libcxx initial import
git-svn-id: https://llvm.org/svn/llvm-project/libcxx/trunk@103490 91177308-0d34-0410-b5e6-96231b3b80d8
diff --git a/include/complex b/include/complex
new file mode 100644
index 0000000..dd6f8aa
--- /dev/null
+++ b/include/complex
@@ -0,0 +1,1528 @@
+// -*- C++ -*-
+//===--------------------------- complex ----------------------------------===//
+//
+// ÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊÊThe LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP_COMPLEX
+#define _LIBCPP_COMPLEX
+
+/*
+ complex synopsis
+
+namespace std
+{
+
+template<class T>
+class complex
+{
+public:
+ typedef T value_type;
+
+ complex(const T& re = T(), const T& im = T());
+ complex(const complex&);
+ template<class X> complex(const complex<X>&);
+
+ T real() const;
+ T imag() const;
+
+ void real(T);
+ void imag(T);
+
+ complex<T>& operator= (const T&);
+ complex<T>& operator+=(const T&);
+ complex<T>& operator-=(const T&);
+ complex<T>& operator*=(const T&);
+ complex<T>& operator/=(const T&);
+
+ complex& operator=(const complex&);
+ template<class X> complex<T>& operator= (const complex<X>&);
+ template<class X> complex<T>& operator+=(const complex<X>&);
+ template<class X> complex<T>& operator-=(const complex<X>&);
+ template<class X> complex<T>& operator*=(const complex<X>&);
+ template<class X> complex<T>& operator/=(const complex<X>&);
+};
+
+template<>
+class complex<float>
+{
+public:
+ typedef float value_type;
+
+ constexpr complex(float re = 0.0f, float im = 0.0f);
+ explicit constexpr complex(const complex<double>&);
+ explicit constexpr complex(const complex<long double>&);
+
+ constexpr float real() const;
+ void real(float);
+ constexpr float imag() const;
+ void imag(float);
+
+ complex<float>& operator= (float);
+ complex<float>& operator+=(float);
+ complex<float>& operator-=(float);
+ complex<float>& operator*=(float);
+ complex<float>& operator/=(float);
+
+ complex<float>& operator=(const complex<float>&);
+ template<class X> complex<float>& operator= (const complex<X>&);
+ template<class X> complex<float>& operator+=(const complex<X>&);
+ template<class X> complex<float>& operator-=(const complex<X>&);
+ template<class X> complex<float>& operator*=(const complex<X>&);
+ template<class X> complex<float>& operator/=(const complex<X>&);
+};
+
+template<>
+class complex<double>
+{
+public:
+ typedef double value_type;
+
+ constexpr complex(double re = 0.0, double im = 0.0);
+ constexpr complex(const complex<float>&);
+ explicit constexpr complex(const complex<long double>&);
+
+ constexpr double real() const;
+ void real(double);
+ constexpr double imag() const;
+ void imag(double);
+
+ complex<double>& operator= (double);
+ complex<double>& operator+=(double);
+ complex<double>& operator-=(double);
+ complex<double>& operator*=(double);
+ complex<double>& operator/=(double);
+ complex<double>& operator=(const complex<double>&);
+
+ template<class X> complex<double>& operator= (const complex<X>&);
+ template<class X> complex<double>& operator+=(const complex<X>&);
+ template<class X> complex<double>& operator-=(const complex<X>&);
+ template<class X> complex<double>& operator*=(const complex<X>&);
+ template<class X> complex<double>& operator/=(const complex<X>&);
+};
+
+template<>
+class complex<long double>
+{
+public:
+ typedef long double value_type;
+
+ constexpr complex(long double re = 0.0L, long double im = 0.0L);
+ constexpr complex(const complex<float>&);
+ constexpr complex(const complex<double>&);
+
+ constexpr long double real() const;
+ void real(long double);
+ constexpr long double imag() const;
+ void imag(long double);
+
+ complex<long double>& operator=(const complex<long double>&);
+ complex<long double>& operator= (long double);
+ complex<long double>& operator+=(long double);
+ complex<long double>& operator-=(long double);
+ complex<long double>& operator*=(long double);
+ complex<long double>& operator/=(long double);
+
+ template<class X> complex<long double>& operator= (const complex<X>&);
+ template<class X> complex<long double>& operator+=(const complex<X>&);
+ template<class X> complex<long double>& operator-=(const complex<X>&);
+ template<class X> complex<long double>& operator*=(const complex<X>&);
+ template<class X> complex<long double>& operator/=(const complex<X>&);
+};
+
+// 26.3.6 operators:
+template<class T> complex<T> operator+(const complex<T>&, const complex<T>&);
