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| 1 | 13 | up20180614 | // -*- C++ -*- |
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| 2 | //===--------------------------- complex ----------------------------------===// |
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| 3 | // |
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| 4 | // The LLVM Compiler Infrastructure |
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| 5 | // |
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| 6 | // This file is dual licensed under the MIT and the University of Illinois Open |
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| 7 | // Source Licenses. See LICENSE.TXT for details. |
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| 8 | // |
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| 9 | //===----------------------------------------------------------------------===// |
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| 10 | |||
| 11 | #ifndef _LIBCPP_COMPLEX |
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| 12 | #define _LIBCPP_COMPLEX |
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| 13 | |||
| 14 | /* |
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| 15 | complex synopsis |
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| 16 | |||
| 17 | namespace std |
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| 18 | {
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| 19 | |||
| 20 | template<class T> |
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| 21 | class complex |
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| 22 | {
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| 23 | public: |
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| 24 | typedef T value_type; |
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| 25 | |||
| 26 | complex(const T& re = T(), const T& im = T()); // constexpr in C++14 |
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| 27 | complex(const complex&); // constexpr in C++14 |
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| 28 | template<class X> complex(const complex<X>&); // constexpr in C++14 |
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| 29 | |||
| 30 | T real() const; // constexpr in C++14 |
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| 31 | T imag() const; // constexpr in C++14 |
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| 32 | |||
| 33 | void real(T); |
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| 34 | void imag(T); |
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| 35 | |||
| 36 | complex<T>& operator= (const T&); |
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| 37 | complex<T>& operator+=(const T&); |
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| 38 | complex<T>& operator-=(const T&); |
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| 39 | complex<T>& operator*=(const T&); |
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| 40 | complex<T>& operator/=(const T&); |
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| 41 | |||
| 42 | complex& operator=(const complex&); |
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| 43 | template<class X> complex<T>& operator= (const complex<X>&); |
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| 44 | template<class X> complex<T>& operator+=(const complex<X>&); |
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| 45 | template<class X> complex<T>& operator-=(const complex<X>&); |
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| 46 | template<class X> complex<T>& operator*=(const complex<X>&); |
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| 47 | template<class X> complex<T>& operator/=(const complex<X>&); |
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| 48 | }; |
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| 49 | |||
| 50 | template<> |
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| 51 | class complex<float> |
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| 52 | {
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| 53 | public: |
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| 54 | typedef float value_type; |
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| 55 | |||
| 56 | constexpr complex(float re = 0.0f, float im = 0.0f); |
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| 57 | explicit constexpr complex(const complex<double>&); |
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| 58 | explicit constexpr complex(const complex<long double>&); |
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| 59 | |||
| 60 | constexpr float real() const; |
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| 61 | void real(float); |
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| 62 | constexpr float imag() const; |
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| 63 | void imag(float); |
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| 64 | |||
| 65 | complex<float>& operator= (float); |
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| 66 | complex<float>& operator+=(float); |
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| 67 | complex<float>& operator-=(float); |
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| 68 | complex<float>& operator*=(float); |
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| 69 | complex<float>& operator/=(float); |
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| 70 | |||
| 71 | complex<float>& operator=(const complex<float>&); |
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| 72 | template<class X> complex<float>& operator= (const complex<X>&); |
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| 73 | template<class X> complex<float>& operator+=(const complex<X>&); |
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| 74 | template<class X> complex<float>& operator-=(const complex<X>&); |
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| 75 | template<class X> complex<float>& operator*=(const complex<X>&); |
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| 76 | template<class X> complex<float>& operator/=(const complex<X>&); |
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| 77 | }; |
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| 78 | |||
| 79 | template<> |
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| 80 | class complex<double> |
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| 81 | {
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| 82 | public: |
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| 83 | typedef double value_type; |
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| 84 | |||
| 85 | constexpr complex(double re = 0.0, double im = 0.0); |
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| 86 | constexpr complex(const complex<float>&); |
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| 87 | explicit constexpr complex(const complex<long double>&); |
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| 88 | |||
| 89 | constexpr double real() const; |
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| 90 | void real(double); |
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| 91 | constexpr double imag() const; |
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| 92 | void imag(double); |
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| 93 | |||
| 94 | complex<double>& operator= (double); |
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| 95 | complex<double>& operator+=(double); |
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| 96 | complex<double>& operator-=(double); |
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| 97 | complex<double>& operator*=(double); |
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| 98 | complex<double>& operator/=(double); |
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| 99 | complex<double>& operator=(const complex<double>&); |
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| 100 | |||
| 101 | template<class X> complex<double>& operator= (const complex<X>&); |
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| 102 | template<class X> complex<double>& operator+=(const complex<X>&); |
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| 103 | template<class X> complex<double>& operator-=(const complex<X>&); |
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| 104 | template<class X> complex<double>& operator*=(const complex<X>&); |
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| 105 | template<class X> complex<double>& operator/=(const complex<X>&); |
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| 106 | }; |
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| 107 | |||
| 108 | template<> |
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| 109 | class complex<long double> |
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| 110 | {
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| 111 | public: |
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| 112 | typedef long double value_type; |
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| 113 | |||
| 114 | constexpr complex(long double re = 0.0L, long double im = 0.0L); |
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| 115 | constexpr complex(const complex<float>&); |
