_Tp>::__type
+ inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
conj(_Tp __x)
- { return __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 201309
+
+ 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
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