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STL/stl/inc/complex

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// complex standard header
// Copyright (c) Microsoft Corporation.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
#pragma once
#ifndef _COMPLEX_
#define _COMPLEX_
#include <yvals_core.h>
#if _STL_COMPILER_PREPROCESSOR
#include <cmath>
#include <cstdint>
#include <sstream>
#include <ymath.h>
#pragma pack(push, _CRT_PACKING)
#pragma warning(push, _STL_WARNING_LEVEL)
#pragma warning(disable : _STL_DISABLED_WARNINGS)
_STL_DISABLE_CLANG_WARNINGS
#pragma push_macro("new")
#undef new
#ifndef _C_COMPLEX_T
#define _C_COMPLEX_T
struct _C_double_complex {
double _Val[2];
};
struct _C_float_complex {
float _Val[2];
};
struct _C_ldouble_complex {
long double _Val[2];
};
#endif // _C_COMPLEX_T
// COMPLEX _Val OFFSETS
#define _RE 0
#define _IM 1
_STD_BEGIN
using _Dcomplex_value = _CSTD _C_double_complex;
using _Fcomplex_value = _CSTD _C_float_complex;
using _Lcomplex_value = _CSTD _C_ldouble_complex;
template <class _Ty>
class complex;
template <>
class complex<float>;
template <>
class complex<double>;
template <>
class complex<long double>;
// CLASS TEMPLATE _Ctraits
template <class _Ty>
class _Ctraits {
public:
static constexpr _Ty _Flt_eps() { // get epsilon
return numeric_limits<_Ty>::epsilon();
}
static constexpr _Ty _Flt_max() {
return (numeric_limits<_Ty>::max)();
}
static _Ty _Cosh(_Ty _Left, _Ty _Right) { // return cosh(_Left) * _Right
return static_cast<_Ty>(_CSTD _Cosh(static_cast<double>(_Left), static_cast<double>(_Right)));
}
static short _Exp(_Ty* _Pleft, _Ty _Right, short _Exponent) { // compute exp(*_Pleft) * _Right * 2 ^ _Exponent
double _Tmp = static_cast<double>(*_Pleft);
short _Ans = _CSTD _Exp(&_Tmp, static_cast<double>(_Right), _Exponent);
*_Pleft = static_cast<_Ty>(_Tmp);
return _Ans;
}
static constexpr _Ty _Infv() { // return infinity
return numeric_limits<_Ty>::infinity();
}
static bool _Isinf(_Ty _Left) { // test for infinity
const auto _Tmp = static_cast<double>(_Left);
const auto _Uint = _Bit_cast<uint64_t>(_Tmp);
return (_Uint & 0x7fffffffffffffffU) == 0x7ff0000000000000U;
}
static _CONSTEXPR20 bool _Isnan(_Ty _Left) {
const auto _Tmp = static_cast<double>(_Left);
const auto _Uint = _Bit_cast<uint64_t>(_Tmp);
return (_Uint & 0x7fffffffffffffffU) > 0x7ff0000000000000U;
}
static constexpr _Ty _Nanv() { // return NaN
return numeric_limits<_Ty>::quiet_NaN();
}
static _Ty _Sinh(_Ty _Left, _Ty _Right) { // return sinh(_Left) * _Right
return static_cast<_Ty>(_CSTD _Sinh(static_cast<double>(_Left), static_cast<double>(_Right)));
}
static _Ty asinh(_Ty _Left) {
constexpr _Ty _Ln2 = 0.69314718055994530941723212145817658L;
bool _Neg = _Left < 0;
_Ty _Ans;
if (_Neg) {
_Left = -_Left;
}
if (_Left < 2 / _Flt_eps()) {
_Ans = log1p(_Left + _Left * _Left / (1 + sqrt(_Left * _Left + 1)));
} else {
_Ans = log(_Left) + _Ln2;
}
return static_cast<_Ty>(_Neg ? -_Ans : _Ans);
}
static _Ty atan2(_Ty _Yval, _Ty _Xval) { // return atan(_Yval / _Xval)
return static_cast<_Ty>(_CSTD atan2(static_cast<double>(_Yval), static_cast<double>(_Xval)));
}
static _Ty cos(_Ty _Left) {
return static_cast<_Ty>(_CSTD cos(static_cast<double>(_Left)));
}
static _Ty exp(_Ty _Left) {
return static_cast<_Ty>(_CSTD exp(static_cast<double>(_Left)));
}
static _Ty ldexp(_Ty _Left, int _Exponent) { // return _Left * 2 ^ _Exponent
return static_cast<_Ty>(_CSTD ldexp(static_cast<double>(_Left), _Exponent));
}
static _Ty log(_Ty _Left) {
return static_cast<_Ty>(_CSTD log(static_cast<double>(_Left)));
}
static _Ty log1p(_Ty _Left) { // return log(1 + _Left)
if (_Left < -1) {
return _Nanv();
} else if (_Left == 0) {
return _Left;
} else { // compute log(1 + _Left) with fixup for small _Left
_Ty _Leftp1 = 1 + _Left;
return log(_Leftp1) - ((_Leftp1 - 1) - _Left) / _Leftp1;
}
}
static _Ty pow(_Ty _Left, _Ty _Right) {
return static_cast<_Ty>(_CSTD pow(static_cast<double>(_Left), static_cast<double>(_Right)));
}
static _Ty sin(_Ty _Left) {
return static_cast<_Ty>(_CSTD sin(static_cast<double>(_Left)));
}
static _Ty sqrt(_Ty _Left) {
return static_cast<_Ty>(_CSTD sqrt(static_cast<double>(_Left)));
}
static _Ty tan(_Ty _Left) {
return static_cast<_Ty>(_CSTD tan(static_cast<double>(_Left)));
}
static _Ty hypot(_Ty _Left, _Ty _Right) {
return static_cast<_Ty>(_CSTD hypot(static_cast<double>(_Left), static_cast<double>(_Right)));
}
};
// CLASS _Ctraits<long double>
template <>
class _Ctraits<long double> {
public:
using _Ty = long double;
static constexpr _Ty _Flt_eps() { // get epsilon
return numeric_limits<long double>::epsilon();
}
static constexpr _Ty _Flt_max() {
return (numeric_limits<long double>::max)();
}
static _Ty _Cosh(_Ty _Left, _Ty _Right) { // return cosh(_Left) * _Right
return _CSTD _LCosh(_Left, _Right);
}
static short _Exp(_Ty* _Pleft, _Ty _Right, short _Exponent) { // compute exp(*_Pleft) * _Right * 2 ^ _Exponent
return _CSTD _LExp(_Pleft, _Right, _Exponent);
}
static constexpr _Ty _Infv() { // return infinity
return numeric_limits<long double>::infinity();
}
static bool _Isinf(_Ty _Left) { // test for infinity
const auto _Uint = _Bit_cast<uint64_t>(_Left);
return (_Uint & 0x7fffffffffffffffU) == 0x7ff0000000000000U;
}
static _CONSTEXPR20 bool _Isnan(_Ty _Left) {
const auto _Uint = _Bit_cast<uint64_t>(_Left);
return (_Uint & 0x7fffffffffffffffU) > 0x7ff0000000000000U;
}
static constexpr _Ty _Nanv() { // return NaN
return numeric_limits<long double>::quiet_NaN();
}
static _Ty _Sinh(_Ty _Left, _Ty _Right) { // return sinh(_Left) * _Right
return _CSTD _LSinh(_Left, _Right);
}
static _Ty asinh(_Ty _Left) {
constexpr _Ty _Ln2 = 0.69314718055994530941723212145817658L;
const bool _Neg = _Left < 0;
_Ty _Ans;
if (_Neg) {
_Left = -_Left;
}
if (_Left < 2 / _Flt_eps()) {
_Ans = log1p(_Left + _Left * _Left / (1 + sqrt(_Left * _Left + 1)));
} else {
_Ans = log(_Left) + _Ln2;
}
return _Neg ? -_Ans : _Ans;
}
static _Ty atan2(_Ty _Yval, _Ty _Xval) { // return atan(_Yval / _Xval)
return _CSTD atan2l(_Yval, _Xval);
}
static _Ty cos(_Ty _Left) {
return _CSTD cosl(_Left);
}
static _Ty exp(_Ty _Left) {
return _CSTD expl(_Left);
}
static _Ty ldexp(_Ty _Left, int _Exponent) { // return _Left * 2 ^ _Exponent
return _CSTD ldexpl(_Left, _Exponent);
}
static _Ty log(_Ty _Left) {
return _CSTD logl(_Left);
}
static _Ty log1p(_Ty _Left) { // return log(1 + _Left)
if (_Left < -1) {
return _Nanv();
} else if (_Left == 0) {
return _Left;
} else { // compute log(1 + _Left) with fixup for small _Left
_Ty _Leftp1 = 1 + _Left;
return log(_Leftp1) - ((_Leftp1 - 1) - _Left) / _Leftp1;
}
}
static _Ty pow(_Ty _Left, _Ty _Right) {
return _CSTD powl(_Left, _Right);
}
static _Ty sin(_Ty _Left) {