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| 116 | constexpr complex(const complex<double>&); |
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| 117 | |||
| 118 | constexpr long double real() const; |
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| 119 | void real(long double); |
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| 120 | constexpr long double imag() const; |
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| 121 | void imag(long double); |
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| 122 | |||
| 123 | complex<long double>& operator=(const complex<long double>&); |
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| 124 | complex<long double>& operator= (long double); |
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| 125 | complex<long double>& operator+=(long double); |
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| 126 | complex<long double>& operator-=(long double); |
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| 127 | complex<long double>& operator*=(long double); |
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| 128 | complex<long double>& operator/=(long double); |
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| 129 | |||
| 130 | template<class X> complex<long double>& operator= (const complex<X>&); |
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| 131 | template<class X> complex<long double>& operator+=(const complex<X>&); |
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| 132 | template<class X> complex<long double>& operator-=(const complex<X>&); |
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| 133 | template<class X> complex<long double>& operator*=(const complex<X>&); |
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| 134 | template<class X> complex<long double>& operator/=(const complex<X>&); |
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| 135 | }; |
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| 136 | |||
| 137 | // 26.3.6 operators: |
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| 138 | template<class T> complex<T> operator+(const complex<T>&, const complex<T>&); |
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| 139 | template<class T> complex<T> operator+(const complex<T>&, const T&); |
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| 140 | template<class T> complex<T> operator+(const T&, const complex<T>&); |
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| 141 | template<class T> complex<T> operator-(const complex<T>&, const complex<T>&); |
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| 142 | template<class T> complex<T> operator-(const complex<T>&, const T&); |
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| 143 | template<class T> complex<T> operator-(const T&, const complex<T>&); |
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| 144 | template<class T> complex<T> operator*(const complex<T>&, const complex<T>&); |
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| 145 | template<class T> complex<T> operator*(const complex<T>&, const T&); |
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| 146 | template<class T> complex<T> operator*(const T&, const complex<T>&); |
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| 147 | template<class T> complex<T> operator/(const complex<T>&, const complex<T>&); |
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| 148 | template<class T> complex<T> operator/(const complex<T>&, const T&); |
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| 149 | template<class T> complex<T> operator/(const T&, const complex<T>&); |
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| 150 | template<class T> complex<T> operator+(const complex<T>&); |
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| 151 | template<class T> complex<T> operator-(const complex<T>&); |
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| 152 | template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14 |
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| 153 | template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14 |
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| 154 | template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14 |
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| 155 | template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14 |
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| 156 | template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14 |
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| 157 | template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14 |
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| 158 | |||
| 159 | template<class T, class charT, class traits> |
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| 160 | basic_istream<charT, traits>& |
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| 161 | operator>>(basic_istream<charT, traits>&, complex<T>&); |
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| 162 | template<class T, class charT, class traits> |
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| 163 | basic_ostream<charT, traits>& |
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| 164 | operator<<(basic_ostream<charT, traits>&, const complex<T>&); |
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| 165 | |||
| 166 | // 26.3.7 values: |
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| 167 | |||
| 168 | template<class T> T real(const complex<T>&); // constexpr in C++14 |
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| 169 | long double real(long double); // constexpr in C++14 |
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| 170 | double real(double); // constexpr in C++14 |
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| 171 | template<Integral T> double real(T); // constexpr in C++14 |
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| 172 | float real(float); // constexpr in C++14 |
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| 173 | |||
| 174 | template<class T> T imag(const complex<T>&); // constexpr in C++14 |
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| 175 | long double imag(long double); // constexpr in C++14 |
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| 176 | double imag(double); // constexpr in C++14 |
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| 177 | template<Integral T> double imag(T); // constexpr in C++14 |
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| 178 | float imag(float); // constexpr in C++14 |
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| 179 | |||
| 180 | template<class T> T abs(const complex<T>&); |
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| 181 | |||
| 182 | template<class T> T arg(const complex<T>&); |
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| 183 | long double arg(long double); |
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| 184 | double arg(double); |
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| 185 | template<Integral T> double arg(T); |
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| 186 | float arg(float); |
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| 187 | |||
| 188 | template<class T> T norm(const complex<T>&); |
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| 189 | long double norm(long double); |
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| 190 | double norm(double); |
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| 191 | template<Integral T> double norm(T); |
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| 192 | float norm(float); |
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| 193 | |||
| 194 | template<class T> complex<T> conj(const complex<T>&); |
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| 195 | complex<long double> conj(long double); |
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| 196 | complex<double> conj(double); |
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| 197 | template<Integral T> complex<double> conj(T); |
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| 198 | complex<float> conj(float); |
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| 199 | |||
| 200 | template<class T> complex<T> proj(const complex<T>&); |
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| 201 | complex<long double> proj(long double); |
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| 202 | complex<double> proj(double); |
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| 203 | template<Integral T> complex<double> proj(T); |
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| 204 | complex<float> proj(float); |
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| 205 | |||
| 206 | template<class T> complex<T> polar(const T&, const T& = 0); |
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| 207 | |||
| 208 | // 26.3.8 transcendentals: |
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| 209 | template<class T> complex<T> acos(const complex<T>&); |
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| 210 | template<class T> complex<T> asin(const complex<T>&); |
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| 211 | template<class T> complex<T> atan(const complex<T>&); |
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| 212 | template<class T> complex<T> acosh(const complex<T>&); |