+template<class T> complex<T> operator+(const complex<T>&, const T&);
+template<class T> complex<T> operator+(const T&, const complex<T>&);
+template<class T> complex<T> operator-(const complex<T>&, const complex<T>&);
+template<class T> complex<T> operator-(const complex<T>&, const T&);
+template<class T> complex<T> operator-(const T&, const complex<T>&);
+template<class T> complex<T> operator*(const complex<T>&, const complex<T>&);
+template<class T> complex<T> operator*(const complex<T>&, const T&);
+template<class T> complex<T> operator*(const T&, const complex<T>&);
+template<class T> complex<T> operator/(const complex<T>&, const complex<T>&);
+template<class T> complex<T> operator/(const complex<T>&, const T&);
+template<class T> complex<T> operator/(const T&, const complex<T>&);
+template<class T> complex<T> operator+(const complex<T>&);
+template<class T> complex<T> operator-(const complex<T>&);
+template<class T> bool operator==(const complex<T>&, const complex<T>&);
+template<class T> bool operator==(const complex<T>&, const T&);
+template<class T> bool operator==(const T&, const complex<T>&);
+template<class T> bool operator!=(const complex<T>&, const complex<T>&);
+template<class T> bool operator!=(const complex<T>&, const T&);
+template<class T> bool operator!=(const T&, const complex<T>&);
+
+template<class T, class charT, class traits>
+ basic_istream<charT, traits>&
+ operator>>(basic_istream<charT, traits>&, complex<T>&);
+template<class T, class charT, class traits>
+ basic_ostream<charT, traits>&
+ operator<<(basic_ostream<charT, traits>&, const complex<T>&);
+
+// 26.3.7 values:
+
+template<class T> T real(const complex<T>&);
+ long double real(long double);
+ double real(double);
+template<Integral T> double real(T);
+ float real(float);
+
+template<class T> T imag(const complex<T>&);
+ long double imag(long double);
+ double imag(double);
+template<Integral T> double imag(T);
+ float imag(float);
+
+template<class T> T abs(const complex<T>&);
+
+template<class T> T arg(const complex<T>&);
+ long double arg(long double);
+ double arg(double);
+template<Integral T> double arg(T);
+ float arg(float);
+
+template<class T> T norm(const complex<T>&);
+ long double norm(long double);
+ double norm(double);
+template<Integral T> double norm(T);
+ float norm(float);
+
+template<class T> complex<T> conj(const complex<T>&);
+ long double conj(long double);
+ double conj(double);
+template<Integral T> double conj(T);
+ float conj(float);
+
+template<class T> complex<T> proj(const complex<T>&);
+ long double proj(long double);
+ double proj(double);
+template<Integral T> double proj(T);
+ float proj(float);
+
+template<class T> complex<T> polar(const T&, const T& = 0);
+
+// 26.3.8 transcendentals:
+template<class T> complex<T> acos(const complex<T>&);
+template<class T> complex<T> asin(const complex<T>&);
+template<class T> complex<T> atan(const complex<T>&);
+template<class T> complex<T> acosh(const complex<T>&);
+template<class T> complex<T> asinh(const complex<T>&);
+template<class T> complex<T> atanh(const complex<T>&);
+template<class T> complex<T> cos (const complex<T>&);
+template<class T> complex<T> cosh (const complex<T>&);
+template<class T> complex<T> exp (const complex<T>&);
+template<class T> complex<T> log (const complex<T>&);
+template<class T> complex<T> log10(const complex<T>&);
+
+template<class T> complex<T> pow(const complex<T>&, const T&);
+template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
+template<class T> complex<T> pow(const T&, const complex<T>&);
+
+template<class T> complex<T> sin (const complex<T>&);
+template<class T> complex<T> sinh (const complex<T>&);
+template<class T> complex<T> sqrt (const complex<T>&);
+template<class T> complex<T> tan (const complex<T>&);
+template<class T> complex<T> tanh (const complex<T>&);
+
+template<class T, class charT, class traits>
+ basic_istream<charT, traits>&
+ operator>>(basic_istream<charT, traits>& is, complex<T>& x);
+
+template<class T, class charT, class traits>
+ basic_ostream<charT, traits>&
+ operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);
+
+} // std
+
+*/
+
+#include <__config>
+#include <type_traits>
+#include <stdexcept>
+#include <cmath>
+#include <sstream>
+#if defined(_LIBCPP_NO_EXCEPTIONS)
+ #include <cassert>
+#endif
+
+#pragma GCC system_header