return _CSTD sinl(_Left);
}
static _Ty sqrt(_Ty _Left) {
return _CSTD sqrtl(_Left);
}
static _Ty tan(_Ty _Left) {
return _CSTD tanl(_Left);
}
static _Ty hypot(_Ty _Left, _Ty _Right) {
return _CSTD hypotl(_Left, _Right);
}
};
// CLASS _Ctraits<double>
template <>
class _Ctraits<double> {
public:
using _Ty = double;
static constexpr _Ty _Flt_eps() { // get epsilon
return numeric_limits<double>::epsilon();
}
static constexpr _Ty _Flt_max() {
return (numeric_limits<double>::max)();
}
static _Ty _Cosh(_Ty _Left, _Ty _Right) { // return cosh(_Left) * _Right
return _CSTD _Cosh(_Left, _Right);
}
static short _Exp(_Ty* _Pleft, _Ty _Right, short _Exponent) { // compute exp(*_Pleft) * _Right * 2 ^ _Exponent
return _CSTD _Exp(_Pleft, _Right, _Exponent);
}
static constexpr _Ty _Infv() { // return infinity
return numeric_limits<double>::infinity();
}
static bool _Isinf(_Ty _Left) { // test for infinity
const auto _Uint = _Bit_cast<uint64_t>(_Left);
return (_Uint & 0x7fffffffffffffffU) == 0x7ff0000000000000U;
}
static _CONSTEXPR20 bool _Isnan(_Ty _Left) {
const auto _Uint = _Bit_cast<uint64_t>(_Left);
return (_Uint & 0x7fffffffffffffffU) > 0x7ff0000000000000U;
}
static constexpr _Ty _Nanv() { // return NaN
return numeric_limits<double>::quiet_NaN();
}
static _Ty _Sinh(_Ty _Left, _Ty _Right) { // return sinh(_Left) * _Right
return _CSTD _Sinh(_Left, _Right);
}
static _Ty asinh(_Ty _Left) {
if (_Isnan(_Left) || _Isinf(_Left) || _Left == 0) {
return 0;
} else { // _Left finite nonzero
const bool _Neg = _Left < 0;
_Ty _Ans;
if (_Neg) {
_Left = -_Left;
}
if (_Left < 2 / _Flt_eps()) {
_Ans = log1p(_Left + _Left * _Left / (1 + sqrt(_Left * _Left + 1)));
} else {
_Ans = log(_Left) // _Left big, compute log(_Left+_Left)
+ static_cast<_Ty>(0.69314718055994530941723212145817658L);
}
return _Neg ? -_Ans : _Ans;
}
}
static _Ty atan2(_Ty _Yval, _Ty _Xval) { // return atan(_Yval / _Xval)
return _CSTD atan2(_Yval, _Xval);
}
static _Ty cos(_Ty _Left) {
return _CSTD cos(_Left);
}
static _Ty exp(_Ty _Left) {
return _CSTD exp(_Left);
}
static _Ty ldexp(_Ty _Left, int _Exponent) { // return _Left * 2 ^ _Exponent
return _CSTD ldexp(_Left, _Exponent);
}
static _Ty log(_Ty _Left) {
return _CSTD log(_Left);
}
static _Ty log1p(_Ty _Left) { // return log(1 + _Left)
if (_Isnan(_Left) || _Left == 0 || (_Isinf(_Left) && 0 < _Left)) {
return _Left;
} else if (_Left < -1) {
return _Nanv();
} else if (_Left == -1) {
return -_Infv();
} else if (_Left == 0) {
return _Left;
} else { // compute log(1 + _Left) with fixup for small _Left
_Ty _Leftp1 = 1 + _Left;
return log(_Leftp1) - ((_Leftp1 - 1) - _Left) / _Leftp1;
}
}
static _Ty pow(_Ty _Left, _Ty _Right) {
return _CSTD pow(_Left, _Right);
}
static _Ty sin(_Ty _Left) {
return _CSTD sin(_Left);
}
static _Ty sqrt(_Ty _Left) {
return _CSTD sqrt(_Left);
}
static _Ty tan(_Ty _Left) {
return _CSTD tan(_Left);
}
static _Ty hypot(_Ty _Left, _Ty _Right) {
return _CSTD hypot(_Left, _Right);
}
};
// CLASS _Ctraits<float>
template <>
class _Ctraits<float> {
public:
using _Ty = float;
static constexpr _Ty _Flt_eps() { // get epsilon
return numeric_limits<float>::epsilon();
}
static constexpr _Ty _Flt_max() {
return (numeric_limits<float>::max)();
}
static _Ty _Cosh(_Ty _Left, _Ty _Right) { // return cosh(_Left) * _Right
return _CSTD _FCosh(_Left, _Right);
}
static short _Exp(_Ty* _Pleft, _Ty _Right, short _Exponent) { // compute exp(*_Pleft) * _Right * 2 ^ _Exponent
return _CSTD _FExp(_Pleft, _Right, _Exponent);
}
static constexpr _Ty _Infv() { // return infinity
return numeric_limits<float>::infinity();
}
static bool _Isinf(_Ty _Left) { // test for infinity
const auto _Uint = _Bit_cast<uint32_t>(_Left);
return (_Uint & 0x7fffffffU) == 0x7f800000U;
}
static _CONSTEXPR20 bool _Isnan(_Ty _Left) {
const auto _Uint = _Bit_cast<uint32_t>(_Left);
return (_Uint & 0x7fffffffU) > 0x7f800000U;
}
static constexpr _Ty _Nanv() { // return NaN
return numeric_limits<float>::quiet_NaN();
}
static _Ty _Sinh(_Ty _Left, _Ty _Right) { // return sinh(_Left) * _Right
return _CSTD _FSinh(_Left, _Right);
}
static _Ty asinh(_Ty _Left) {
constexpr _Ty _Ln2 = 0.69314718055994530941723212145817658F;
const bool _Neg = _Left < 0;
_Ty _Ans;
if (_Neg) {
_Left = -_Left;
}
if (_Left < 2 / _Flt_eps()) {
_Ans = log1p(_Left + _Left * _Left / (1 + sqrt(_Left * _Left + 1)));
} else {
_Ans = log(_Left) + _Ln2;
}
return _Neg ? -_Ans : _Ans;
}
static _Ty atan2(_Ty _Yval, _Ty _Xval) { // return atan(_Yval / _Xval)
return _CSTD atan2f(_Yval, _Xval);
}
static _Ty cos(_Ty _Left) {
return _CSTD cosf(_Left);
}
static _Ty exp(_Ty _Left) {
return _CSTD expf(_Left);
}
static _Ty ldexp(_Ty _Left, int _Exponent) { // return _Left * 2 ^ _Exponent
return _CSTD ldexpf(_Left, _Exponent);
}
static _Ty log(_Ty _Left) {
return _CSTD logf(_Left);
}
static _Ty log1p(_Ty _Left) { // return log(1 + _Left)
if (_Left < -1) {
return _Nanv();
} else if (_Left == 0) {
return _Left;
} else { // compute log(1 + _Left) with fixup for small _Left
_Ty _Leftp1 = 1 + _Left;
return log(_Leftp1) - ((_Leftp1 - 1) - _Left) / _Leftp1;
}
}
static _Ty pow(_Ty _Left, _Ty _Right) {
return _CSTD powf(_Left, _Right);
}
static _Ty sin(_Ty _Left) {
return _CSTD sinf(_Left);
}
static _Ty sqrt(_Ty _Left) {
return _CSTD sqrtf(_Left);
}
static _Ty tan(_Ty _Left) {
return _CSTD tanf(_Left);
}
static _Ty hypot(_Ty _Left, _Ty _Right) {
return _CSTD hypotf(_Left, _Right);
}
};
// STRUCT TEMPLATE _Complex_value
template <class _Ty>
struct _Complex_value {
enum { _Re = 0, _Im = 1 };
_Ty _Val[2];
};
// CLASS TEMPLATE _Complex_base
template <class _Ty, class _Valbase>
class _Complex_base : public _Valbase {
public:
using _Myctraits = _Ctraits<_Ty>;
using value_type = _Ty;
constexpr _Complex_base(const _Ty& _Realval, const _Ty& _Imagval) : _Valbase{{_Realval, _Imagval}} {}
_CONSTEXPR20 void real(const _Ty& _Right) { // set real component
this->_Val[_RE] = _Right;
}
_CONSTEXPR20 void imag(const _Ty& _Right) { // set imaginary component
this->_Val[_IM] = _Right;
}
_NODISCARD constexpr _Ty real() const { // return real component
return this->_Val[_RE];
}
_NODISCARD constexpr _Ty imag() const { // return imaginary component
return this->_Val[_IM];
}
protected:
template <class _Other>
_CONSTEXPR20 void _Add(const complex<_Other>& _Right) {
this->_Val[_RE] = this->_Val[_RE] + static_cast<_Ty>(_Right.real());
this->_Val[_IM] = this->_Val[_IM] + static_cast<_Ty>(_Right.imag());
}
template <class _Other>
_CONSTEXPR20 void _Sub(const complex<_Other>& _Right) {
this->_Val[_RE] = this->_Val[_RE] - static_cast<_Ty>(_Right.real());
this->_Val[_IM] = this->_Val[_IM] - static_cast<_Ty>(_Right.imag());
}
template <class _Other>
_CONSTEXPR20 void _Mul(const complex<_Other>& _Right) {