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| 213 | template<class T> complex<T> asinh(const complex<T>&); |
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| 214 | template<class T> complex<T> atanh(const complex<T>&); |
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| 215 | template<class T> complex<T> cos (const complex<T>&); |
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| 216 | template<class T> complex<T> cosh (const complex<T>&); |
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| 217 | template<class T> complex<T> exp (const complex<T>&); |
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| 218 | template<class T> complex<T> log (const complex<T>&); |
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| 219 | template<class T> complex<T> log10(const complex<T>&); |
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| 220 | |||
| 221 | template<class T> complex<T> pow(const complex<T>&, const T&); |
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| 222 | template<class T> complex<T> pow(const complex<T>&, const complex<T>&); |
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| 223 | template<class T> complex<T> pow(const T&, const complex<T>&); |
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| 224 | |||
| 225 | template<class T> complex<T> sin (const complex<T>&); |
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| 226 | template<class T> complex<T> sinh (const complex<T>&); |
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| 227 | template<class T> complex<T> sqrt (const complex<T>&); |
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| 228 | template<class T> complex<T> tan (const complex<T>&); |
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| 229 | template<class T> complex<T> tanh (const complex<T>&); |
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| 230 | |||
| 231 | template<class T, class charT, class traits> |
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| 232 | basic_istream<charT, traits>& |
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| 233 | operator>>(basic_istream<charT, traits>& is, complex<T>& x); |
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| 234 | |||
| 235 | template<class T, class charT, class traits> |
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| 236 | basic_ostream<charT, traits>& |
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| 237 | operator<<(basic_ostream<charT, traits>& o, const complex<T>& x); |
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| 238 | |||
| 239 | } // std |
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| 240 | |||
| 241 | */ |
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| 242 | |||
| 243 | #include <__config> |
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| 244 | #include <type_traits> |
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| 245 | #include <stdexcept> |
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| 246 | #include <cmath> |
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| 247 | #include <sstream> |
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| 248 | #if defined(_LIBCPP_NO_EXCEPTIONS) |
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| 249 | #include <cassert> |
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| 250 | #endif |
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| 251 | |||
| 252 | #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) |
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| 253 | #pragma GCC system_header |
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| 254 | #endif |
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| 255 | |||
| 256 | _LIBCPP_BEGIN_NAMESPACE_STD |
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| 257 | |||
| 258 | template<class _Tp> class _LIBCPP_TYPE_VIS_ONLY complex; |
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| 259 | |||
| 260 | template<class _Tp> complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w); |
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| 261 | template<class _Tp> complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y); |
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| 262 | |||
| 263 | template<class _Tp> |
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| 264 | class _LIBCPP_TYPE_VIS_ONLY complex |
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| 265 | {
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| 266 | public: |
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| 267 | typedef _Tp value_type; |
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| 268 | private: |
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| 269 | value_type __re_; |
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| 270 | value_type __im_; |
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| 271 | public: |
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| 272 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
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| 273 | complex(const value_type& __re = value_type(), const value_type& __im = value_type()) |
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| 274 | : __re_(__re), __im_(__im) {}
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| 275 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
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| 276 | complex(const complex<_Xp>& __c) |
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| 277 | : __re_(__c.real()), __im_(__c.imag()) {}
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| 278 | |||
| 279 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type real() const {return __re_;}
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| 280 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type imag() const {return __im_;}
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| 281 | |||
| 282 | _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
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| 283 | _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
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| 284 | |||
| 285 | _LIBCPP_INLINE_VISIBILITY complex& operator= (const value_type& __re) |
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| 286 | {__re_ = __re; __im_ = value_type(); return *this;}
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| 287 | _LIBCPP_INLINE_VISIBILITY complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
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| 288 | _LIBCPP_INLINE_VISIBILITY complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
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| 289 | _LIBCPP_INLINE_VISIBILITY complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
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| 290 | _LIBCPP_INLINE_VISIBILITY complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
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| 291 | |||
| 292 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c) |
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| 293 | {
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| 294 | __re_ = __c.real(); |
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| 295 | __im_ = __c.imag(); |
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| 296 | return *this; |
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| 297 | } |
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| 298 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c) |
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| 299 | {
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| 300 | __re_ += __c.real(); |
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| 301 | __im_ += __c.imag(); |
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| 302 | return *this; |
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| 303 | } |
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| 304 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c) |
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| 305 | {
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| 306 | __re_ -= __c.real(); |
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| 307 | __im_ -= __c.imag(); |
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| 308 | return *this; |
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| 309 | } |
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| 310 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c) |
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| 311 | {
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| 312 | *this = *this * complex(__c.real(), __c.imag()); |
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| 313 | return *this; |
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| 314 | } |
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| 315 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c) |
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| 316 | {
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| 317 | *this = *this / complex(__c.real(), __c.imag()); |
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| 318 | return *this; |
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| 319 | } |
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| 320 | }; |
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| 321 | |||
