diff options
Diffstat (limited to 'include/complex')
| -rw-r--r-- | include/complex | 1516 |
1 files changed, 1516 insertions, 0 deletions
diff --git a/include/complex b/include/complex new file mode 100644 index 000000000000..e7f63eac3a1e --- /dev/null +++ b/include/complex @@ -0,0 +1,1516 @@ +// -*- C++ -*- +//===--------------------------- complex ----------------------------------===// +// +// The LLVM Compiler Infrastructure +// +// This file is dual licensed under the MIT and the University of Illinois Open +// Source Licenses. 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>&); + complex<long double> conj(long double); + complex<double> conj(double); +template<Integral T> complex<double> conj(T); + complex<float> conj(float); + +template<class T> complex<T> proj(const complex<T>&); + complex<long double> proj(long double); + complex<double> proj(double); +template<Integral T> complex<double> proj(T); + complex<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 + +#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) +#pragma GCC system_header +#endif + +_LIBCPP_BEGIN_NAMESPACE_STD + +template<class _Tp> class _LIBCPP_VISIBLE 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 _LIBCPP_VISIBLE 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 _LIBCPP_VISIBLE complex<double>; +template<> class _LIBCPP_VISIBLE complex<long double>; + +template<> +class _LIBCPP_VISIBLE 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 _LIBCPP_VISIBLE 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 _LIBCPP_VISIBLE 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); +} + +// 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 +complex<long double> +conj(long double __re) +{ + return complex<long double>(__re); +} + +inline _LIBCPP_INLINE_VISIBILITY +complex<double> +conj(double __re) +{ + return complex<double>(__re); +} + +template<class _Tp> +inline _LIBCPP_INLINE_VISIBILITY +typename enable_if +< + is_integral<_Tp>::value, + complex<double> +>::type +conj(_Tp __re) +{ + return complex<double>(__re); +} + +inline _LIBCPP_INLINE_VISIBILITY +complex<float> +conj(float __re) +{ + return complex<float>(__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 +complex<long double> +proj(long double __re) +{ + if (isinf(__re)) + __re = abs(__re); + return complex<long double>(__re); +} + +inline _LIBCPP_INLINE_VISIBILITY +complex<double> +proj(double __re) +{ + if (isinf(__re)) + __re = abs(__re); + return complex<double>(__re); +} + +template<class _Tp> +inline _LIBCPP_INLINE_VISIBILITY +typename enable_if +< + is_integral<_Tp>::value, + complex<double> +>::type +proj(_Tp __re) +{ + return complex<double>(__re); +} + +inline _LIBCPP_INLINE_VISIBILITY +complex<float> +proj(float __re) +{ + if (isinf(__re)) + __re = abs(__re); + return complex<float>(__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 _VSTD::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 _VSTD::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 _VSTD::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 |