_Ty _Rightreal = static_cast<_Ty>(_Right.real());
_Ty _Rightimag = static_cast<_Ty>(_Right.imag());
_Ty _Tmp = this->_Val[_RE] * _Rightreal - this->_Val[_IM] * _Rightimag;
this->_Val[_IM] = this->_Val[_RE] * _Rightimag + this->_Val[_IM] * _Rightreal;
this->_Val[_RE] = _Tmp;
}
template <class _Other>
_CONSTEXPR20 void _Div(const complex<_Other>& _Right) {
using _Myctraits = _Ctraits<_Ty>;
_Ty _Rightreal = static_cast<_Ty>(_Right.real());
_Ty _Rightimag = static_cast<_Ty>(_Right.imag());
if (_Myctraits::_Isnan(_Rightreal) || _Myctraits::_Isnan(_Rightimag)) { // set NaN result
this->_Val[_RE] = _Myctraits::_Nanv();
this->_Val[_IM] = this->_Val[_RE];
} else if ((_Rightimag < 0 ? -_Rightimag : +_Rightimag)
< (_Rightreal < 0 ? -_Rightreal : +_Rightreal)) { // |_Right.imag()| < |_Right.real()|
_Ty _Wr = _Rightimag / _Rightreal;
_Ty _Wd = _Rightreal + _Wr * _Rightimag;
if (_Myctraits::_Isnan(_Wd) || _Wd == 0) { // set NaN result
this->_Val[_RE] = _Myctraits::_Nanv();
this->_Val[_IM] = this->_Val[_RE];
} else { // compute representable result
_Ty _Tmp = (this->_Val[_RE] + this->_Val[_IM] * _Wr) / _Wd;
this->_Val[_IM] = (this->_Val[_IM] - this->_Val[_RE] * _Wr) / _Wd;
this->_Val[_RE] = _Tmp;
}
} else if (_Rightimag == 0) { // set NaN result
this->_Val[_RE] = _Myctraits::_Nanv();
this->_Val[_IM] = this->_Val[_RE];
} else { // 0 < |_Right.real()| <= |_Right.imag()|
_Ty _Wr = _Rightreal / _Rightimag;
_Ty _Wd = _Rightimag + _Wr * _Rightreal;
if (_Myctraits::_Isnan(_Wd) || _Wd == 0) { // set NaN result
this->_Val[_RE] = _Myctraits::_Nanv();
this->_Val[_IM] = this->_Val[_RE];
} else { // compute representable result
_Ty _Tmp = (this->_Val[_RE] * _Wr + this->_Val[_IM]) / _Wd;
this->_Val[_IM] = (this->_Val[_IM] * _Wr - this->_Val[_RE]) / _Wd;
this->_Val[_RE] = _Tmp;
}
}
}
};
// CLASS complex<float>
template <>
class complex<float> : public _Complex_base<float, _Fcomplex_value> {
public:
using _Ty = float;
constexpr explicit complex(const complex<double>&); // defined below
constexpr explicit complex(const complex<long double>&); // defined below
constexpr complex(const _Ty& _Realval = 0, const _Ty& _Imagval = 0)
: _Complex_base<float, _Fcomplex_value>(_Realval, _Imagval) {}
constexpr complex(const _Fcomplex_value& _Right)
: _Complex_base<float, _Fcomplex_value>(_Right._Val[_RE], _Right._Val[_IM]) {}
constexpr complex(const _Dcomplex_value& _Right)
: _Complex_base<float, _Fcomplex_value>(
static_cast<float>(_Right._Val[_RE]), static_cast<float>(_Right._Val[_IM])) {}
constexpr complex(const _Lcomplex_value& _Right)
: _Complex_base<float, _Fcomplex_value>(
static_cast<float>(_Right._Val[_RE]), static_cast<float>(_Right._Val[_IM])) {}
_CONSTEXPR20 complex& operator=(const _Ty& _Right) {
_Val[_RE] = _Right;
_Val[_IM] = 0;
return *this;
}
_CONSTEXPR20 complex& operator+=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] + _Right;
return *this;
}
_CONSTEXPR20 complex& operator-=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] - _Right;
return *this;
}
_CONSTEXPR20 complex& operator*=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] * _Right;
_Val[_IM] = _Val[_IM] * _Right;
return *this;
}
_CONSTEXPR20 complex& operator/=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] / _Right;
_Val[_IM] = _Val[_IM] / _Right;
return *this;
}
_CONSTEXPR20 complex& operator+=(const complex& _Right) {
this->_Add(_Right);
return *this;
}
_CONSTEXPR20 complex& operator-=(const complex& _Right) {
this->_Sub(_Right);
return *this;
}
_CONSTEXPR20 complex& operator*=(const complex& _Right) {
this->_Mul(_Right);
return *this;
}
_CONSTEXPR20 complex& operator/=(const complex& _Right) {
this->_Div(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator=(const complex<_Other>& _Right) {
_Val[_RE] = static_cast<_Ty>(_Right._Val[_RE]);
_Val[_IM] = static_cast<_Ty>(_Right._Val[_IM]);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator+=(const complex<_Other>& _Right) {
this->_Add(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator-=(const complex<_Other>& _Right) {
this->_Sub(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator*=(const complex<_Other>& _Right) {
this->_Mul(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator/=(const complex<_Other>& _Right) {
this->_Div(_Right);
return *this;
}
};
// CLASS complex<double>
template <>
class complex<double> : public _Complex_base<double, _Dcomplex_value> {
public:
using _Ty = double;
constexpr complex(const complex<float>&); // defined below
constexpr explicit complex(const complex<long double>&); // defined below
constexpr complex(const _Ty& _Realval = 0, const _Ty& _Imagval = 0)
: _Complex_base<double, _Dcomplex_value>(_Realval, _Imagval) {}
constexpr complex(const _Dcomplex_value& _Right)
: _Complex_base<double, _Dcomplex_value>(_Right._Val[_RE], _Right._Val[_IM]) {}
constexpr complex(const _Lcomplex_value& _Right)
: _Complex_base<double, _Dcomplex_value>(
static_cast<double>(_Right._Val[_RE]), static_cast<double>(_Right._Val[_IM])) {}
_CONSTEXPR20 complex& operator=(const _Ty& _Right) {
_Val[_RE] = _Right;
_Val[_IM] = 0;
return *this;
}
_CONSTEXPR20 complex& operator+=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] + _Right;
return *this;
}
_CONSTEXPR20 complex& operator-=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] - _Right;
return *this;
}
_CONSTEXPR20 complex& operator*=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] * _Right;
_Val[_IM] = _Val[_IM] * _Right;
return *this;
}
_CONSTEXPR20 complex& operator/=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] / _Right;
_Val[_IM] = _Val[_IM] / _Right;
return *this;
}
_CONSTEXPR20 complex& operator+=(const complex& _Right) {
this->_Add(_Right);
return *this;
}
_CONSTEXPR20 complex& operator-=(const complex& _Right) {
this->_Sub(_Right);
return *this;
}
_CONSTEXPR20 complex& operator*=(const complex& _Right) {
this->_Mul(_Right);
return *this;
}
_CONSTEXPR20 complex& operator/=(const complex& _Right) {
this->_Div(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator=(const complex<_Other>& _Right) {
_Val[_RE] = static_cast<_Ty>(_Right._Val[_RE]);
_Val[_IM] = static_cast<_Ty>(_Right._Val[_IM]);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator+=(const complex<_Other>& _Right) {
this->_Add(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator-=(const complex<_Other>& _Right) {
this->_Sub(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator*=(const complex<_Other>& _Right) {
this->_Mul(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator/=(const complex<_Other>& _Right) {
this->_Div(_Right);
return *this;
}
};
// CLASS complex<long double>
template <>
class complex<long double> : public _Complex_base<long double, _Lcomplex_value> {