| 322 | template<> class _LIBCPP_TYPE_VIS_ONLY complex<double>; |
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| 323 | template<> class _LIBCPP_TYPE_VIS_ONLY complex<long double>; |
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| 324 | |||
| 325 | template<> |
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| 326 | class _LIBCPP_TYPE_VIS_ONLY complex<float> |
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| 327 | {
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| 328 | float __re_; |
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| 329 | float __im_; |
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| 330 | public: |
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| 331 | typedef float value_type; |
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| 332 | |||
| 333 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f) |
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| 334 | : __re_(__re), __im_(__im) {}
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| 335 | explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c); |
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| 336 | explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c); |
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| 337 | |||
| 338 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;}
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| 339 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;}
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| 340 | |||
| 341 | _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
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| 342 | _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
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| 343 | |||
| 344 | _LIBCPP_INLINE_VISIBILITY complex& operator= (float __re) |
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| 345 | {__re_ = __re; __im_ = value_type(); return *this;}
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| 346 | _LIBCPP_INLINE_VISIBILITY complex& operator+=(float __re) {__re_ += __re; return *this;}
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| 347 | _LIBCPP_INLINE_VISIBILITY complex& operator-=(float __re) {__re_ -= __re; return *this;}
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| 348 | _LIBCPP_INLINE_VISIBILITY complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
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| 349 | _LIBCPP_INLINE_VISIBILITY complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
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| 350 | |||
| 351 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c) |
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| 352 | {
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| 353 | __re_ = __c.real(); |
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| 354 | __im_ = __c.imag(); |
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| 355 | return *this; |
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| 356 | } |
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| 357 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c) |
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| 358 | {
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| 359 | __re_ += __c.real(); |
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| 360 | __im_ += __c.imag(); |
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| 361 | return *this; |
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| 362 | } |
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| 363 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c) |
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| 364 | {
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| 365 | __re_ -= __c.real(); |
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| 366 | __im_ -= __c.imag(); |
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| 367 | return *this; |
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| 368 | } |
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| 369 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c) |
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| 370 | {
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| 371 | *this = *this * complex(__c.real(), __c.imag()); |
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| 372 | return *this; |
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| 373 | } |
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| 374 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c) |
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| 375 | {
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| 376 | *this = *this / complex(__c.real(), __c.imag()); |
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| 377 | return *this; |
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| 378 | } |
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| 379 | }; |
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| 380 | |||
| 381 | template<> |
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| 382 | class _LIBCPP_TYPE_VIS_ONLY complex<double> |
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| 383 | {
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| 384 | double __re_; |
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| 385 | double __im_; |
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| 386 | public: |
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| 387 | typedef double value_type; |
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| 388 | |||
| 389 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0) |
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| 390 | : __re_(__re), __im_(__im) {}
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| 391 | _LIBCPP_CONSTEXPR complex(const complex<float>& __c); |
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| 392 | explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c); |
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| 393 | |||
| 394 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;}
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| 395 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;}
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| 396 | |||
| 397 | _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
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| 398 | _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
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| 399 | |||
| 400 | _LIBCPP_INLINE_VISIBILITY complex& operator= (double __re) |
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| 401 | {__re_ = __re; __im_ = value_type(); return *this;}
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| 402 | _LIBCPP_INLINE_VISIBILITY complex& operator+=(double __re) {__re_ += __re; return *this;}
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| 403 | _LIBCPP_INLINE_VISIBILITY complex& operator-=(double __re) {__re_ -= __re; return *this;}
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| 404 | _LIBCPP_INLINE_VISIBILITY complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
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| 405 | _LIBCPP_INLINE_VISIBILITY complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
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| 406 | |||
| 407 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c) |
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| 408 | {
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| 409 | __re_ = __c.real(); |
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| 410 | __im_ = __c.imag(); |
||
| 411 | return *this; |
||
| 412 | } |
||
| 413 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c) |
||
| 414 | {
|
||
| 415 | __re_ += __c.real(); |
||
| 416 | __im_ += __c.imag(); |
||
| 417 | return *this; |
||
| 418 | } |
||
| 419 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c) |
||
| 420 | {
|
||
| 421 | __re_ -= __c.real(); |
||
| 422 | __im_ -= __c.imag(); |
||
| 423 | return *this; |
||
| 424 | } |
||
| 425 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c) |
||
| 426 | {
|
||
| 427 | *this = *this * complex(__c.real(), __c.imag()); |
||
| 428 | return *this; |
||
| 429 | } |
||
| 430 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c) |
||
| 431 | {
|
||
| 432 | *this = *this / complex(__c.real(), __c.imag()); |
||
| 433 | return *this; |
||
| 434 | } |
||
| 435 | }; |
||
| 436 | |||
| 437 | template<> |
||
| 438 | class _LIBCPP_TYPE_VIS_ONLY complex<long double> |
||
| 439 | {
|
||
| 440 | long double __re_; |
||
| 441 | long double __im_; |
||
| 442 | public: |
||
| 443 | typedef long double value_type; |
||
| 444 | |||
| 445 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L) |
||
| 446 | : __re_(__re), __im_(__im) {}
|
||
| 447 | _LIBCPP_CONSTEXPR complex(const complex<float>& __c); |
||
| 448 | _LIBCPP_CONSTEXPR complex(const complex<double>& __c); |
||
| 449 | |||
| 450 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
|
||
| 451 | _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
|
||
| 452 | |||
| 453 | _LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
|
||
| 454 | _LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
|
||
| 455 | |||
| 456 | _LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re) |