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+template<class _Tp> class complex;
+
+template<class _Tp> complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
+template<class _Tp> complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
+
+template<class _Tp>
+class complex
+{
+public:
+ typedef _Tp value_type;
+private:
+ value_type __re_;
+ value_type __im_;
+public:
+ _LIBCPP_INLINE_VISIBILITY
+ complex(const value_type& __re = value_type(), const value_type& __im = value_type())
+ : __re_(__re), __im_(__im) {}
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY
+ complex(const complex<_Xp>& __c)
+ : __re_(__c.real()), __im_(__c.imag()) {}
+
+ _LIBCPP_INLINE_VISIBILITY value_type real() const {return __re_;}
+ _LIBCPP_INLINE_VISIBILITY value_type imag() const {return __im_;}
+
+ _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
+ _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
+
+ _LIBCPP_INLINE_VISIBILITY complex& operator= (const value_type& __re) {__re_ = __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
+
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
+ {
+ __re_ = __c.real();
+ __im_ = __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
+ {
+ __re_ += __c.real();
+ __im_ += __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
+ {
+ __re_ -= __c.real();
+ __im_ -= __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
+ {
+ *this = *this * __c;
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
+ {
+ *this = *this / __c;
+ return *this;
+ }
+};
+
+template<> class complex<double>;
+template<> class complex<long double>;
+
+template<>
+class complex<float>
+{
+ float __re_;
+ float __im_;
+public:
+ typedef float value_type;
+
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY complex(float __re = 0.0f, float __im = 0.0f)
+ : __re_(__re), __im_(__im) {}
+ explicit /*constexpr*/ complex(const complex<double>& __c);
+ explicit /*constexpr*/ complex(const complex<long double>& __c);
+
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY float real() const {return __re_;}
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY float imag() const {return __im_;}
+
+ _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
+ _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
+
+ _LIBCPP_INLINE_VISIBILITY complex& operator= (float __re) {__re_ = __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator+=(float __re) {__re_ += __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator-=(float __re) {__re_ -= __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
+
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
+ {
+ __re_ = __c.real();
+ __im_ = __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
+ {
+ __re_ += __c.real();
+ __im_ += __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
+ {
+ __re_ -= __c.real();
+ __im_ -= __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
+ {
+ *this = *this * __c;
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
+ {
+ *this = *this / __c;
+ return *this;
+ }
+};
+
+template<>
+class complex<double>
+{
+ double __re_;
+ double __im_;
+public:
+ typedef double value_type;
+
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY complex(double __re = 0.0, double __im = 0.0)
+ : __re_(__re), __im_(__im) {}
+ /*constexpr*/ complex(const complex<float>& __c);
+ explicit /*constexpr*/ complex(const complex<long double>& __c);
+
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY double real() const {return __re_;}
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY double imag() const {return __im_;}
+
+ _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
+ _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
+
+ _LIBCPP_INLINE_VISIBILITY complex& operator= (double __re) {__re_ = __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator+=(double __re) {__re_ += __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator-=(double __re) {__re_ -= __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
+
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
+ {
+ __re_ = __c.real();
+ __im_ = __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
+ {
+ __re_ += __c.real();
+ __im_ += __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
+ {
+ __re_ -= __c.real();
+ __im_ -= __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
+ {
+ *this = *this * __c;
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