public:
using _Ty = long double;
constexpr complex(const complex<float>&); // defined below
constexpr complex(const complex<double>&); // defined below
constexpr complex(const _Ty& _Realval = 0, const _Ty& _Imagval = 0)
: _Complex_base<long double, _Lcomplex_value>(_Realval, _Imagval) {}
constexpr complex(const _Lcomplex_value& _Right)
: _Complex_base<long double, _Lcomplex_value>(_Right._Val[_RE], _Right._Val[_IM]) {}
_CONSTEXPR20 complex& operator=(const _Ty& _Right) {
_Val[_RE] = _Right;
_Val[_IM] = 0;
return *this;
}
_CONSTEXPR20 complex& operator+=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] + _Right;
return *this;
}
_CONSTEXPR20 complex& operator-=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] - _Right;
return *this;
}
_CONSTEXPR20 complex& operator*=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] * _Right;
_Val[_IM] = _Val[_IM] * _Right;
return *this;
}
_CONSTEXPR20 complex& operator/=(const _Ty& _Right) {
_Val[_RE] = _Val[_RE] / _Right;
_Val[_IM] = _Val[_IM] / _Right;
return *this;
}
_CONSTEXPR20 complex& operator+=(const complex& _Right) {
this->_Add(_Right);
return *this;
}
_CONSTEXPR20 complex& operator-=(const complex& _Right) {
this->_Sub(_Right);
return *this;
}
_CONSTEXPR20 complex& operator*=(const complex& _Right) {
this->_Mul(_Right);
return *this;
}
_CONSTEXPR20 complex& operator/=(const complex& _Right) {
this->_Div(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator=(const complex<_Other>& _Right) {
_Val[_RE] = static_cast<_Ty>(_Right._Val[_RE]);
_Val[_IM] = static_cast<_Ty>(_Right._Val[_IM]);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator+=(const complex<_Other>& _Right) {
this->_Add(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator-=(const complex<_Other>& _Right) {
this->_Sub(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator*=(const complex<_Other>& _Right) {
this->_Mul(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator/=(const complex<_Other>& _Right) {
this->_Div(_Right);
return *this;
}
};
// CONSTRUCTORS FOR complex SPECIALIZATIONS
constexpr complex<float>::complex(const complex<double>& _Right)
: _Complex_base<float, _Fcomplex_value>(static_cast<_Ty>(_Right.real()), static_cast<_Ty>(_Right.imag())) {}
constexpr complex<float>::complex(const complex<long double>& _Right)
: _Complex_base<float, _Fcomplex_value>(static_cast<_Ty>(_Right.real()), static_cast<_Ty>(_Right.imag())) {}
constexpr complex<double>::complex(const complex<float>& _Right)
: _Complex_base<double, _Dcomplex_value>(_Right.real(), _Right.imag()) {}
constexpr complex<double>::complex(const complex<long double>& _Right)
: _Complex_base<double, _Dcomplex_value>(static_cast<_Ty>(_Right.real()), static_cast<_Ty>(_Right.imag())) {}
constexpr complex<long double>::complex(const complex<float>& _Right)
: _Complex_base<long double, _Lcomplex_value>(_Right.real(), _Right.imag()) {}
constexpr complex<long double>::complex(const complex<double>& _Right)
: _Complex_base<long double, _Lcomplex_value>(_Right.real(), _Right.imag()) {}
// CLASS TEMPLATE complex
template <class _Ty>
class complex : public _Complex_base<_Ty, _Complex_value<_Ty>> {
public:
using _Mybase = _Complex_base<_Ty, _Complex_value<_Ty>>;
constexpr complex(const _Ty& _Realval = _Ty(), const _Ty& _Imagval = _Ty()) : _Mybase(_Realval, _Imagval) {}
_CONSTEXPR20 complex& operator=(const _Ty& _Right) {
this->_Val[_RE] = _Right;
this->_Val[_IM] = _Ty();
return *this;
}
template <class _Other>
constexpr complex(const complex<_Other>& _Right)
: _Mybase(static_cast<_Ty>(_Right.real()), static_cast<_Ty>(_Right.imag())) {}
template <class _Other>
_CONSTEXPR20 complex& operator=(const complex<_Other>& _Right) {
this->_Val[_RE] = static_cast<_Ty>(_Right.real());
this->_Val[_IM] = static_cast<_Ty>(_Right.imag());
return *this;
}
_CONSTEXPR20 complex& operator+=(const _Ty& _Right) {
this->_Val[_RE] = this->_Val[_RE] + _Right;
return *this;
}
_CONSTEXPR20 complex& operator-=(const _Ty& _Right) {
this->_Val[_RE] = this->_Val[_RE] - _Right;
return *this;
}
_CONSTEXPR20 complex& operator*=(const _Ty& _Right) {
this->_Val[_RE] = this->_Val[_RE] * _Right;
this->_Val[_IM] = this->_Val[_IM] * _Right;
return *this;
}
_CONSTEXPR20 complex& operator/=(const _Ty& _Right) {
this->_Val[_RE] = this->_Val[_RE] / _Right;
this->_Val[_IM] = this->_Val[_IM] / _Right;
return *this;
}
_CONSTEXPR20 complex& operator+=(const complex& _Right) {
this->_Add(_Right);
return *this;
}
_CONSTEXPR20 complex& operator-=(const complex& _Right) {
this->_Sub(_Right);
return *this;
}
_CONSTEXPR20 complex& operator*=(const complex& _Right) {
this->_Mul(_Right);
return *this;
}
_CONSTEXPR20 complex& operator/=(const complex& _Right) {
this->_Div(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator+=(const complex<_Other>& _Right) {
this->_Add(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator-=(const complex<_Other>& _Right) {
this->_Sub(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator*=(const complex<_Other>& _Right) {
this->_Mul(_Right);
return *this;
}
template <class _Other>
_CONSTEXPR20 complex& operator/=(const complex<_Other>& _Right) {
this->_Div(_Right);
return *this;
}
};
// FUNCTION TEMPLATE operator+
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator+(const complex<_Ty>& _Left, const complex<_Ty>& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp += _Right;
return _Tmp;
}
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator+(const complex<_Ty>& _Left, const _Ty& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp.real(_Tmp.real() + _Right);
return _Tmp;
}
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator+(const _Ty& _Left, const complex<_Ty>& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp += _Right;
return _Tmp;
}
// FUNCTION TEMPLATE operator-
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator-(const complex<_Ty>& _Left, const complex<_Ty>& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp -= _Right;
return _Tmp;
}
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator-(const complex<_Ty>& _Left, const _Ty& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp.real(_Tmp.real() - _Right);
return _Tmp;
}
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator-(const _Ty& _Left, const complex<_Ty>& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp -= _Right;
return _Tmp;
}
// FUNCTION TEMPLATE operator*
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator*(const complex<_Ty>& _Left, const complex<_Ty>& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp *= _Right;
return _Tmp;
}
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator*(const complex<_Ty>& _Left, const _Ty& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp.real(_Tmp.real() * _Right);