||
| 457 | {__re_ = __re; __im_ = value_type(); return *this;}
|
||
| 458 | _LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
|
||
| 459 | _LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
|
||
| 460 | _LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
|
||
| 461 | _LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
|
||
| 462 | |||
| 463 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c) |
||
| 464 | {
|
||
| 465 | __re_ = __c.real(); |
||
| 466 | __im_ = __c.imag(); |
||
| 467 | return *this; |
||
| 468 | } |
||
| 469 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c) |
||
| 470 | {
|
||
| 471 | __re_ += __c.real(); |
||
| 472 | __im_ += __c.imag(); |
||
| 473 | return *this; |
||
| 474 | } |
||
| 475 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c) |
||
| 476 | {
|
||
| 477 | __re_ -= __c.real(); |
||
| 478 | __im_ -= __c.imag(); |
||
| 479 | return *this; |
||
| 480 | } |
||
| 481 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c) |
||
| 482 | {
|
||
| 483 | *this = *this * complex(__c.real(), __c.imag()); |
||
| 484 | return *this; |
||
| 485 | } |
||
| 486 | template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c) |
||
| 487 | {
|
||
| 488 | *this = *this / complex(__c.real(), __c.imag()); |
||
| 489 | return *this; |
||
| 490 | } |
||
| 491 | }; |
||
| 492 | |||
| 493 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 494 | _LIBCPP_CONSTEXPR |
||
| 495 | complex<float>::complex(const complex<double>& __c) |
||
| 496 | : __re_(__c.real()), __im_(__c.imag()) {}
|
||
| 497 | |||
| 498 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 499 | _LIBCPP_CONSTEXPR |
||
| 500 | complex<float>::complex(const complex<long double>& __c) |
||
| 501 | : __re_(__c.real()), __im_(__c.imag()) {}
|
||
| 502 | |||
| 503 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 504 | _LIBCPP_CONSTEXPR |
||
| 505 | complex<double>::complex(const complex<float>& __c) |
||
| 506 | : __re_(__c.real()), __im_(__c.imag()) {}
|
||
| 507 | |||
| 508 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 509 | _LIBCPP_CONSTEXPR |
||
| 510 | complex<double>::complex(const complex<long double>& __c) |
||
| 511 | : __re_(__c.real()), __im_(__c.imag()) {}
|
||
| 512 | |||
| 513 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 514 | _LIBCPP_CONSTEXPR |
||
| 515 | complex<long double>::complex(const complex<float>& __c) |
||
| 516 | : __re_(__c.real()), __im_(__c.imag()) {}
|
||
| 517 | |||
| 518 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 519 | _LIBCPP_CONSTEXPR |
||
| 520 | complex<long double>::complex(const complex<double>& __c) |
||
| 521 | : __re_(__c.real()), __im_(__c.imag()) {}
|
||
| 522 | |||
| 523 | // 26.3.6 operators: |
||
| 524 | |||
| 525 | template<class _Tp> |
||
| 526 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 527 | complex<_Tp> |
||
| 528 | operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) |
||
| 529 | {
|
||
| 530 | complex<_Tp> __t(__x); |
||
| 531 | __t += __y; |
||
| 532 | return __t; |
||
| 533 | } |
||
| 534 | |||
| 535 | template<class _Tp> |
||
| 536 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 537 | complex<_Tp> |
||
| 538 | operator+(const complex<_Tp>& __x, const _Tp& __y) |
||
| 539 | {
|
||
| 540 | complex<_Tp> __t(__x); |
||
| 541 | __t += __y; |
||
| 542 | return __t; |
||
| 543 | } |
||
| 544 | |||
| 545 | template<class _Tp> |
||
| 546 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 547 | complex<_Tp> |
||
| 548 | operator+(const _Tp& __x, const complex<_Tp>& __y) |
||
| 549 | {
|
||
| 550 | complex<_Tp> __t(__y); |
||
| 551 | __t += __x; |
||
| 552 | return __t; |
||
| 553 | } |
||
| 554 | |||
| 555 | template<class _Tp> |
||
| 556 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 557 | complex<_Tp> |
||
| 558 | operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) |
||
| 559 | {
|
||
| 560 | complex<_Tp> __t(__x); |
||
| 561 | __t -= __y; |
||
| 562 | return __t; |
||
| 563 | } |
||
| 564 | |||
| 565 | template<class _Tp> |
||
| 566 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 567 | complex<_Tp> |
||
| 568 | operator-(const complex<_Tp>& __x, const _Tp& __y) |
||
| 569 | {
|
||
| 570 | complex<_Tp> __t(__x); |
||
| 571 | __t -= __y; |
||
| 572 | return __t; |
||
| 573 | } |
||
| 574 | |||
| 575 | template<class _Tp> |
||
| 576 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 577 | complex<_Tp> |
||
| 578 | operator-(const _Tp& __x, const complex<_Tp>& __y) |
||
| 579 | {
|
||
| 580 | complex<_Tp> __t(-__y); |
||
| 581 | __t += __x; |
||
| 582 | return __t; |
||
| 583 | } |
||
| 584 | |||
| 585 | template<class _Tp> |
||
| 586 | complex<_Tp> |
||
| 587 | operator*(const complex<_Tp>& __z, const complex<_Tp>& __w) |
||
| 588 | {
|
||
| 589 | _Tp __a = __z.real(); |
||
| 590 | _Tp __b = __z.imag(); |
||
| 591 | _Tp __c = __w.real(); |
||
| 592 | _Tp __d = __w.imag(); |
||
| 593 | _Tp __ac = __a * __c; |
||
| 594 | _Tp __bd = __b * __d; |
||
| 595 | _Tp __ad = __a * __d; |
||
| 596 | _Tp __bc = __b * __c; |
||
| 597 | _Tp __x = __ac - __bd; |
||
| 598 | _Tp __y = __ad + __bc; |
||
| 599 | if (isnan(__x) && isnan(__y)) |
||
| 600 | {
|
||
| 601 | bool __recalc = false; |
||
| 602 | if (isinf(__a) || isinf(__b)) |
||
| 603 | {
|
||
| 604 | __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a); |
||
| 605 | __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b); |
||
| 606 | if (isnan(__c)) |
||
| 607 | __c = copysign(_Tp(0), __c); |
||
| 608 | if (isnan(__d)) |
||
| 609 | __d = copysign(_Tp(0), __d); |
||
| 610 | __recalc = true; |
||
| 611 | } |
||
| 612 | if (isinf(__c) || isinf(__d)) |
||
| 613 | {
|
||
| 614 | __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c); |
||
| 615 | __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d); |
||
| 616 | if (isnan(__a)) |
||
| 617 | __a = copysign(_Tp(0), __a); |
||
| 618 | if (isnan(__b)) |
||
| 619 | __b = copysign(_Tp(0), __b); |
||
| 620 | __recalc = true; |
||
| 621 | } |
||
| 622 | if (!__recalc && (isinf(__ac) || isinf(__bd) || |
||
| 623 | isinf(__ad) || isinf(__bc))) |
||
| 624 | {
|
||
| 625 | if (isnan(__a)) |
||
| 626 | __a = copysign(_Tp(0), __a); |
||
| 627 | if (isnan(__b)) |
||
| 628 | __b = copysign(_Tp(0), __b); |
||
| 629 | if (isnan(__c)) |
||
| 630 | __c = copysign(_Tp(0), __c); |
||
| 631 | if (isnan(__d)) |
||
| 632 | __d = copysign(_Tp(0), __d); |
||
| 633 | __recalc = true; |
||
| 634 | } |
||
| 635 | if (__recalc) |
||
| 636 | {
|
||
| 637 | __x = _Tp(INFINITY) * (__a * __c - __b * __d); |
||
| 638 | __y = _Tp(INFINITY) * (__a * __d + __b * __c); |
||
| 639 | } |
||
| 640 | } |
||
| 641 | return complex<_Tp>(__x, __y); |
||
| 642 | } |
||
| 643 | |||
| 644 | template<class _Tp> |
||
| 645 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 646 | complex<_Tp> |
||
| 647 | operator*(const complex<_Tp>& __x, const _Tp& __y) |
||
| 648 | {
|
||
| 649 | complex<_Tp> __t(__x); |
||
| 650 | __t *= __y; |
||
| 651 | return __t; |
||
| 652 | } |
||
| 653 | |||
| 654 | template<class _Tp> |
||
| 655 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 656 | complex<_Tp> |
||
| 657 | operator*(const _Tp& __x, const complex<_Tp>& __y) |
||
| 658 | {
|
||
| 659 | complex<_Tp> __t(__y); |
||
| 660 | __t *= __x; |
||
| 661 | return __t; |
||
| 662 | } |
||
| 663 | |||
| 664 | template<class _Tp> |
||
| 665 | complex<_Tp> |
||
| 666 | operator/(const complex<_Tp>& __z, const complex<_Tp>& __w) |
||
| 667 | {
|
||
| 668 | int __ilogbw = 0; |
||
| 669 | _Tp __a = __z.real(); |
||
| 670 | _Tp __b = __z.imag(); |
||
| 671 | _Tp __c = __w.real(); |
||
| 672 | _Tp __d = __w.imag(); |
||
| 673 | _Tp __logbw = logb(fmax(fabs(__c), fabs(__d))); |
||
| 674 | if (isfinite(__logbw)) |
||
| 675 | {
|
||
| 676 | __ilogbw = static_cast<int>(__logbw); |
||
| 677 | __c = scalbn(__c, -__ilogbw); |
||
| 678 | __d = scalbn(__d, -__ilogbw); |
||
| 679 | } |
||
| 680 | _Tp __denom = __c * __c + __d * __d; |
||
| 681 | _Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw); |
||
| 682 | _Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw); |
||
| 683 | if (isnan(__x) && isnan(__y)) |
||
| 684 | {
|
||
| 685 | if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b))) |
||
| 686 | {
|
||
| 687 | __x = copysign(_Tp(INFINITY), __c) * __a; |
||
| 688 | __y = copysign(_Tp(INFINITY), __c) * __b; |
||
| 689 | } |
||
| 690 | else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d)) |
||
| 691 | {
|
||
| 692 | __a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a); |
||
| 693 | __b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b); |
||
| 694 | __x = _Tp(INFINITY) * (__a * __c + __b * __d); |
||
| 695 | __y = _Tp(INFINITY) * (__b * __c - __a * __d); |
||
| 696 | } |
||
| 697 | else if (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) && isfinite(__b)) |
||
| 698 | {
|
||
| 699 | __c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c); |
||
| 700 | __d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d); |
||
| 701 | __x = _Tp(0) * (__a * __c + __b * __d); |
||
| 702 | __y = _Tp(0) * (__b * __c - __a * __d); |
||
| 703 | } |
||
| 704 | } |
||
| 705 | return complex<_Tp>(__x, __y); |
||
| 706 | } |
||
| 707 | |||
| 708 | template<class _Tp> |
||
| 709 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 710 | complex<_Tp> |
||
| 711 | operator/(const complex<_Tp>& __x, const _Tp& __y) |
||
| 712 | {