+ {
+ *this = *this / __c;
+ return *this;
+ }
+};
+
+template<>
+class complex<long double>
+{
+ long double __re_;
+ long double __im_;
+public:
+ typedef long double value_type;
+
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY complex(long double __re = 0.0L, long double __im = 0.0L)
+ : __re_(__re), __im_(__im) {}
+ /*constexpr*/ complex(const complex<float>& __c);
+ /*constexpr*/ complex(const complex<double>& __c);
+
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY long double real() const {return __re_;}
+ /*constexpr*/ _LIBCPP_INLINE_VISIBILITY long double imag() const {return __im_;}
+
+ _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
+ _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
+
+ _LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re) {__re_ = __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
+ _LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
+
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
+ {
+ __re_ = __c.real();
+ __im_ = __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
+ {
+ __re_ += __c.real();
+ __im_ += __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
+ {
+ __re_ -= __c.real();
+ __im_ -= __c.imag();
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
+ {
+ *this = *this * __c;
+ return *this;
+ }
+ template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
+ {
+ *this = *this / __c;
+ return *this;
+ }
+};
+
+//constexpr
+inline _LIBCPP_INLINE_VISIBILITY
+complex<float>::complex(const complex<double>& __c)
+ : __re_(__c.real()), __im_(__c.imag()) {}
+
+//constexpr
+inline _LIBCPP_INLINE_VISIBILITY
+complex<float>::complex(const complex<long double>& __c)
+ : __re_(__c.real()), __im_(__c.imag()) {}
+
+//constexpr
+inline _LIBCPP_INLINE_VISIBILITY
+complex<double>::complex(const complex<float>& __c)
+ : __re_(__c.real()), __im_(__c.imag()) {}
+
+//constexpr
+inline _LIBCPP_INLINE_VISIBILITY
+complex<double>::complex(const complex<long double>& __c)
+ : __re_(__c.real()), __im_(__c.imag()) {}
+
+//constexpr
+inline _LIBCPP_INLINE_VISIBILITY
+complex<long double>::complex(const complex<float>& __c)
+ : __re_(__c.real()), __im_(__c.imag()) {}
+
+//constexpr
+inline _LIBCPP_INLINE_VISIBILITY
+complex<long double>::complex(const complex<double>& __c)
+ : __re_(__c.real()), __im_(__c.imag()) {}
+
+// 26.3.6 operators:
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+ complex<_Tp> __t(__x);
+ __t += __y;
+ return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator+(const complex<_Tp>& __x, const _Tp& __y)
+{
+ complex<_Tp> __t(__x);
+ __t += __y;
+ return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator+(const _Tp& __x, const complex<_Tp>& __y)
+{
+ complex<_Tp> __t(__y);
+ __t += __x;
+ return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+ complex<_Tp> __t(__x);
+ __t -= __y;
+ return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator-(const complex<_Tp>& __x, const _Tp& __y)
+{
+ complex<_Tp> __t(__x);
+ __t -= __y;
+ return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator-(const _Tp& __x, const complex<_Tp>& __y)
+{
+ complex<_Tp> __t(-__y);
+ __t += __x;
+ return __t;
+}
+
+template<class _Tp>
+complex<_Tp>
+operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
+{
+ _Tp __a = __z.real();
+ _Tp __b = __z.imag();
+ _Tp __c = __w.real();
+ _Tp __d = __w.imag();
+ _Tp __ac = __a * __c;
+ _Tp __bd = __b * __d;
+ _Tp __ad = __a * __d;
+ _Tp __bc = __b * __c;
+ _Tp __x = __ac - __bd;
+ _Tp __y = __ad + __bc;
+ if (isnan(__x) && isnan(__y))
+ {
+ bool __recalc = false;
+ if (isinf(__a) || isinf(__b))
+ {
+ __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
+ __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
+ if (isnan(__c))
+ __c = copysign(_Tp(0), __c);
+ if (isnan(__d))
+ __d = copysign(_Tp(0), __d);
+ __recalc = true;
+ }
+ if (isinf(__c) || isinf(__d))
+ {
+ __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
+ __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
+ if (isnan(__a))
+ __a = copysign(_Tp(0), __a);
+ if (isnan(__b))
+ __b = copysign(_Tp(0), __b);
+ __recalc = true;
+ }
+ if (!__recalc && (isinf(__ac) || isinf(__bd) ||
+ isinf(__ad) || isinf(__bc)))
+ {
+ if (isnan(__a))
+ __a = copysign(_Tp(0), __a);
+ if (isnan(__b))
+ __b = copysign(_Tp(0), __b);
+ if (isnan(__c))
+ __c = copysign(_Tp(0), __c);
+ if (isnan(__d))
+ __d = copysign(_Tp(0), __d);