_Tmp.imag(_Tmp.imag() * _Right);
return _Tmp;
}
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator*(const _Ty& _Left, const complex<_Ty>& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp *= _Right;
return _Tmp;
}
// FUNCTION TEMPLATE operator/
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator/(const complex<_Ty>& _Left, const complex<_Ty>& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp /= _Right;
return _Tmp;
}
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator/(const complex<_Ty>& _Left, const _Ty& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp.real(_Tmp.real() / _Right);
_Tmp.imag(_Tmp.imag() / _Right);
return _Tmp;
}
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator/(const _Ty& _Left, const complex<_Ty>& _Right) {
complex<_Ty> _Tmp(_Left);
_Tmp /= _Right;
return _Tmp;
}
// FUNCTION TEMPLATE UNARY operator+
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator+(const complex<_Ty>& _Left) {
return _Left;
}
// FUNCTION TEMPLATE UNARY operator-
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> operator-(const complex<_Ty>& _Left) {
return complex<_Ty>(-_Left.real(), -_Left.imag());
}
// FUNCTION TEMPLATE operator==
template <class _Ty>
_NODISCARD constexpr bool operator==(const complex<_Ty>& _Left, const complex<_Ty>& _Right) {
return _Left.real() == _Right.real() && _Left.imag() == _Right.imag();
}
template <class _Ty>
_NODISCARD constexpr bool operator==(const complex<_Ty>& _Left, const _Ty& _Right) {
return _Left.real() == _Right && _Left.imag() == 0;
}
template <class _Ty>
_NODISCARD constexpr bool operator==(const _Ty& _Left, const complex<_Ty>& _Right) {
return _Left == _Right.real() && 0 == _Right.imag();
}
// FUNCTION TEMPLATE operator!=
template <class _Ty>
_NODISCARD constexpr bool operator!=(const complex<_Ty>& _Left, const complex<_Ty>& _Right) {
return !(_Left == _Right);
}
template <class _Ty>
_NODISCARD constexpr bool operator!=(const complex<_Ty>& _Left, const _Ty& _Right) {
return !(_Left == _Right);
}
template <class _Ty>
_NODISCARD constexpr bool operator!=(const _Ty& _Left, const complex<_Ty>& _Right) {
return !(_Left == _Right);
}
// FUNCTION TEMPLATE imag
template <class _Ty>
_NODISCARD constexpr _Ty imag(const complex<_Ty>& _Left) {
return _Left.imag();
}
// FUNCTION TEMPLATE real
template <class _Ty>
_NODISCARD constexpr _Ty real(const complex<_Ty>& _Left) {
return _Left.real();
}
template <class _Ty>
_NODISCARD complex<_Ty> sqrt(const complex<_Ty>& _Left);
// FUNCTION TEMPLATE abs
template <class _Ty>
_NODISCARD _Ty abs(const complex<_Ty>& _Left) {
return _Ctraits<_Ty>::hypot(_Left.real(), _Left.imag());
}
// FUNCTION TEMPLATE acos
template <class _Ty>
_NODISCARD complex<_Ty> acos(const complex<_Ty>& _Left) {
const _Ty _Arcbig = static_cast<_Ty>(0.25) * _Ctraits<_Ty>::sqrt(_Ctraits<_Ty>::_Flt_max());
constexpr _Ty _Pi = static_cast<_Ty>(3.1415926535897932384626433832795029L);
const _Ty _Re = real(_Left);
const _Ty _Im = imag(_Left);
_Ty _Ux;
_Ty _Vx;
if (_Ctraits<_Ty>::_Isnan(_Re) || _Ctraits<_Ty>::_Isnan(_Im)) { // at least one NaN
_Ux = _Ctraits<_Ty>::_Nanv();
_Vx = _Ux;
} else if (_Ctraits<_Ty>::_Isinf(_Re)) { // (+/-Inf, not NaN)
if (_Ctraits<_Ty>::_Isinf(_Im)) {
if (_Re < 0) {
_Ux = static_cast<_Ty>(0.75) * _Pi; // (-Inf, +/-Inf)
} else {
_Ux = static_cast<_Ty>(0.25) * _Pi; // (+Inf, +/-Inf)
}
} else if (_Re < 0) {
_Ux = _Pi; // (-Inf, finite)
} else {
_Ux = 0; // (+Inf, finite)
}
_Vx = -_Ctraits<_Ty>::_Infv();
if (_Im < 0) {
_Vx = -_Vx;
}
} else if (_Ctraits<_Ty>::_Isinf(_Im)) { // (finite, finite)
_Ux = static_cast<_Ty>(0.50) * _Pi; // (finite, +/-Inf)
_Vx = -_Im;
} else { // (finite, finite)
const complex<_Ty> _Wx = sqrt(complex<_Ty>(1 + _Re, -_Im));
const complex<_Ty> _Zx = sqrt(complex<_Ty>(1 - _Re, -_Im));
const _Ty _Wr = real(_Wx);
const _Ty _Wi = imag(_Wx);
const _Ty _Zr = real(_Zx);
const _Ty _Zi = imag(_Zx);
_Ty _Alfa;
_Ty _Beta;
_Ux = 2 * _Ctraits<_Ty>::atan2(_Zr, _Wr);
if (_Arcbig < _Wr) { // real parts large
_Alfa = _Wr;
_Beta = _Zi + _Wi * (_Zr / _Alfa);
} else if (_Arcbig < _Wi) { // imag parts large
_Alfa = _Wi;
_Beta = _Wr * (_Zi / _Alfa) + _Zr;
} else if (_Wi < -_Arcbig) { // imag part of w large negative
_Alfa = -_Wi;
_Beta = _Wr * (_Zi / _Alfa) - _Zr;
} else { // shouldn't overflow
_Alfa = 0;
_Beta = _Wr * _Zi + _Wi * _Zr; // Im(w * z)
}
_Vx = _Ctraits<_Ty>::asinh(_Beta);
if (_Alfa != 0) {
if (0 <= _Vx) {
_Vx += _Ctraits<_Ty>::log(_Alfa);
} else {
_Vx -= _Ctraits<_Ty>::log(_Alfa); // asinh(a*b) = asinh(a)+log(b)
}
}
}
return complex<_Ty>(_Ux, _Vx);
}
// FUNCTION TEMPLATE acosh
template <class _Ty>
_NODISCARD complex<_Ty> acosh(const complex<_Ty>& _Left) {
const _Ty _Arcbig = static_cast<_Ty>(0.25) * _Ctraits<_Ty>::sqrt(_Ctraits<_Ty>::_Flt_max());
constexpr _Ty _Pi = static_cast<_Ty>(3.1415926535897932384626433832795029L);
const _Ty _Re = real(_Left);
_Ty _Im = imag(_Left);
_Ty _Ux;
_Ty _Vx;
if (_Ctraits<_Ty>::_Isnan(_Re) || _Ctraits<_Ty>::_Isnan(_Im)) { // at least one NaN
_Ux = _Ctraits<_Ty>::_Nanv();
_Vx = _Ux;
} else if (_Ctraits<_Ty>::_Isinf(_Re)) { // (+/-Inf, not NaN)
_Ux = _Ctraits<_Ty>::_Infv();
if (_Ctraits<_Ty>::_Isinf(_Im)) {
if (_Re < 0) {
_Vx = static_cast<_Ty>(0.75) * _Pi; // (-Inf, +/-Inf)
} else {
_Vx = static_cast<_Ty>(0.25) * _Pi; // (+Inf, +/-Inf)
}
} else if (_Re < 0) {
_Vx = _Pi; // (-Inf, finite)
} else {
_Vx = 0; // (+Inf, finite)
}
if (_Im < 0) {
_Vx = -_Vx;
}
} else if (_Ctraits<_Ty>::_Isinf(_Im)) { // (finite, +/-Inf)
_Ux = _Ctraits<_Ty>::_Infv();
_Vx = _Im < 0 ? -static_cast<_Ty>(0.50) * _Pi : static_cast<_Ty>(0.50) * _Pi;
} else { // (finite, finite)
const complex<_Ty> _Wx = sqrt(complex<_Ty>(_Re - 1, -_Im));
const complex<_Ty> _Zx = sqrt(complex<_Ty>(_Re + 1, _Im));
const _Ty _Wr = real(_Wx);
const _Ty _Wi = imag(_Wx);
const _Ty _Zr = real(_Zx);
const _Ty _Zi = imag(_Zx);
_Ty _Alfa;
_Ty _Beta;
if (_Arcbig < _Wr) { // real parts large
_Alfa = _Wr;
_Beta = _Zr - _Wi * (_Zi / _Alfa);
} else if (_Arcbig < _Wi) { // imag parts large
_Alfa = _Wi;
_Beta = _Wr * (_Zr / _Alfa) - _Zi;
} else if (_Wi < -_Arcbig) { // imag part of w large negative
_Alfa = -_Wi;
_Beta = _Wr * (_Zr / _Alfa) + _Zi;
} else { // shouldn't overflow
_Alfa = 0;
_Beta = _Wr * _Zr - _Wi * _Zi; // Re(w * z)
}
_Ux = _Ctraits<_Ty>::asinh(_Beta);
if (_Alfa != 0) {
if (0 <= _Ux) {
_Ux += _Ctraits<_Ty>::log(_Alfa);
} else {
_Ux -= _Ctraits<_Ty>::log(_Alfa); // asinh(a*b) = asinh(a)+log(b)
}
}
bool _Neg = true;
if (_Im < 0) {
_Im = -_Im;
} else {
_Neg = false;
}
_Vx = 2 * _Ctraits<_Ty>::atan2(imag(sqrt(complex<_Ty>(_Re - 1, _Im))), _Zr);
if (_Neg) {
_Vx = -_Vx;
}
}
return complex<_Ty>(_Ux, _Vx);
}