|
||
| 713 | return complex<_Tp>(__x.real() / __y, __x.imag() / __y); |
||
| 714 | } |
||
| 715 | |||
| 716 | template<class _Tp> |
||
| 717 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 718 | complex<_Tp> |
||
| 719 | operator/(const _Tp& __x, const complex<_Tp>& __y) |
||
| 720 | {
|
||
| 721 | complex<_Tp> __t(__x); |
||
| 722 | __t /= __y; |
||
| 723 | return __t; |
||
| 724 | } |
||
| 725 | |||
| 726 | template<class _Tp> |
||
| 727 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 728 | complex<_Tp> |
||
| 729 | operator+(const complex<_Tp>& __x) |
||
| 730 | {
|
||
| 731 | return __x; |
||
| 732 | } |
||
| 733 | |||
| 734 | template<class _Tp> |
||
| 735 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 736 | complex<_Tp> |
||
| 737 | operator-(const complex<_Tp>& __x) |
||
| 738 | {
|
||
| 739 | return complex<_Tp>(-__x.real(), -__x.imag()); |
||
| 740 | } |
||
| 741 | |||
| 742 | template<class _Tp> |
||
| 743 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 744 | bool |
||
| 745 | operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) |
||
| 746 | {
|
||
| 747 | return __x.real() == __y.real() && __x.imag() == __y.imag(); |
||
| 748 | } |
||
| 749 | |||
| 750 | template<class _Tp> |
||
| 751 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 752 | bool |
||
| 753 | operator==(const complex<_Tp>& __x, const _Tp& __y) |
||
| 754 | {
|
||
| 755 | return __x.real() == __y && __x.imag() == 0; |
||
| 756 | } |
||
| 757 | |||
| 758 | template<class _Tp> |
||
| 759 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 760 | bool |
||
| 761 | operator==(const _Tp& __x, const complex<_Tp>& __y) |
||
| 762 | {
|
||
| 763 | return __x == __y.real() && 0 == __y.imag(); |
||
| 764 | } |
||
| 765 | |||
| 766 | template<class _Tp> |
||
| 767 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 768 | bool |
||
| 769 | operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) |
||
| 770 | {
|
||
| 771 | return !(__x == __y); |
||
| 772 | } |
||
| 773 | |||
| 774 | template<class _Tp> |
||
| 775 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 776 | bool |
||
| 777 | operator!=(const complex<_Tp>& __x, const _Tp& __y) |
||
| 778 | {
|
||
| 779 | return !(__x == __y); |
||
| 780 | } |
||
| 781 | |||
| 782 | template<class _Tp> |
||
| 783 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 784 | bool |
||
| 785 | operator!=(const _Tp& __x, const complex<_Tp>& __y) |
||
| 786 | {
|
||
| 787 | return !(__x == __y); |
||
| 788 | } |
||
| 789 | |||
| 790 | // 26.3.7 values: |
||
| 791 | |||
| 792 | // real |
||
| 793 | |||
| 794 | template<class _Tp> |
||
| 795 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 796 | _Tp |
||
| 797 | real(const complex<_Tp>& __c) |
||
| 798 | {
|
||
| 799 | return __c.real(); |
||
| 800 | } |
||
| 801 | |||
| 802 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 803 | long double |
||
| 804 | real(long double __re) |
||
| 805 | {
|
||
| 806 | return __re; |
||
| 807 | } |
||
| 808 | |||
| 809 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 810 | double |
||
| 811 | real(double __re) |
||
| 812 | {
|
||
| 813 | return __re; |
||
| 814 | } |
||
| 815 | |||
| 816 | template<class _Tp> |
||
| 817 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 818 | typename enable_if |
||
| 819 | < |
||
| 820 | is_integral<_Tp>::value, |
||
| 821 | double |
||
| 822 | >::type |
||
| 823 | real(_Tp __re) |
||
| 824 | {
|
||
| 825 | return __re; |
||
| 826 | } |
||
| 827 | |||
| 828 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 829 | float |
||
| 830 | real(float __re) |
||
| 831 | {
|
||
| 832 | return __re; |
||
| 833 | } |
||
| 834 | |||
| 835 | // imag |
||
| 836 | |||
| 837 | template<class _Tp> |
||
| 838 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 839 | _Tp |
||
| 840 | imag(const complex<_Tp>& __c) |
||
| 841 | {
|
||
| 842 | return __c.imag(); |
||
| 843 | } |
||
| 844 | |||
| 845 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 846 | long double |
||
| 847 | imag(long double __re) |
||
| 848 | {
|
||
| 849 | return 0; |
||
| 850 | } |
||
| 851 | |||
| 852 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 853 | double |
||
| 854 | imag(double __re) |
||
| 855 | {
|
||
| 856 | return 0; |
||
| 857 | } |
||
| 858 | |||
| 859 | template<class _Tp> |
||
| 860 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 861 | typename enable_if |
||
| 862 | < |
||
| 863 | is_integral<_Tp>::value, |
||
| 864 | double |
||
| 865 | >::type |
||
| 866 | imag(_Tp __re) |
||
| 867 | {
|
||
| 868 | return 0; |
||
| 869 | } |
||
| 870 | |||
| 871 | inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 |
||
| 872 | float |
||
| 873 | imag(float __re) |
||
| 874 | {
|
||
| 875 | return 0; |
||
| 876 | } |
||
| 877 | |||
| 878 | // abs |
||
| 879 | |||
| 880 | template<class _Tp> |
||
| 881 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 882 | _Tp |
||
| 883 | abs(const complex<_Tp>& __c) |
||
| 884 | {
|
||
| 885 | return hypot(__c.real(), __c.imag()); |
||
| 886 | } |
||
| 887 | |||
| 888 | // arg |
||
| 889 | |||
| 890 | template<class _Tp> |
||
| 891 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 892 | _Tp |
||
| 893 | arg(const complex<_Tp>& __c) |
||
| 894 | {
|
||
| 895 | return atan2(__c.imag(), __c.real()); |
||
| 896 | } |
||
| 897 | |||
| 898 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 899 | long double |
||
| 900 | arg(long double __re) |
||
| 901 | {
|
||
| 902 | return atan2l(0.L, __re); |
||
| 903 | } |
||
| 904 | |||
| 905 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 906 | double |
||
| 907 | arg(double __re) |
||
| 908 | {
|
||
| 909 | return atan2(0., __re); |
||
| 910 | } |
||
| 911 | |||
| 912 | template<class _Tp> |
||
| 913 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 914 | typename enable_if |
||
| 915 | < |
||
| 916 | is_integral<_Tp>::value, |
||
| 917 | double |
||
| 918 | >::type |
||
| 919 | arg(_Tp __re) |
||
| 920 | {
|
||
| 921 | return atan2(0., __re); |
||
| 922 | } |
||
| 923 | |||
| 924 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 925 | float |
||
| 926 | arg(float __re) |
||
| 927 | {
|
||
| 928 | return atan2f(0.F, __re); |
||
| 929 | } |
||
| 930 | |||
| 931 | // norm |
||
| 932 | |||
| 933 | template<class _Tp> |
||
| 934 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 935 | _Tp |
||
| 936 | norm(const complex<_Tp>& __c) |
||
| 937 | {
|
||
| 938 | if (isinf(__c.real())) |
||
| 939 | return abs(__c.real()); |
||
| 940 | if (isinf(__c.imag())) |
||
| 941 | return abs(__c.imag()); |
||
| 942 | return __c.real() * __c.real() + __c.imag() * __c.imag(); |
||
| 943 | } |
||
| 944 | |||
| 945 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 946 | long double |
||
| 947 | norm(long double __re) |
||
| 948 | {
|
||
| 949 | return __re * __re; |
||
| 950 | } |
||
| 951 | |||
| 952 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 953 | double |
||
| 954 | norm(double __re) |
||
| 955 | {
|
||
| 956 | return __re * __re; |
||
| 957 | } |
||
| 958 | |||
| 959 | template<class _Tp> |
||
| 960 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 961 | typename enable_if |
||
| 962 | < |
||
| 963 | is_integral<_Tp>::value, |
||
| 964 | double |
||
| 965 | >::type |
||
| 966 | norm(_Tp __re) |
||
| 967 | {
|
||
| 968 | return (double)__re * __re; |
||
| 969 | } |
||
| 970 | |||
| 971 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 972 | float |
||
| 973 | norm(float __re) |
||
| 974 | {
|
||
| 975 | return __re * __re; |
||
| 976 | } |
||
| 977 | |||
| 978 | // conj |
||
| 979 | |||
| 980 | template<class _Tp> |
||
| 981 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 982 | complex<_Tp> |
||
| 983 | conj(const complex<_Tp>& __c) |
||
| 984 | {
|
||
| 985 | return complex<_Tp>(__c.real(), -__c.imag()); |
||
| 986 | } |
||
| 987 | |||
| 988 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 989 | complex<long double> |
||
| 990 | conj(long double __re) |
||
| 991 | {
|
||
| 992 | return complex<long double>(__re); |
||
| 993 | } |
||
| 994 | |||
| 995 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 996 | complex<double> |
||
| 997 | conj(double __re) |
||
| 998 | {
|
||
| 999 | return complex<double>(__re); |
||
| 1000 | } |
||
| 1001 | |||
| 1002 | template<class _Tp> |
||
| 1003 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1004 | typename enable_if |
||
| 1005 | < |
||
| 1006 | is_integral<_Tp>::value, |
||
| 1007 | complex<double> |
||
| 1008 | >::type |
||
| 1009 | conj(_Tp __re) |
||
| 1010 | {
|
||
| 1011 | return complex<double>(__re); |
||
| 1012 | } |
||
| 1013 | |||
| 1014 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1015 | complex<float> |
||
| 1016 | conj(float __re) |
||
| 1017 | {
|
||
| 1018 | return complex<float>(__re); |
||
| 1019 | } |
||
| 1020 | |||
| 1021 | // proj |
||
| 1022 | |||
| 1023 | template<class _Tp> |
||
| 1024 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1025 | complex<_Tp> |
||
| 1026 | proj(const complex<_Tp>& __c) |
||
| 1027 | {
|
||
| 1028 | std::complex<_Tp> __r = __c; |
||
| 1029 | if (isinf(__c.real()) || isinf(__c.imag())) |
||
| 1030 | __r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag())); |
||
| 1031 | return __r; |
||
| 1032 | } |
||
| 1033 | |||
| 1034 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1035 | complex<long double> |
||
