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Stephan Seitz authoredf9b8ee6e
cuda_complex.hpp 37.91 KiB
// An implementation of C++ std::complex for use on CUDA devices.
// Written by John C. Travers <jtravs@gmail.com> (2012)
//
// Missing:
// - long double support (not supported on CUDA)
// - some integral pow functions (due to lack of C++11 support on CUDA)
//
// Heavily derived from the LLVM libcpp project (svn revision 147853).
// Based on libcxx/include/complex.
// The git history contains the complete change history from the original.
// The modifications are licensed as per the original LLVM license below.
//
// -*- C++ -*-
//===--------------------------- complex ----------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
extern "C++" {
#ifndef CUDA_COMPLEX_HPP
#define CUDA_COMPLEX_HPP
#ifdef __CUDACC__
#define CUDA_CALLABLE_MEMBER __host__ __device__
#else
#define CUDA_CALLABLE_MEMBER
#endif
/*
complex synopsis
template<class T>
class complex
{
public:
typedef T value_type;
complex(const T& re = T(), const T& im = T());
complex(const complex&);
template<class X> complex(const complex<X>&);
T real() const;
T imag() const;
void real(T);
void imag(T);
complex<T>& operator= (const T&);
complex<T>& operator+=(const T&);
complex<T>& operator-=(const T&);
complex<T>& operator*=(const T&);
complex<T>& operator/=(const T&);
complex& operator=(const complex&);
template<class X> complex<T>& operator= (const complex<X>&);
template<class X> complex<T>& operator+=(const complex<X>&);
template<class X> complex<T>& operator-=(const complex<X>&);
template<class X> complex<T>& operator*=(const complex<X>&);
template<class X> complex<T>& operator/=(const complex<X>&);
};
template<>
class complex<float>
{
public:
typedef float value_type;
constexpr complex(float re = 0.0f, float im = 0.0f);
explicit constexpr complex(const complex<double>&);
constexpr float real() const;
void real(float);
constexpr float imag() const;
void imag(float);
complex<float>& operator= (float);
complex<float>& operator+=(float);
complex<float>& operator-=(float);
complex<float>& operator*=(float);
complex<float>& operator/=(float);
complex<float>& operator=(const complex<float>&);
template<class X> complex<float>& operator= (const complex<X>&);
template<class X> complex<float>& operator+=(const complex<X>&);
template<class X> complex<float>& operator-=(const complex<X>&);
template<class X> complex<float>& operator*=(const complex<X>&);
template<class X> complex<float>& operator/=(const complex<X>&);
};
template<>
class complex<double>
{
public:
typedef double value_type;
constexpr complex(double re = 0.0, double im = 0.0);
constexpr complex(const complex<float>&);
constexpr double real() const;
void real(double);
constexpr double imag() const;
void imag(double);
complex<double>& operator= (double);
complex<double>& operator+=(double);
complex<double>& operator-=(double);
complex<double>& operator*=(double);
complex<double>& operator/=(double);
complex<double>& operator=(const complex<double>&);
template<class X> complex<double>& operator= (const complex<X>&);
template<class X> complex<double>& operator+=(const complex<X>&);
template<class X> complex<double>& operator-=(const complex<X>&);
template<class X> complex<double>& operator*=(const complex<X>&);
template<class X> complex<double>& operator/=(const complex<X>&);
};
// 26.3.6 operators:
template<class T> complex<T> operator+(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator+(const complex<T>&, const T&);
template<class T> complex<T> operator+(const T&, const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&, const T&);
template<class T> complex<T> operator-(const T&, const complex<T>&);
template<class T> complex<T> operator*(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator*(const complex<T>&, const T&);
template<class T> complex<T> operator*(const T&, const complex<T>&);
template<class T> complex<T> operator/(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator/(const complex<T>&, const T&);
template<class T> complex<T> operator/(const T&, const complex<T>&);
template<class T> complex<T> operator+(const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&);
template<class T> bool operator==(const complex<T>&, const complex<T>&);
template<class T> bool operator==(const complex<T>&, const T&);
template<class T> bool operator==(const T&, const complex<T>&);
template<class T> bool operator!=(const complex<T>&, const complex<T>&);template<class T> bool operator!=(const complex<T>&, const T&);
template<class T> bool operator!=(const T&, const complex<T>&);
template<class T, class charT, class traits>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>&, complex<T>&);
template<class T, class charT, class traits>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>&, const complex<T>&);
// 26.3.7 values:
template<class T> T real(const complex<T>&);
double real(double);
template<Integral T> double real(T);
float real(float);
template<class T> T imag(const complex<T>&);
double imag(double);
template<Integral T> double imag(T);
float imag(float);
template<class T> T abs(const complex<T>&);
template<class T> T arg(const complex<T>&);
double arg(double);
template<Integral T> double arg(T);
float arg(float);
template<class T> T norm(const complex<T>&);
double norm(double);
template<Integral T> double norm(T);
float norm(float);
template<class T> complex<T> conj(const complex<T>&);
complex<double> conj(double);
template<Integral T> complex<double> conj(T);