// FUNCTION TEMPLATE asinh
template <class _Ty>
_NODISCARD complex<_Ty> asinh(const complex<_Ty>& _Left) {
const _Ty _Arcbig = static_cast<_Ty>(0.25) * _Ctraits<_Ty>::sqrt(_Ctraits<_Ty>::_Flt_max());
constexpr _Ty _Pi = static_cast<_Ty>(3.1415926535897932384626433832795029L);
const _Ty _Re = real(_Left);
_Ty _Im = imag(_Left);
_Ty _Ux;
_Ty _Vx;
if (_Ctraits<_Ty>::_Isnan(_Re) || _Ctraits<_Ty>::_Isnan(_Im)) { // at least one NaN/Inf
_Ux = _Ctraits<_Ty>::_Nanv();
_Vx = _Ux;
} else if (_Ctraits<_Ty>::_Isinf(_Re)) { // (+/-Inf, not NaN)
_Ux = _Ctraits<_Ty>::_Infv();
if (_Ctraits<_Ty>::_Isinf(_Im)) { // (+/-Inf, +/-Inf)
_Ux = _Re;
_Vx = _Im < 0 ? -static_cast<_Ty>(0.25) * _Pi : static_cast<_Ty>(0.25) * _Pi;
} else { // (+/-Inf, finite)
_Ux = _Re;
_Vx = _Im < 0 ? -_Ty{0} : _Ty{0};
}
} else if (_Ctraits<_Ty>::_Isinf(_Im)) { // (finite, +/-Inf)
_Ux = _Im;
_Vx = _Im < 0 ? -static_cast<_Ty>(0.50) * _Pi : static_cast<_Ty>(0.50) * _Pi;
} else { // (finite, finite)
const complex<_Ty> _Wx = sqrt(complex<_Ty>(1 - _Im, _Re));
const complex<_Ty> _Zx = sqrt(complex<_Ty>(1 + _Im, -_Re));
const _Ty _Wr = real(_Wx);
const _Ty _Wi = imag(_Wx);
const _Ty _Zr = real(_Zx);
const _Ty _Zi = imag(_Zx);
_Ty _Alfa;
_Ty _Beta;
if (_Arcbig < _Wr) { // real parts large
_Alfa = _Wr;
_Beta = _Wi * (_Zr / _Alfa) - _Zi;
} else if (_Arcbig < _Wi) { // imag parts large
_Alfa = _Wi;
_Beta = _Zr - _Wr * (_Zi / _Alfa);
} else if (_Wi < -_Arcbig) { // imag part of w large negative
_Alfa = -_Wi;
_Beta = -_Zr - _Wr * (_Zi / _Alfa);
} else { // shouldn't overflow
_Alfa = 0;
_Beta = _Wi * _Zr - _Wr * _Zi; // Im(w * conj(z))
}
_Ux = _Ctraits<_Ty>::asinh(_Beta);
if (_Alfa != 0) {
if (0 <= _Ux) {
_Ux += _Ctraits<_Ty>::log(_Alfa);
} else {
_Ux -= _Ctraits<_Ty>::log(_Alfa); // asinh(a*b) = asinh(a)+log(b)
}
}
_Vx = _Ctraits<_Ty>::atan2(_Im, real(_Wx * _Zx));
}
return complex<_Ty>(_Ux, _Vx);
}
// FUNCTION TEMPLATE asin
template <class _Ty>
_NODISCARD complex<_Ty> asin(const complex<_Ty>& _Left) {
complex<_Ty> _Asinh = _STD asinh(complex<_Ty>(-imag(_Left), real(_Left)));
return complex<_Ty>(imag(_Asinh), -real(_Asinh));
}
// FUNCTION TEMPLATE atanh
template <class _Ty>
_NODISCARD complex<_Ty> atanh(const complex<_Ty>& _Left) {
const _Ty _Arcbig = static_cast<_Ty>(0.25) * _Ctraits<_Ty>::sqrt(_Ctraits<_Ty>::_Flt_max());
constexpr _Ty _Piby2 = static_cast<_Ty>(1.5707963267948966192313216916397514L);
_Ty _Re = real(_Left);
_Ty _Im = imag(_Left);
_Ty _Ux;
_Ty _Vx;
if (_Ctraits<_Ty>::_Isnan(_Re) || _Ctraits<_Ty>::_Isnan(_Im)) { // at least one NaN
_Ux = _Ctraits<_Ty>::_Nanv();
_Vx = _Ux;
} else if (_Ctraits<_Ty>::_Isinf(_Re)) { // (+/-Inf, not NaN)
_Ux = _Re < 0 ? -_Ty{0} : _Ty{0};
_Vx = _Im < 0 ? -_Piby2 : _Piby2;
} else { // (finite, not _NaN)
_Ty _Magim = _Im < 0 ? -_Im : _Im;
bool _Neg = _Re < 0;
if (_Neg) {
_Re = -_Re;
} else {
_Im = -_Im;
}
if (_Arcbig < _Re) { // |re| is large
_Ty _Fx = _Im / _Re;
_Ux = 1 / _Re / (1 + _Fx * _Fx);
_Vx = _Im < 0 ? -_Piby2 : _Piby2;
} else if (_Arcbig < _Magim) { // |im| is large
_Ty _Fx = _Re / _Im;
_Ux = _Fx / _Im / (1 + _Fx * _Fx);
_Vx = _Im < 0 ? -_Piby2 : _Piby2;
} else if (_Re != 1) { // |re| is small
_Ty _Refrom1 = 1 - _Re;
_Ty _Imeps2 = _Magim * _Magim;
_Ux = static_cast<_Ty>(0.25) * _Ctraits<_Ty>::log1p(4 * _Re / (_Refrom1 * _Refrom1 + _Imeps2));
_Vx = static_cast<_Ty>(0.50) * _Ctraits<_Ty>::atan2(2 * _Im, _Refrom1 * (1 + _Re) - _Imeps2);
} else if (_Im == 0) { // {+/-1, 0)
_Ux = _Ctraits<_Ty>::_Infv();
_Vx = _Im;
} else { // {+/-1, nonzero)
_Ux = _Ctraits<_Ty>::log(
_Ctraits<_Ty>::sqrt(_Ctraits<_Ty>::sqrt(4 + _Im * _Im)) / _Ctraits<_Ty>::sqrt(_Magim));
_Vx = static_cast<_Ty>(0.50) * (_Piby2 + _Ctraits<_Ty>::atan2(_Magim, 2));
if (_Im < 0) {
_Vx = -_Vx;
}
}
if (_Neg) {
_Ux = -_Ux;
} else {
_Vx = -_Vx;
}
}
return complex<_Ty>(_Ux, _Vx);
}
// FUNCTION TEMPLATE atan
template <class _Ty>
_NODISCARD complex<_Ty> atan(const complex<_Ty>& _Left) {
complex<_Ty> _Atanh = _STD atanh(complex<_Ty>(-imag(_Left), real(_Left)));
return complex<_Ty>(imag(_Atanh), -real(_Atanh));
}
// FUNCTION TEMPLATE cosh
template <class _Ty>
_NODISCARD complex<_Ty> cosh(const complex<_Ty>& _Left) {
return complex<_Ty>(_Ctraits<_Ty>::_Cosh(real(_Left), _Ctraits<_Ty>::cos(imag(_Left))),
_Ctraits<_Ty>::_Sinh(real(_Left), _Ctraits<_Ty>::sin(imag(_Left))));
}
// FUNCTION TEMPLATE exp
template <class _Ty>
_NODISCARD complex<_Ty> exp(const complex<_Ty>& _Left) {
_Ty _Real(real(_Left)), _Imag(real(_Left));
_Ctraits<_Ty>::_Exp(&_Real, _Ctraits<_Ty>::cos(imag(_Left)), 0);
_Ctraits<_Ty>::_Exp(&_Imag, _Ctraits<_Ty>::sin(imag(_Left)), 0);
return complex<_Ty>(_Real, _Imag);
}
// FUNCTION TEMPLATE _Fabs
template <class _Ty>
_Ty _Fabs(const complex<_Ty>& _Left, int* _Pexp) { // return magnitude and scale factor
*_Pexp = 0;
_Ty _Av = real(_Left);
_Ty _Bv = imag(_Left);
if (_Ctraits<_Ty>::_Isinf(_Av) || _Ctraits<_Ty>::_Isinf(_Bv)) {
return _Ctraits<_Ty>::_Infv(); // at least one component is INF
} else if (_Ctraits<_Ty>::_Isnan(_Av)) {
return _Av; // real component is NaN
} else if (_Ctraits<_Ty>::_Isnan(_Bv)) {
return _Bv; // imaginary component is NaN
} else { // neither component is NaN or INF
if (_Av < 0) {
_Av = -_Av;
}
if (_Bv < 0) {
_Bv = -_Bv;
}
if (_Av < _Bv) { // ensure that |_Bv| <= |_Av|
_Ty _Tmp = _Av;
_Av = _Bv;
_Bv = _Tmp;
}
if (_Av == 0) {
return _Av; // |0| == 0
}
if (1 <= _Av) {
*_Pexp = 2;
_Av = _Av * static_cast<_Ty>(0.25);
_Bv = _Bv * static_cast<_Ty>(0.25);
} else {
*_Pexp = -2;
_Av = _Av * 4;
_Bv = _Bv * 4;
}
_Ty _Tmp = _Av - _Bv;
if (_Tmp == _Av) {
return _Av; // _Bv unimportant
} else if (_Bv < _Tmp) { // use simple approximation
const _Ty _Qv = _Av / _Bv;
return _Av + _Bv / (_Qv + _Ctraits<_Ty>::sqrt(_Qv * _Qv + 1));
} else { // use 1 1/2 precision to preserve bits
constexpr _Ty _Root2 = static_cast<_Ty>(1.4142135623730950488016887242096981L);
constexpr _Ty _Oneplusroot2high = static_cast<_Ty>(10125945.0 / 4194304.0); // exact if prec >= 24 bits
constexpr _Ty _Oneplusroot2low = static_cast<_Ty>(1.4341252375973918872420969807856967e-7L);
const _Ty _Qv = _Tmp / _Bv;
const _Ty _Rv = (_Qv + 2) * _Qv;
const _Ty _Sv = _Rv / (_Root2 + _Ctraits<_Ty>::sqrt(_Rv + 2)) + _Oneplusroot2low + _Qv + _Oneplusroot2high;
return _Av + _Bv / _Sv;
}
}
}
// FUNCTION TEMPLATE log
template <class _Ty>
_NODISCARD complex<_Ty> log(const complex<_Ty>& _Left) {
_Ty _Theta = _Ctraits<_Ty>::atan2(imag(_Left), real(_Left)); // get phase
if (_Ctraits<_Ty>::_Isnan(_Theta)) {
return complex<_Ty>(_Theta, _Theta); // real or imag is NaN
} else { // use 1 1/2 precision to preserve bits
constexpr _Ty _Cm = static_cast<_Ty>(22713.0L / 32768.0L);
constexpr _Ty _Cl = static_cast<_Ty>(1.4286068203094172321214581765680755e-6L);
int _Leftexp;