| 1036 | proj(long double __re) |
||
| 1037 | {
|
||
| 1038 | if (isinf(__re)) |
||
| 1039 | __re = abs(__re); |
||
| 1040 | return complex<long double>(__re); |
||
| 1041 | } |
||
| 1042 | |||
| 1043 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1044 | complex<double> |
||
| 1045 | proj(double __re) |
||
| 1046 | {
|
||
| 1047 | if (isinf(__re)) |
||
| 1048 | __re = abs(__re); |
||
| 1049 | return complex<double>(__re); |
||
| 1050 | } |
||
| 1051 | |||
| 1052 | template<class _Tp> |
||
| 1053 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1054 | typename enable_if |
||
| 1055 | < |
||
| 1056 | is_integral<_Tp>::value, |
||
| 1057 | complex<double> |
||
| 1058 | >::type |
||
| 1059 | proj(_Tp __re) |
||
| 1060 | {
|
||
| 1061 | return complex<double>(__re); |
||
| 1062 | } |
||
| 1063 | |||
| 1064 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1065 | complex<float> |
||
| 1066 | proj(float __re) |
||
| 1067 | {
|
||
| 1068 | if (isinf(__re)) |
||
| 1069 | __re = abs(__re); |
||
| 1070 | return complex<float>(__re); |
||
| 1071 | } |
||
| 1072 | |||
| 1073 | // polar |
||
| 1074 | |||
| 1075 | template<class _Tp> |
||
| 1076 | complex<_Tp> |
||
| 1077 | polar(const _Tp& __rho, const _Tp& __theta = _Tp(0)) |
||
| 1078 | {
|
||
| 1079 | if (isnan(__rho) || signbit(__rho)) |
||
| 1080 | return complex<_Tp>(_Tp(NAN), _Tp(NAN)); |
||
| 1081 | if (isnan(__theta)) |
||
| 1082 | {
|
||
| 1083 | if (isinf(__rho)) |
||
| 1084 | return complex<_Tp>(__rho, __theta); |
||
| 1085 | return complex<_Tp>(__theta, __theta); |
||
| 1086 | } |
||
| 1087 | if (isinf(__theta)) |
||
| 1088 | {
|
||
| 1089 | if (isinf(__rho)) |
||
| 1090 | return complex<_Tp>(__rho, _Tp(NAN)); |
||
| 1091 | return complex<_Tp>(_Tp(NAN), _Tp(NAN)); |
||
| 1092 | } |
||
| 1093 | _Tp __x = __rho * cos(__theta); |
||
| 1094 | if (isnan(__x)) |
||
| 1095 | __x = 0; |
||
| 1096 | _Tp __y = __rho * sin(__theta); |
||
| 1097 | if (isnan(__y)) |
||
| 1098 | __y = 0; |
||
| 1099 | return complex<_Tp>(__x, __y); |
||
| 1100 | } |
||
| 1101 | |||
| 1102 | // log |
||
| 1103 | |||
| 1104 | template<class _Tp> |
||
| 1105 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1106 | complex<_Tp> |
||
| 1107 | log(const complex<_Tp>& __x) |
||
| 1108 | {
|
||
| 1109 | return complex<_Tp>(log(abs(__x)), arg(__x)); |
||
| 1110 | } |
||
| 1111 | |||
| 1112 | // log10 |
||
| 1113 | |||
| 1114 | template<class _Tp> |
||
| 1115 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1116 | complex<_Tp> |
||
| 1117 | log10(const complex<_Tp>& __x) |
||
| 1118 | {
|
||
| 1119 | return log(__x) / log(_Tp(10)); |
||
| 1120 | } |
||
| 1121 | |||
| 1122 | // sqrt |
||
| 1123 | |||
| 1124 | template<class _Tp> |
||
| 1125 | complex<_Tp> |
||
| 1126 | sqrt(const complex<_Tp>& __x) |
||
| 1127 | {
|
||
| 1128 | if (isinf(__x.imag())) |
||
| 1129 | return complex<_Tp>(_Tp(INFINITY), __x.imag()); |
||
| 1130 | if (isinf(__x.real())) |
||
| 1131 | {
|
||
| 1132 | if (__x.real() > _Tp(0)) |
||
| 1133 | return complex<_Tp>(__x.real(), isnan(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag())); |
||
| 1134 | return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag())); |
||
| 1135 | } |
||
| 1136 | return polar(sqrt(abs(__x)), arg(__x) / _Tp(2)); |
||
| 1137 | } |
||
| 1138 | |||
| 1139 | // exp |
||
| 1140 | |||
| 1141 | template<class _Tp> |
||
| 1142 | complex<_Tp> |
||
| 1143 | exp(const complex<_Tp>& __x) |
||
| 1144 | {
|
||
| 1145 | _Tp __i = __x.imag(); |
||
| 1146 | if (isinf(__x.real())) |
||
| 1147 | {
|
||
| 1148 | if (__x.real() < _Tp(0)) |
||
| 1149 | {
|
||
| 1150 | if (!isfinite(__i)) |
||
| 1151 | __i = _Tp(1); |
||
| 1152 | } |
||
| 1153 | else if (__i == 0 || !isfinite(__i)) |
||
| 1154 | {
|
||
| 1155 | if (isinf(__i)) |
||
| 1156 | __i = _Tp(NAN); |
||
| 1157 | return complex<_Tp>(__x.real(), __i); |
||
| 1158 | } |
||
| 1159 | } |
||
| 1160 | else if (isnan(__x.real()) && __x.imag() == 0) |
||
| 1161 | return __x; |
||
| 1162 | _Tp __e = exp(__x.real()); |
||
| 1163 | return complex<_Tp>(__e * cos(__i), __e * sin(__i)); |
||
| 1164 | } |
||
| 1165 | |||
| 1166 | // pow |
||
| 1167 | |||
| 1168 | template<class _Tp> |
||
| 1169 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1170 | complex<_Tp> |
||
| 1171 | pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
||
| 1172 | {
|
||
| 1173 | return exp(__y * log(__x)); |
||
| 1174 | } |
||
| 1175 | |||
| 1176 | template<class _Tp, class _Up> |
||
| 1177 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1178 | complex<typename __promote<_Tp, _Up>::type> |
||
| 1179 | pow(const complex<_Tp>& __x, const complex<_Up>& __y) |
||
| 1180 | {
|
||
| 1181 | typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
||
| 1182 | return _VSTD::pow(result_type(__x), result_type(__y)); |
||
| 1183 | } |
||
| 1184 | |||
| 1185 | template<class _Tp, class _Up> |
||
| 1186 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1187 | typename enable_if |
||
| 1188 | < |
||
| 1189 | is_arithmetic<_Up>::value, |
||
| 1190 | complex<typename __promote<_Tp, _Up>::type> |
||
| 1191 | >::type |
||
| 1192 | pow(const complex<_Tp>& __x, const _Up& __y) |
||
| 1193 | {
|
||
| 1194 | typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
||
| 1195 | return _VSTD::pow(result_type(__x), result_type(__y)); |
||
| 1196 | } |
||
| 1197 | |||
| 1198 | template<class _Tp, class _Up> |
||
| 1199 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1200 | typename enable_if |
||
| 1201 | < |
||
| 1202 | is_arithmetic<_Tp>::value, |
||
| 1203 | complex<typename __promote<_Tp, _Up>::type> |
||
| 1204 | >::type |
||
| 1205 | pow(const _Tp& __x, const complex<_Up>& __y) |
||
| 1206 | {
|
||
| 1207 | typedef complex<typename __promote<_Tp, _Up>::type> result_type; |
||
| 1208 | return _VSTD::pow(result_type(__x), result_type(__y)); |
||
| 1209 | } |
||
| 1210 | |||
| 1211 | // asinh |
||
| 1212 | |||
| 1213 | template<class _Tp> |
||
| 1214 | complex<_Tp> |
||
| 1215 | asinh(const complex<_Tp>& __x) |
||
| 1216 | {
|
||
| 1217 | const _Tp __pi(atan2(+0., -0.)); |
||
| 1218 | if (isinf(__x.real())) |
||
| 1219 | {
|
||
| 1220 | if (isnan(__x.imag())) |
||
| 1221 | return __x; |
||
| 1222 | if (isinf(__x.imag())) |
||
| 1223 | return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag())); |
||
| 1224 | return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag())); |
||
| 1225 | } |
||
| 1226 | if (isnan(__x.real())) |
||
| 1227 | {
|
||
| 1228 | if (isinf(__x.imag())) |
||
| 1229 | return complex<_Tp>(__x.imag(), __x.real()); |
||
| 1230 | if (__x.imag() == 0) |
||
| 1231 | return __x; |
||
| 1232 | return complex<_Tp>(__x.real(), __x.real()); |
||
| 1233 | } |
||
| 1234 | if (isinf(__x.imag())) |
||
| 1235 | return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag())); |
||
| 1236 | complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1))); |
||
| 1237 | return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag())); |
||
| 1238 | } |
||
| 1239 | |||
| 1240 | // acosh |
||
| 1241 | |||
| 1242 | template<class _Tp> |
||
| 1243 | complex<_Tp> |
||
| 1244 | acosh(const complex<_Tp>& __x) |
||
| 1245 | {
|
||
| 1246 | const _Tp __pi(atan2(+0., -0.)); |
||
| 1247 | if (isinf(__x.real())) |
||
| 1248 | {
|
||
| 1249 | if (isnan(__x.imag())) |
||
| 1250 | return complex<_Tp>(abs(__x.real()), __x.imag()); |
||
| 1251 | if (isinf(__x.imag())) |
||
| 1252 | {
|
||
| 1253 | if (__x.real() > 0) |
||
| 1254 | return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag())); |
||
| 1255 | else |
||
| 1256 | return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag())); |
||
| 1257 | } |
||
| 1258 | if (__x.real() < 0) |
||
| 1259 | return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag())); |
||
| 1260 | return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag())); |
||
| 1261 | } |
||
| 1262 | if (isnan(__x.real())) |
||
| 1263 | {
|
||
| 1264 | if (isinf(__x.imag())) |
||
| 1265 | return complex<_Tp>(abs(__x.imag()), __x.real()); |
||
| 1266 | return complex<_Tp>(__x.real(), __x.real()); |
||
| 1267 | } |
||
| 1268 | if (isinf(__x.imag())) |
||
| 1269 | return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag())); |
||
| 1270 | complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1))); |
||
| 1271 | return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag())); |
||
| 1272 | } |
||
| 1273 | |||
| 1274 | // atanh |
||
| 1275 | |||
| 1276 | template<class _Tp> |
||
| 1277 | complex<_Tp> |
||
| 1278 | atanh(const complex<_Tp>& __x) |
||
| 1279 | {
|
||
| 1280 | const _Tp __pi(atan2(+0., -0.)); |
||
| 1281 | if (isinf(__x.imag())) |
||
| 1282 | {
|
||
| 1283 | return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag())); |
||
| 1284 | } |
||
| 1285 | if (isnan(__x.imag())) |
||
| 1286 | {
|
||
| 1287 | if (isinf(__x.real()) || __x.real() == 0) |
||
| 1288 | return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag()); |
||
| 1289 | return complex<_Tp>(__x.imag(), __x.imag()); |
||
| 1290 | } |
||
| 1291 | if (isnan(__x.real())) |
||
| 1292 | {
|
||
| 1293 | return complex<_Tp>(__x.real(), __x.real()); |
||
| 1294 | } |
||
| 1295 | if (isinf(__x.real())) |
||
| 1296 | {
|
||
| 1297 | return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag())); |
||
| 1298 | } |
||
| 1299 | if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) |
||
| 1300 | {
|
||