+ __recalc = true;
+ }
+ if (__recalc)
+ {
+ __x = _Tp(INFINITY) * (__a * __c - __b * __d);
+ __y = _Tp(INFINITY) * (__a * __d + __b * __c);
+ }
+ }
+ return complex<_Tp>(__x, __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator*(const complex<_Tp>& __x, const _Tp& __y)
+{
+ complex<_Tp> __t(__x);
+ __t *= __y;
+ return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator*(const _Tp& __x, const complex<_Tp>& __y)
+{
+ complex<_Tp> __t(__y);
+ __t *= __x;
+ return __t;
+}
+
+template<class _Tp>
+complex<_Tp>
+operator/(const complex<_Tp>& __z, const complex<_Tp>& __w)
+{
+ int __ilogbw = 0;
+ _Tp __a = __z.real();
+ _Tp __b = __z.imag();
+ _Tp __c = __w.real();
+ _Tp __d = __w.imag();
+ _Tp __logbw = logb(fmax(fabs(__c), fabs(__d)));
+ if (isfinite(__logbw))
+ {
+ __ilogbw = static_cast<int>(__logbw);
+ __c = scalbn(__c, -__ilogbw);
+ __d = scalbn(__d, -__ilogbw);
+ }
+ _Tp __denom = __c * __c + __d * __d;
+ _Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
+ _Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
+ if (isnan(__x) && isnan(__y))
+ {
+ if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b)))
+ {
+ __x = copysign(_Tp(INFINITY), __c) * __a;
+ __y = copysign(_Tp(INFINITY), __c) * __b;
+ }
+ else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d))
+ {
+ __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
+ __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
+ __x = _Tp(INFINITY) * (__a * __c + __b * __d);
+ __y = _Tp(INFINITY) * (__b * __c - __a * __d);
+ }
+ else if (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) && isfinite(__b))
+ {
+ __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
+ __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
+ __x = _Tp(0) * (__a * __c + __b * __d);
+ __y = _Tp(0) * (__b * __c - __a * __d);
+ }
+ }
+ return complex<_Tp>(__x, __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator/(const complex<_Tp>& __x, const _Tp& __y)
+{
+ return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator/(const _Tp& __x, const complex<_Tp>& __y)
+{
+ complex<_Tp> __t(__x);
+ __t /= __y;
+ return __t;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator+(const complex<_Tp>& __x)
+{
+ return __x;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+operator-(const complex<_Tp>& __x)
+{
+ return complex<_Tp>(-__x.real(), -__x.imag());
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+bool
+operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+ return __x.real() == __y.real() && __x.imag() == __y.imag();
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+bool
+operator==(const complex<_Tp>& __x, const _Tp& __y)
+{
+ return __x.real() == __y && __x.imag() == 0;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+bool
+operator==(const _Tp& __x, const complex<_Tp>& __y)
+{
+ return __x == __y.real() && 0 == __y.imag();
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+bool
+operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+ return !(__x == __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+bool
+operator!=(const complex<_Tp>& __x, const _Tp& __y)
+{
+ return !(__x == __y);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+bool
+operator!=(const _Tp& __x, const complex<_Tp>& __y)
+{
+ return !(__x == __y);
+}
+
+/*
+ Move to <istream>
+
+template<class T, class charT, class traits>
+basic_istream<charT, traits>&
+operator>>(basic_istream<charT, traits>&, complex<T>&);
+
+ Move to <ostream>
+
+template<class T, class charT, class traits>
+basic_ostream<charT, traits>&
+operator<<(basic_ostream<charT, traits>&, const complex<T>&);
+*/
+
+// 26.3.7 values:
+
+// real
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+real(const complex<_Tp>& __c)
+{
+ return __c.real();
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+long double
+real(long double __re)
+{
+ return __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+double
+real(double __re)
+{
+ return __re;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+ is_integral<_Tp>::value,
+ double
+>::type
+real(_Tp __re)
+{
+ return __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+float
+real(float __re)
+{
+ return __re;
+}
+
+// imag
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+imag(const complex<_Tp>& __c)
+{
+ return __c.imag();
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+long double
+imag(long double __re)
+{