_Ty _Rho = _Fabs(_Left, &_Leftexp); // get magnitude and scale factor
_Ty _Leftn = static_cast<_Ty>(_Leftexp);
_Ty _Real;
if (_Rho == 0) {
_Real = -_Ctraits<_Ty>::_Infv(); // log(0) == -INF
} else if (_Ctraits<_Ty>::_Isinf(_Rho)) {
_Real = _Rho; // log(INF) == INF
} else {
_Real = _Ctraits<_Ty>::log(_Rho) + _Leftn * _Cl + _Leftn * _Cm;
}
return complex<_Ty>(_Real, _Theta);
}
}
// FUNCTION TEMPLATE pow
template <class _Ty>
complex<_Ty> _Pow(const _Ty& _Left, const _Ty& _Right) {
if (0 <= _Left) {
return _Ctraits<_Ty>::pow(_Left, _Right);
} else {
return exp(_Right * log(complex<_Ty>(_Left)));
}
}
template <class _Ty>
_NODISCARD complex<_Ty> pow(const complex<_Ty>& _Left, const _Ty& _Right) {
if (imag(_Left) == 0) {
return _Pow(real(_Left), _Right);
} else {
return exp(_Right * log(_Left));
}
}
template <class _Ty>
_NODISCARD complex<_Ty> pow(const _Ty& _Left, const complex<_Ty>& _Right) {
if (imag(_Right) == 0) {
return _Pow(_Left, real(_Right));
} else if (0 < _Left) {
return exp(_Right * _Ctraits<_Ty>::log(_Left));
} else {
return exp(_Right * log(complex<_Ty>(_Left)));
}
}
template <class _Ty>
_NODISCARD complex<_Ty> pow(const complex<_Ty>& _Left, const complex<_Ty>& _Right) {
if (imag(_Left) == 0) {
return pow(real(_Left), _Right);
} else {
return exp(_Right * log(_Left));
}
}
// FUNCTION TEMPLATE sinh
template <class _Ty>
_NODISCARD complex<_Ty> sinh(const complex<_Ty>& _Left) {
return complex<_Ty>(_Ctraits<_Ty>::_Sinh(real(_Left), _Ctraits<_Ty>::cos(imag(_Left))),
_Ctraits<_Ty>::_Cosh(real(_Left), _Ctraits<_Ty>::sin(imag(_Left))));
}
// FUNCTION TEMPLATE sqrt
template <class _Ty>
_NODISCARD complex<_Ty> sqrt(const complex<_Ty>& _Left) {
int _Leftexp;
_Ty _Rho = _Fabs(_Left, &_Leftexp); // get magnitude and scale factor
if (_Leftexp == 0) {
return complex<_Ty>(_Rho, _Rho); // argument is zero, INF, or NaN
} else { // compute in safest quadrant
_Ty _Realmag = _Ctraits<_Ty>::ldexp(real(_Left) < 0 ? -real(_Left) : real(_Left), -_Leftexp);
_Rho = _Ctraits<_Ty>::ldexp(_Ctraits<_Ty>::sqrt(2 * (_Realmag + _Rho)), _Leftexp / 2 - 1);
if (0 <= real(_Left)) {
return complex<_Ty>(_Rho, imag(_Left) / (2 * _Rho));
} else if (imag(_Left) < 0) {
return complex<_Ty>(-imag(_Left) / (2 * _Rho), -_Rho);
} else {
return complex<_Ty>(imag(_Left) / (2 * _Rho), _Rho);
}
}
}
// FUNCTION TEMPLATE tanh
template <class _Ty>
_NODISCARD complex<_Ty> tanh(const complex<_Ty>& _Left) {
_Ty _Tv = _Ctraits<_Ty>::tan(imag(_Left));
_Ty _Sv = _Ctraits<_Ty>::_Sinh(real(_Left), _Ty{1});
_Ty _Bv = _Sv * (_Ty{1} + _Tv * _Tv);
_Ty _Dv = _Ty{1} + _Bv * _Sv;
if (_Ctraits<_Ty>::_Isinf(_Dv)) {
_Ty _Real;
if (_Sv < _Ty{0}) {
_Real = -_Ty{1};
} else {
_Real = _Ty{1};
}
return complex<_Ty>(_Real, _Tv * _Ty{0});
}
return complex<_Ty>((_Ctraits<_Ty>::sqrt(_Ty{1} + _Sv * _Sv)) * _Bv / _Dv, _Tv / _Dv);
}
// FUNCTION TEMPLATE arg
template <class _Ty>
_NODISCARD _Ty arg(const complex<_Ty>& _Left) { // return phase angle of complex as real
return _Ctraits<_Ty>::atan2(imag(_Left), real(_Left));
}
// FUNCTION TEMPLATE conj
template <class _Ty>
_NODISCARD _CONSTEXPR20 complex<_Ty> conj(const complex<_Ty>& _Left) { // return complex conjugate
return complex<_Ty>(real(_Left), -imag(_Left));
}
// FUNCTION TEMPLATE proj
template <class _Ty>
_NODISCARD complex<_Ty> proj(const complex<_Ty>& _Left) { // return complex projection
if (_Ctraits<_Ty>::_Isinf(real(_Left)) || _Ctraits<_Ty>::_Isinf(imag(_Left))) {
_Ty _Imag;
if (imag(_Left) < 0) {
_Imag = -_Ty{0};
} else {
_Imag = _Ty{0};
}
return complex<_Ty>(_Ctraits<_Ty>::_Infv(), _Imag);
}
return _Left;
}
// FUNCTION TEMPLATE cos
template <class _Ty>
_NODISCARD complex<_Ty> cos(const complex<_Ty>& _Left) {
return complex<_Ty>(_Ctraits<_Ty>::_Cosh(imag(_Left), _Ctraits<_Ty>::cos(real(_Left))),
-_Ctraits<_Ty>::_Sinh(imag(_Left), _Ctraits<_Ty>::sin(real(_Left))));
}
// FUNCTION TEMPLATE log10
template <class _Ty>
_NODISCARD complex<_Ty> log10(const complex<_Ty>& _Left) {
return log(_Left) * static_cast<_Ty>(0.43429448190325182765112891891660508L);
}
// FUNCTION TEMPLATE norm
template <class _Ty>
_NODISCARD _CONSTEXPR20 _Ty norm(const complex<_Ty>& _Left) { // return squared magnitude
return real(_Left) * real(_Left) + imag(_Left) * imag(_Left);
}
// FUNCTION TEMPLATE polar
template <class _Ty>
_NODISCARD complex<_Ty> polar(const _Ty& _Rho, const _Ty& _Theta) { // return _Rho * exp(i * _Theta) as complex
return complex<_Ty>(_Rho * _Ctraits<_Ty>::cos(_Theta), _Rho * _Ctraits<_Ty>::sin(_Theta));
}
template <class _Ty>
_NODISCARD complex<_Ty> polar(const _Ty& _Rho) { // return _Rho * exp(i * 0) as complex
return complex<_Ty>(_Rho, _Ty{0});
}
// FUNCTION TEMPLATE sin
template <class _Ty>
_NODISCARD complex<_Ty> sin(const complex<_Ty>& _Left) {
return complex<_Ty>(_Ctraits<_Ty>::_Cosh(imag(_Left), _Ctraits<_Ty>::sin(real(_Left))),
_Ctraits<_Ty>::_Sinh(imag(_Left), _Ctraits<_Ty>::cos(real(_Left))));
}
// FUNCTION TEMPLATE tan
template <class _Ty>
_NODISCARD complex<_Ty> tan(const complex<_Ty>& _Left) {
complex<_Ty> _Zv(tanh(complex<_Ty>(-imag(_Left), real(_Left))));
return complex<_Ty>(imag(_Zv), -real(_Zv));
}
// ADDITIONAL OVERLOADS
template <class _Ty>
using _Upgrade_to_double = conditional_t<is_integral_v<_Ty>, double, _Ty>;
template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
_NODISCARD _Upgrade_to_double<_Ty> arg(_Ty _Left) {
using _Upgraded = _Upgrade_to_double<_Ty>;
const auto _Val = static_cast<_Upgraded>(_Left);
return _Ctraits<_Upgraded>::atan2(0, _Val);
}
template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
_NODISCARD _CONSTEXPR20 _Upgrade_to_double<_Ty> imag(_Ty) {
return 0;
}
template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
_NODISCARD _CONSTEXPR20 _Upgrade_to_double<_Ty> real(_Ty _Left) {
using _Upgraded = _Upgrade_to_double<_Ty>;
const auto _Val = static_cast<_Upgraded>(_Left);
return _Val;
}
template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
_NODISCARD _CONSTEXPR20 _Upgrade_to_double<_Ty> norm(_Ty _Left) {
using _Upgraded = _Upgrade_to_double<_Ty>;
const auto _Val = static_cast<_Upgraded>(_Left);
return _Val * _Val;
}
template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
_NODISCARD _CONSTEXPR20 complex<_Upgrade_to_double<_Ty>> conj(_Ty _Left) {
using _Upgraded = _Upgrade_to_double<_Ty>;
const auto _Val = static_cast<_Upgraded>(_Left);
return complex<_Upgraded>(_Val, -_Upgraded{0});
}
template <class _Ty, enable_if_t<is_arithmetic_v<_Ty>, int> = 0>
_NODISCARD complex<_Upgrade_to_double<_Ty>> proj(_Ty _Left) {
using _Upgraded = _Upgrade_to_double<_Ty>;
const auto _Val = static_cast<_Upgraded>(_Left);
if (_Ctraits<_Upgraded>::_Isinf(_Val)) {
// C11 7.3.9.5/2: "z projects to z except that all complex infinities [...]