| 1301 | return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag())); |
||
| 1302 | } |
||
| 1303 | complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2); |
||
| 1304 | return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag())); |
||
| 1305 | } |
||
| 1306 | |||
| 1307 | // sinh |
||
| 1308 | |||
| 1309 | template<class _Tp> |
||
| 1310 | complex<_Tp> |
||
| 1311 | sinh(const complex<_Tp>& __x) |
||
| 1312 | {
|
||
| 1313 | if (isinf(__x.real()) && !isfinite(__x.imag())) |
||
| 1314 | return complex<_Tp>(__x.real(), _Tp(NAN)); |
||
| 1315 | if (__x.real() == 0 && !isfinite(__x.imag())) |
||
| 1316 | return complex<_Tp>(__x.real(), _Tp(NAN)); |
||
| 1317 | if (__x.imag() == 0 && !isfinite(__x.real())) |
||
| 1318 | return __x; |
||
| 1319 | return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag())); |
||
| 1320 | } |
||
| 1321 | |||
| 1322 | // cosh |
||
| 1323 | |||
| 1324 | template<class _Tp> |
||
| 1325 | complex<_Tp> |
||
| 1326 | cosh(const complex<_Tp>& __x) |
||
| 1327 | {
|
||
| 1328 | if (isinf(__x.real()) && !isfinite(__x.imag())) |
||
| 1329 | return complex<_Tp>(abs(__x.real()), _Tp(NAN)); |
||
| 1330 | if (__x.real() == 0 && !isfinite(__x.imag())) |
||
| 1331 | return complex<_Tp>(_Tp(NAN), __x.real()); |
||
| 1332 | if (__x.real() == 0 && __x.imag() == 0) |
||
| 1333 | return complex<_Tp>(_Tp(1), __x.imag()); |
||
| 1334 | if (__x.imag() == 0 && !isfinite(__x.real())) |
||
| 1335 | return complex<_Tp>(abs(__x.real()), __x.imag()); |
||
| 1336 | return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag())); |
||
| 1337 | } |
||
| 1338 | |||
| 1339 | // tanh |
||
| 1340 | |||
| 1341 | template<class _Tp> |
||
| 1342 | complex<_Tp> |
||
| 1343 | tanh(const complex<_Tp>& __x) |
||
| 1344 | {
|
||
| 1345 | if (isinf(__x.real())) |
||
| 1346 | {
|
||
| 1347 | if (!isfinite(__x.imag())) |
||
| 1348 | return complex<_Tp>(_Tp(1), _Tp(0)); |
||
| 1349 | return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag()))); |
||
| 1350 | } |
||
| 1351 | if (isnan(__x.real()) && __x.imag() == 0) |
||
| 1352 | return __x; |
||
| 1353 | _Tp __2r(_Tp(2) * __x.real()); |
||
| 1354 | _Tp __2i(_Tp(2) * __x.imag()); |
||
| 1355 | _Tp __d(cosh(__2r) + cos(__2i)); |
||
| 1356 | _Tp __2rsh(sinh(__2r)); |
||
| 1357 | if (isinf(__2rsh) && isinf(__d)) |
||
| 1358 | return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1), |
||
| 1359 | __2i > _Tp(0) ? _Tp(0) : _Tp(-0.)); |
||
| 1360 | return complex<_Tp>(__2rsh/__d, sin(__2i)/__d); |
||
| 1361 | } |
||
| 1362 | |||
| 1363 | // asin |
||
| 1364 | |||
| 1365 | template<class _Tp> |
||
| 1366 | complex<_Tp> |
||
| 1367 | asin(const complex<_Tp>& __x) |
||
| 1368 | {
|
||
| 1369 | complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real())); |
||
| 1370 | return complex<_Tp>(__z.imag(), -__z.real()); |
||
| 1371 | } |
||
| 1372 | |||
| 1373 | // acos |
||
| 1374 | |||
| 1375 | template<class _Tp> |
||
| 1376 | complex<_Tp> |
||
| 1377 | acos(const complex<_Tp>& __x) |
||
| 1378 | {
|
||
| 1379 | const _Tp __pi(atan2(+0., -0.)); |
||
| 1380 | if (isinf(__x.real())) |
||
| 1381 | {
|
||
| 1382 | if (isnan(__x.imag())) |
||
| 1383 | return complex<_Tp>(__x.imag(), __x.real()); |
||
| 1384 | if (isinf(__x.imag())) |
||
| 1385 | {
|
||
| 1386 | if (__x.real() < _Tp(0)) |
||
| 1387 | return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag()); |
||
| 1388 | return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag()); |
||
| 1389 | } |
||
| 1390 | if (__x.real() < _Tp(0)) |
||
| 1391 | return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real()); |
||
| 1392 | return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real()); |
||
| 1393 | } |
||
| 1394 | if (isnan(__x.real())) |
||
| 1395 | {
|
||
| 1396 | if (isinf(__x.imag())) |
||
| 1397 | return complex<_Tp>(__x.real(), -__x.imag()); |
||
| 1398 | return complex<_Tp>(__x.real(), __x.real()); |
||
| 1399 | } |
||
| 1400 | if (isinf(__x.imag())) |
||
| 1401 | return complex<_Tp>(__pi/_Tp(2), -__x.imag()); |
||
| 1402 | if (__x.real() == 0) |
||
| 1403 | return complex<_Tp>(__pi/_Tp(2), -__x.imag()); |
||
| 1404 | complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1))); |
||
| 1405 | if (signbit(__x.imag())) |
||
| 1406 | return complex<_Tp>(abs(__z.imag()), abs(__z.real())); |
||
| 1407 | return complex<_Tp>(abs(__z.imag()), -abs(__z.real())); |
||
| 1408 | } |
||
| 1409 | |||
| 1410 | // atan |
||
| 1411 | |||
| 1412 | template<class _Tp> |
||
| 1413 | complex<_Tp> |
||
| 1414 | atan(const complex<_Tp>& __x) |
||
| 1415 | {
|
||
| 1416 | complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real())); |
||
| 1417 | return complex<_Tp>(__z.imag(), -__z.real()); |
||
| 1418 | } |
||
| 1419 | |||
| 1420 | // sin |
||
| 1421 | |||
| 1422 | template<class _Tp> |
||
| 1423 | complex<_Tp> |
||
| 1424 | sin(const complex<_Tp>& __x) |
||
| 1425 | {
|
||
| 1426 | complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real())); |
||
| 1427 | return complex<_Tp>(__z.imag(), -__z.real()); |
||
| 1428 | } |
||
| 1429 | |||
| 1430 | // cos |
||
| 1431 | |||
| 1432 | template<class _Tp> |
||
| 1433 | inline _LIBCPP_INLINE_VISIBILITY |
||
| 1434 | complex<_Tp> |
||
| 1435 | cos(const complex<_Tp>& __x) |
||
| 1436 | {
|
||
| 1437 | return cosh(complex<_Tp>(-__x.imag(), __x.real())); |
||
| 1438 | } |
||
| 1439 | |||
| 1440 | // tan |
||
| 1441 | |||
| 1442 | template<class _Tp> |
||
| 1443 | complex<_Tp> |
||
| 1444 | tan(const complex<_Tp>& __x) |
||
| 1445 | {
|
||
| 1446 | complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real())); |
||
| 1447 | return complex<_Tp>(__z.imag(), -__z.real()); |
||
| 1448 | } |
||
| 1449 | |||
| 1450 | template<class _Tp, class _CharT, class _Traits> |
||
| 1451 | basic_istream<_CharT, _Traits>& |
||
| 1452 | operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) |
||
| 1453 | {
|
||
| 1454 | if (__is.good()) |
||
| 1455 | {
|
||
| 1456 | ws(__is); |
||
| 1457 | if (__is.peek() == _CharT('('))
|
||
| 1458 | {
|
||
| 1459 | __is.get(); |
||
| 1460 | _Tp __r; |
||
| 1461 | __is >> __r; |
||
| 1462 | if (!__is.fail()) |
||
| 1463 | {
|
||
| 1464 | ws(__is); |
||
| 1465 | _CharT __c = __is.peek(); |
||
| 1466 | if (__c == _CharT(','))
|
||
| 1467 | {
|
||
| 1468 | __is.get(); |
||
| 1469 | _Tp __i; |
||
| 1470 | __is >> __i; |
||
| 1471 | if (!__is.fail()) |
||
| 1472 | {
|
||
| 1473 | ws(__is); |
||
| 1474 | __c = __is.peek(); |
||
| 1475 | if (__c == _CharT(')'))
|
||
| 1476 | {
|
||
| 1477 | __is.get(); |
||
| 1478 | __x = complex<_Tp>(__r, __i); |
||
| 1479 | } |
||
| 1480 | else |
||
| 1481 | __is.setstate(ios_base::failbit); |
||
| 1482 | } |
||
| 1483 | else |
||
| 1484 | __is.setstate(ios_base::failbit); |
||
| 1485 | } |
||
| 1486 | else if (__c == _CharT(')'))
|
||
| 1487 | {
|
||
| 1488 | __is.get(); |
||
| 1489 | __x = complex<_Tp>(__r, _Tp(0)); |
||
| 1490 | } |
||
| 1491 | else |
||
| 1492 | __is.setstate(ios_base::failbit); |
||
| 1493 | } |
||
| 1494 | else |
||
| 1495 | __is.setstate(ios_base::failbit); |
||
| 1496 | } |
||
| 1497 | else |
||
| 1498 | {
|
||
| 1499 | _Tp __r; |
||
| 1500 | __is >> __r; |
||
| 1501 | if (!__is.fail()) |
||
| 1502 | __x = complex<_Tp>(__r, _Tp(0)); |
||
| 1503 | else |
||
| 1504 | __is.setstate(ios_base::failbit); |
||
| 1505 | } |
||
| 1506 | } |
||
| 1507 | else |
||
| 1508 | __is.setstate(ios_base::failbit); |
||
| 1509 | return __is; |
||
| 1510 | } |
||
| 1511 | |||
| 1512 | template<class _Tp, class _CharT, class _Traits> |
||
| 1513 | basic_ostream<_CharT, _Traits>& |
||
| 1514 | operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) |
||
| 1515 | {
|
||
| 1516 | basic_ostringstream<_CharT, _Traits> __s; |
||
| 1517 | __s.flags(__os.flags()); |
||
| 1518 | __s.imbue(__os.getloc()); |
||
| 1519 | __s.precision(__os.precision()); |
||
| 1520 | __s << '(' << __x.real() << ',' << __x.imag() << ')';
|
||
| 1521 | return __os << __s.str(); |
||
| 1522 | } |
||
| 1523 | |||
| 1524 | #if _LIBCPP_STD_VER > 11 |
||
| 1525 | // Literal suffix for complex number literals [complex.literals] |
||
| 1526 | inline namespace literals |
||
| 1527 | {
|
||
| 1528 | inline namespace complex_literals |
||
| 1529 | {
|
||
| 1530 | constexpr complex<long double> operator""il(long double __im) |
||
| 1531 | {
|
||
| 1532 | return { 0.0l, __im };
|
||
| 1533 | } |
||
| 1534 | |||
| 1535 | constexpr complex<long double> operator""il(unsigned long long __im) |
||
| 1536 | {
|
||
| 1537 | return { 0.0l, static_cast<long double>(__im) };
|
||
| 1538 | } |
||
| 1539 | |||
| 1540 | |||
| 1541 | constexpr complex<double> operator""i(long double __im) |
||
| 1542 | {
|
||
| 1543 | return { 0.0, static_cast<double>(__im) };
|
||
| 1544 | } |
||
| 1545 | |||
| 1546 | constexpr complex<double> operator""i(unsigned long long __im) |
||
| 1547 | {
|
||
| 1548 | return { 0.0, static_cast<double>(__im) };
|
||
| 1549 | } |
||
| 1550 | |||
| 1551 | |||
| 1552 | constexpr complex<float> operator""if(long double __im) |
||
| 1553 | {
|
||
| 1554 | return { 0.0f, static_cast<float>(__im) };
|
||
| 1555 | } |
||
| 1556 | |||
| 1557 | constexpr complex<float> operator""if(unsigned long long __im) |
||
| 1558 | {
|
||
| 1559 | return { 0.0f, static_cast<float>(__im) };
|
||
| 1560 | } |
||
| 1561 | } |
||
| 1562 | } |
||
| 1563 | #endif |
||
| 1564 | |||
| 1565 | _LIBCPP_END_NAMESPACE_STD |
||
| 1566 | |||
| 1567 | #endif // _LIBCPP_COMPLEX |