+ return 0;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+double
+imag(double __re)
+{
+ return 0;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+ is_integral<_Tp>::value,
+ double
+>::type
+imag(_Tp __re)
+{
+ return 0;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+float
+imag(float __re)
+{
+ return 0;
+}
+
+// abs
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+abs(const complex<_Tp>& __c)
+{
+ return hypot(__c.real(), __c.imag());
+}
+
+// arg
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+arg(const complex<_Tp>& __c)
+{
+ return atan2(__c.imag(), __c.real());
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+long double
+arg(long double __re)
+{
+ return atan2l(0.L, __re);
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+double
+arg(double __re)
+{
+ return atan2(0., __re);
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+ is_integral<_Tp>::value,
+ double
+>::type
+arg(_Tp __re)
+{
+ return atan2(0., __re);
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+float
+arg(float __re)
+{
+ return atan2f(0.F, __re);
+}
+
+// norm
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+_Tp
+norm(const complex<_Tp>& __c)
+{
+ if (isinf(__c.real()))
+ return abs(__c.real());
+ if (isinf(__c.imag()))
+ return abs(__c.imag());
+ return __c.real() * __c.real() + __c.imag() * __c.imag();
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+long double
+norm(long double __re)
+{
+ return __re * __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+double
+norm(double __re)
+{
+ return __re * __re;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+ is_integral<_Tp>::value,
+ double
+>::type
+norm(_Tp __re)
+{
+ return (double)__re * __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+float
+norm(float __re)
+{
+ return __re * __re;
+}
+
+// conj
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+conj(const complex<_Tp>& __c)
+{
+ return complex<_Tp>(__c.real(), -__c.imag());
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+long double
+conj(long double __re)
+{
+ return __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+double
+conj(double __re)
+{
+ return __re;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+ is_integral<_Tp>::value,
+ double
+>::type
+conj(_Tp __re)
+{
+ return __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+float
+conj(float __re)
+{
+ return __re;
+}
+
+// proj
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+proj(const complex<_Tp>& __c)
+{
+ std::complex<_Tp> __r = __c;
+ if (isinf(__c.real()) || isinf(__c.imag()))
+ __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
+ return __r;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+long double
+proj(long double __re)
+{
+ if (isinf(__re))
+ __re = abs(__re);
+ return __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+double
+proj(double __re)
+{
+ if (isinf(__re))
+ __re = abs(__re);
+ return __re;
+}
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+ is_integral<_Tp>::value,
+ double
+>::type
+proj(_Tp __re)
+{
+ return __re;
+}
+
+inline _LIBCPP_INLINE_VISIBILITY
+float
+proj(float __re)
+{
+ if (isinf(__re))
+ __re = abs(__re);
+ return __re;
+}
+
+// polar
+
+template<class _Tp>
+complex<_Tp>
+polar(const _Tp& __rho, const _Tp& __theta = _Tp(0))
+{
+ if (isnan(__rho) || signbit(__rho))
+ return complex<_Tp>(_Tp(NAN), _Tp(NAN));
+ if (isnan(__theta))
+ {
+ if (isinf(__rho))
+ return complex<_Tp>(__rho, __theta);
+ return complex<_Tp>(__theta, __theta);
+ }
+ if (isinf(__theta))
+ {
+ if (isinf(__rho))
+ return complex<_Tp>(__rho, _Tp(NAN));
+ return complex<_Tp>(_Tp(NAN), _Tp(NAN));
+ }
+ _Tp __x = __rho * cos(__theta);
+ if (isnan(__x))
+ __x = 0;
+ _Tp __y = __rho * sin(__theta);
+ if (isnan(__y))
+ __y = 0;
+ return complex<_Tp>(__x, __y);
+}
+
+// log
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+log(const complex<_Tp>& __x)
+{
+ return complex<_Tp>(log(abs(__x)), arg(__x));
+}
+
+// log10
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+log10(const complex<_Tp>& __x)
+{
+ return log(__x) / log(_Tp(10));
+}
+
+// sqrt
+
+template<class _Tp>
+complex<_Tp>
+sqrt(const complex<_Tp>& __x)
+{
+ if (isinf(__x.imag()))
+ return complex<_Tp>(_Tp(INFINITY), __x.imag());
+ if (isinf(__x.real()))
+ {
+ if (__x.real() > _Tp(0))
+ return complex<_Tp>(__x.real(), isnan(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