// project to positive infinity on the real axis."
return complex<_Upgraded>(_Ctraits<_Upgraded>::_Infv(), 0);
}
return complex<_Upgraded>(_Val, 0);
}
// FUNCTION TEMPLATE pow
template <class _Ty1, class _Ty2>
_NODISCARD complex<_Common_float_type_t<_Ty1, _Ty2>> pow(const complex<_Ty1>& _Left, const complex<_Ty2>& _Right) {
using type = complex<_Common_float_type_t<_Ty1, _Ty2>>;
return _STD pow(type(_Left), type(_Right));
}
template <class _Ty1, class _Ty2, enable_if_t<!is_integral_v<_Ty2>, int> = 0>
_NODISCARD complex<_Common_float_type_t<_Ty1, _Ty2>> pow(const complex<_Ty1>& _Left, const _Ty2& _Right) {
using type = complex<_Common_float_type_t<_Ty1, _Ty2>>;
return _STD pow(type(_Left), type(_Right));
}
template <class _Ty1, class _Ty2, enable_if_t<!is_integral_v<_Ty1> && is_integral_v<_Ty2>, int> = 0>
_NODISCARD complex<_Common_float_type_t<_Ty1, _Ty2>> pow(const complex<_Ty1>& _Left, const _Ty2 _Right) {
using type = complex<_Common_float_type_t<_Ty1, _Ty2>>;
type _Tmp = _Left;
auto _Count = static_cast<make_unsigned_t<_Ty2>>(_Right);
if (_Right < 0) {
_Count = 0 - _Count; // safe negation as unsigned
}
for (type _Zv(1);; _Tmp *= _Tmp) { // fold in _Left ^ (2 ^ _Count) as needed
if ((_Count & 1) != 0) {
_Zv *= _Tmp;
}
if ((_Count >>= 1) == 0) {
return _Right < 0 ? type(1) / _Zv : _Zv;
}
}
}
template <class _Ty1, class _Ty2, enable_if_t<is_integral_v<_Ty1> && is_integral_v<_Ty2>, int> = 0>
_NODISCARD complex<_Ty1> pow(const complex<_Ty1>& _Left, _Ty2 _Right) {
// raise Gaussian integer to an integer power
using type = complex<_Ty1>;
type _Ans = type(1, 0);
if (_Right < 0) {
_Ans = type(0, 0); // ignore 1/type(0, 0) error
} else if (0 < _Right) { // raise to a positive power
for (type _Factor = _Left;; _Factor *= _Factor) { // fold in _Left^(2^N))
if ((_Right & 1) != 0) {
_Ans *= _Factor;
}
if ((_Right >>= 1) == 0) {
break;
}
}
}
return _Ans;
}
template <class _Ty1, class _Ty2>
_NODISCARD complex<_Common_float_type_t<_Ty1, _Ty2>> pow(const _Ty1& _Left, const complex<_Ty2>& _Right) {
using type = complex<_Common_float_type_t<_Ty1, _Ty2>>;
return _STD pow(type(_Left), type(_Right));
}
// FUNCTION TEMPLATE operator>>
template <class _Ty, class _Elem, class _Tr>
basic_istream<_Elem, _Tr>& operator>>(basic_istream<_Elem, _Tr>& _Istr, complex<_Ty>& _Right) {
const ctype<_Elem>& _Ctype_fac = _STD use_facet<ctype<_Elem>>(_Istr.getloc());
_Elem _Ch = 0;
long double _Real = 0;
long double _Imag = 0;
if (_Istr >> _Ch && _Ch != _Ctype_fac.widen('(')) { // no leading '(', treat as real only
_Istr.putback(_Ch);
_Istr >> _Real;
_Imag = 0;
} else if (_Istr >> _Real >> _Ch && _Ch != _Ctype_fac.widen(',')) {
if (_Ch == _Ctype_fac.widen(')')) {
_Imag = 0; // (real)
} else { // no trailing ')' after real, treat as bad field
_Istr.putback(_Ch);
_Istr.setstate(ios_base::failbit);
}
} else if (_Istr >> _Imag >> _Ch && _Ch != _Ctype_fac.widen(')')) { // no imag or trailing ')', treat as bad field
_Istr.putback(_Ch);
_Istr.setstate(ios_base::failbit);
}
if (!_Istr.fail()) { // store valid result
_Ty _Tyreal(static_cast<_Ty>(_Real)), _Tyimag(static_cast<_Ty>(_Imag));
_Right = complex<_Ty>(_Tyreal, _Tyimag);
}
return _Istr;
}
// FUNCTION TEMPLATE operator<<
template <class _Ty, class _Elem, class _Tr>
basic_ostream<_Elem, _Tr>& operator<<(basic_ostream<_Elem, _Tr>& _Ostr, const complex<_Ty>& _Right) {
const ctype<_Elem>& _Ctype_fac = _STD use_facet<ctype<_Elem>>(_Ostr.getloc());
basic_ostringstream<_Elem, _Tr, allocator<_Elem>> _Sstr;
_Sstr.flags(_Ostr.flags());
_Sstr.imbue(_Ostr.getloc());
_Sstr.precision(_Ostr.precision());
_Sstr << _Ctype_fac.widen('(') << real(_Right) << _Ctype_fac.widen(',') << imag(_Right) << _Ctype_fac.widen(')');
return _Ostr << _Sstr.str();
}
// complex LITERALS
inline namespace literals {
inline namespace complex_literals {
_NODISCARD constexpr complex<long double> operator""il(long double _Val) {
return complex<long double>(0.0L, static_cast<long double>(_Val));
}
_NODISCARD constexpr complex<long double> operator""il(unsigned long long _Val) {
return complex<long double>(0.0L, static_cast<long double>(_Val));
}
_NODISCARD constexpr complex<double> operator""i(long double _Val) {
return complex<double>(0.0, static_cast<double>(_Val));
}
_NODISCARD constexpr complex<double> operator""i(unsigned long long _Val) {
return complex<double>(0.0, static_cast<double>(_Val));
}
_NODISCARD constexpr complex<float> operator""if(long double _Val) {
return complex<float>(0.0f, static_cast<float>(_Val));
}
_NODISCARD constexpr complex<float> operator""if(unsigned long long _Val) {
return complex<float>(0.0f, static_cast<float>(_Val));
}
} // namespace complex_literals
} // namespace literals
_STD_END
#undef _RE
#undef _IM
#pragma pop_macro("new")
_STL_RESTORE_CLANG_WARNINGS
#pragma warning(pop)
#pragma pack(pop)
#endif // _STL_COMPILER_PREPROCESSOR
#endif // _COMPLEX_
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