+ return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
+ }
+ return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
+}
+
+// exp
+
+template<class _Tp>
+complex<_Tp>
+exp(const complex<_Tp>& __x)
+{
+ _Tp __i = __x.imag();
+ if (isinf(__x.real()))
+ {
+ if (__x.real() < _Tp(0))
+ {
+ if (!isfinite(__i))
+ __i = _Tp(1);
+ }
+ else if (__i == 0 || !isfinite(__i))
+ {
+ if (isinf(__i))
+ __i = _Tp(NAN);
+ return complex<_Tp>(__x.real(), __i);
+ }
+ }
+ else if (isnan(__x.real()) && __x.imag() == 0)
+ return __x;
+ _Tp __e = exp(__x.real());
+ return complex<_Tp>(__e * cos(__i), __e * sin(__i));
+}
+
+// pow
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
+{
+ return exp(__y * log(__x));
+}
+
+template<class _Tp, class _Up>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<typename __promote<_Tp, _Up>::type>
+pow(const complex<_Tp>& __x, const complex<_Up>& __y)
+{
+ typedef complex<typename __promote<_Tp, _Up>::type> result_type;
+ return _STD::pow(result_type(__x), result_type(__y));
+}
+
+template<class _Tp, class _Up>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+ is_arithmetic<_Up>::value,
+ complex<typename __promote<_Tp, _Up>::type>
+>::type
+pow(const complex<_Tp>& __x, const _Up& __y)
+{
+ typedef complex<typename __promote<_Tp, _Up>::type> result_type;
+ return _STD::pow(result_type(__x), result_type(__y));
+}
+
+template<class _Tp, class _Up>
+inline _LIBCPP_INLINE_VISIBILITY
+typename enable_if
+<
+ is_arithmetic<_Tp>::value,
+ complex<typename __promote<_Tp, _Up>::type>
+>::type
+pow(const _Tp& __x, const complex<_Up>& __y)
+{
+ typedef complex<typename __promote<_Tp, _Up>::type> result_type;
+ return _STD::pow(result_type(__x), result_type(__y));
+}
+
+// asinh
+
+template<class _Tp>
+complex<_Tp>
+asinh(const complex<_Tp>& __x)
+{
+ const _Tp __pi(atan2(+0., -0.));
+ if (isinf(__x.real()))
+ {
+ if (isnan(__x.imag()))
+ return __x;
+ if (isinf(__x.imag()))
+ return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
+ return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
+ }
+ if (isnan(__x.real()))
+ {
+ if (isinf(__x.imag()))
+ return complex<_Tp>(__x.imag(), __x.real());
+ if (__x.imag() == 0)
+ return __x;
+ return complex<_Tp>(__x.real(), __x.real());
+ }
+ if (isinf(__x.imag()))
+ return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
+ complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
+ return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
+}
+
+// acosh
+
+template<class _Tp>
+complex<_Tp>
+acosh(const complex<_Tp>& __x)
+{
+ const _Tp __pi(atan2(+0., -0.));
+ if (isinf(__x.real()))
+ {
+ if (isnan(__x.imag()))
+ return complex<_Tp>(abs(__x.real()), __x.imag());
+ if (isinf(__x.imag()))
+ if (__x.real() > 0)
+ return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
+ else
+ return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
+ if (__x.real() < 0)
+ return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
+ return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
+ }
+ if (isnan(__x.real()))
+ {
+ if (isinf(__x.imag()))
+ return complex<_Tp>(abs(__x.imag()), __x.real());
+ return complex<_Tp>(__x.real(), __x.real());
+ }
+ if (isinf(__x.imag()))
+ return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
+ complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
+ return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
+}
+
+// atanh
+
+template<class _Tp>
+complex<_Tp>
+atanh(const complex<_Tp>& __x)
+{
+ const _Tp __pi(atan2(+0., -0.));
+ if (isinf(__x.imag()))
+ {
+ return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
+ }
+ if (isnan(__x.imag()))
+ {
+ if (isinf(__x.real()) || __x.real() == 0)
+ return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
+ return complex<_Tp>(__x.imag(), __x.imag());
+ }
+ if (isnan(__x.real()))
+ {
+ return complex<_Tp>(__x.real(), __x.real());
+ }
+ if (isinf(__x.real()))
+ {
+ return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
+ }
+ if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
+ {
+ return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
+ }
+ complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
+ return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
+}
+
+// sinh
+
+template<class _Tp>
+complex<_Tp>
+sinh(const complex<_Tp>& __x)
+{
+ if (isinf(__x.real()) && !isfinite(__x.imag()))
+ return complex<_Tp>(__x.real(), _Tp(NAN));
+ if (__x.real() == 0 && !isfinite(__x.imag()))
+ return complex<_Tp>(__x.real(), _Tp(NAN));
+ if (__x.imag() == 0 && !isfinite(__x.real()))
+ return __x;
+ return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
+}
+
+// cosh
+
+template<class _Tp>
+complex<_Tp>
+cosh(const complex<_Tp>& __x)
+{
+ if (isinf(__x.real()) && !isfinite(__x.imag()))
+ return complex<_Tp>(abs(__x.real()), _Tp(NAN));
+ if (__x.real() == 0 && !isfinite(__x.imag()))
+ return complex<_Tp>(_Tp(NAN), __x.real());
+ if (__x.real() == 0 && __x.imag() == 0)
+ return complex<_Tp>(_Tp(1), __x.imag());
+ if (__x.imag() == 0 && !isfinite(__x.real()))
+ return complex<_Tp>(abs(__x.real()), __x.imag());
+ return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
+}
+
+// tanh
+
+template<class _Tp>
+complex<_Tp>
+tanh(const complex<_Tp>& __x)
+{
+ if (isinf(__x.real()))
+ {
+ if (!isfinite(__x.imag()))
+ return complex<_Tp>(_Tp(1), _Tp(0));
+ return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
+ }
+ if (isnan(__x.real()) && __x.imag() == 0)
+ return __x;
+ _Tp __2r(_Tp(2) * __x.real());
+ _Tp __2i(_Tp(2) * __x.imag());
+ _Tp __d(cosh(__2r) + cos(__2i));
+ return complex<_Tp>(sinh(__2r)/__d, sin(__2i)/__d);
+}
+
+// asin
+
+template<class _Tp>
+complex<_Tp>
+asin(const complex<_Tp>& __x)
+{
+ complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
+ return complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// acos
+
+template<class _Tp>
+complex<_Tp>
+acos(const complex<_Tp>& __x)
+{
+ const _Tp __pi(atan2(+0., -0.));
+ if (isinf(__x.real()))
+ {
+ if (isnan(__x.imag()))
+ return complex<_Tp>(__x.imag(), __x.real());
+ if (isinf(__x.imag()))
+ {
+ if (__x.real() < _Tp(0))
+ return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
+ return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
+ }
+ if (__x.real() < _Tp(0))
+ return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
+ return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
+ }
+ if (isnan(__x.real()))
+ {
+ if (isinf(__x.imag()))
+ return complex<_Tp>(__x.real(), -__x.imag());
+ return complex<_Tp>(__x.real(), __x.real());
+ }
+ if (isinf(__x.imag()))
+ return complex<_Tp>(__pi/_Tp(2), -__x.imag());
+ if (__x.real() == 0)
+ return complex<_Tp>(__pi/_Tp(2), -__x.imag());
+ complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
+ if (signbit(__x.imag()))
+ return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
+ return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
+}
+
+// atan
+
+template<class _Tp>
+complex<_Tp>
+atan(const complex<_Tp>& __x)
+{
+ complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
+ return complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// sin
+
+template<class _Tp>
+complex<_Tp>
+sin(const complex<_Tp>& __x)
+{
+ complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
+ return complex<_Tp>(__z.imag(), -__z.real());
+}
+
+// cos
+
+template<class _Tp>
+inline _LIBCPP_INLINE_VISIBILITY
+complex<_Tp>
+cos(const complex<_Tp>& __x)
+{
+ return cosh(complex<_Tp>(-__x.imag(), __x.real()));
+}
+
+// tan
+
+template<class _Tp>
+complex<_Tp>
+tan(const complex<_Tp>& __x)
+{
+ complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
+ return complex<_Tp>(__z.imag(), -__z.real());
+}
+
+template<class _Tp, class _CharT, class _Traits>
+basic_istream<_CharT, _Traits>&
+operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
+{
+ if (__is.good())
+ {
+ ws(__is);
+ if (__is.peek() == _CharT('('))
+ {
+ __is.get();
+ _Tp __r;
+ __is >> __r;
+ if (!__is.fail())
+ {
+ ws(__is);
+ _CharT __c = __is.peek();
+ if (__c == _CharT(','))
+ {
+ __is.get();
+ _Tp __i;
+ __is >> __i;
+ if (!__is.fail())
+ {
+ ws(__is);
+ __c = __is.peek();
+ if (__c == _CharT(')'))
+ {
+ __is.get();
+ __x = complex<_Tp>(__r, __i);
+ }
+ else
+ __is.setstate(ios_base::failbit);
+ }
+ else
+ __is.setstate(ios_base::failbit);
+ }
+ else if (__c == _CharT(')'))
+ {
+ __is.get();
+ __x = complex<_Tp>(__r, _Tp(0));
+ }
+ else
+ __is.setstate(ios_base::failbit);
+ }
+ else
+ __is.setstate(ios_base::failbit);
+ }
+ else
+ {
+ _Tp __r;
+ __is >> __r;
+ if (!__is.fail())
+ __x = complex<_Tp>(__r, _Tp(0));
+ else
+ __is.setstate(ios_base::failbit);
+ }
+ }
+ else
+ __is.setstate(ios_base::failbit);
+ return __is;
+}
+
+template<class _Tp, class _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();
+}
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_COMPLEX