complex<float> conj(float);
template<class T> complex<T> proj(const complex<T>&);
complex<double> proj(double);
template<Integral T> complex<double> proj(T);
complex<float> proj(float);
template<class T> complex<T> polar(const T&, const T& = 0);
// 26.3.8 transcendentals:
template<class T> complex<T> acos(const complex<T>&);
template<class T> complex<T> asin(const complex<T>&);
template<class T> complex<T> atan(const complex<T>&);
template<class T> complex<T> acosh(const complex<T>&);
template<class T> complex<T> asinh(const complex<T>&);
template<class T> complex<T> atanh(const complex<T>&);
template<class T> complex<T> cos (const complex<T>&);
template<class T> complex<T> cosh (const complex<T>&);
template<class T> complex<T> exp (const complex<T>&);
template<class T> complex<T> log (const complex<T>&);
template<class T> complex<T> log10(const complex<T>&);
template<class T> complex<T> pow(const complex<T>&, const T&);
template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
template<class T> complex<T> pow(const T&, const complex<T>&);
template<class T> complex<T> sin (const complex<T>&);
template<class T> complex<T> sinh (const complex<T>&);
template<class T> complex<T> sqrt (const complex<T>&);
template<class T> complex<T> tan (const complex<T>&);
template<class T> complex<T> tanh (const complex<T>&);
template<class T, class charT, class traits> basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is, complex<T>& x);
template<class T, class charT, class traits>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);
*/
#include <math.h>
#include <sstream>
template <class _Tp> class complex;
template <class _Tp>
complex<_Tp> operator*(const complex<_Tp> &__z, const complex<_Tp> &__w);
template <class _Tp>
complex<_Tp> operator/(const complex<_Tp> &__x, const complex<_Tp> &__y);
template <class _Tp> class complex {
public:
typedef _Tp value_type;
private:
value_type __re_;
value_type __im_;
public:
CUDA_CALLABLE_MEMBER
complex(const value_type &__re = value_type(),
const value_type &__im = value_type())
: __re_(__re), __im_(__im) {}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex(const complex<_Xp> &__c)
: __re_(__c.real()), __im_(__c.imag()) {}
CUDA_CALLABLE_MEMBER value_type real() const { return __re_; }
CUDA_CALLABLE_MEMBER value_type imag() const { return __im_; }
CUDA_CALLABLE_MEMBER void real(value_type __re) { __re_ = __re; }
CUDA_CALLABLE_MEMBER void imag(value_type __im) { __im_ = __im; }
CUDA_CALLABLE_MEMBER complex &operator=(const value_type &__re) {
__re_ = __re;
__im_ = value_type();
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator+=(const value_type &__re) {
__re_ += __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator-=(const value_type &__re) {
__re_ -= __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator*=(const value_type &__re) {
__re_ *= __re;
__im_ *= __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator/=(const value_type &__re) {
__re_ /= __re;
__im_ /= __re;
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator=(const complex<_Xp> &__c) {
__re_ = __c.real();
__im_ = __c.imag(); return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator+=(const complex<_Xp> &__c) {
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator-=(const complex<_Xp> &__c) {
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator*=(const complex<_Xp> &__c) {
*this = *this * __c;
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator/=(const complex<_Xp> &__c) {
*this = *this / __c;
return *this;
}
};
template <> class complex<double>;
template <> class complex<float> {
float __re_;
float __im_;
public:
typedef float value_type;
/*constexpr*/ CUDA_CALLABLE_MEMBER complex(float __re = 0.0f,
float __im = 0.0f)
: __re_(__re), __im_(__im) {}
explicit /*constexpr*/ complex(const complex<double> &__c);
/*constexpr*/ CUDA_CALLABLE_MEMBER float real() const { return __re_; }
/*constexpr*/ CUDA_CALLABLE_MEMBER float imag() const { return __im_; }
CUDA_CALLABLE_MEMBER void real(value_type __re) { __re_ = __re; }
CUDA_CALLABLE_MEMBER void imag(value_type __im) { __im_ = __im; }
CUDA_CALLABLE_MEMBER complex &operator=(float __re) {
__re_ = __re;
__im_ = value_type();
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator+=(float __re) {
__re_ += __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator-=(float __re) {
__re_ -= __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator*=(float __re) {
__re_ *= __re;
__im_ *= __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator/=(float __re) {
__re_ /= __re;
__im_ /= __re;
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator=(const complex<_Xp> &__c) {
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator+=(const complex<_Xp> &__c) {
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator-=(const complex<_Xp> &__c) {
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator*=(const complex<_Xp> &__c) {
*this = *this * __c;
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator/=(const complex<_Xp> &__c) {
*this = *this / __c;
return *this;
}
};
template <> class complex<double> {
double __re_;
double __im_;
public:
typedef double value_type;
/*constexpr*/ CUDA_CALLABLE_MEMBER complex(double __re = 0.0,
double __im = 0.0)
: __re_(__re), __im_(__im) {}
/*constexpr*/ complex(const complex<float> &__c);
/*constexpr*/ CUDA_CALLABLE_MEMBER double real() const { return __re_; }
/*constexpr*/ CUDA_CALLABLE_MEMBER double imag() const { return __im_; }
CUDA_CALLABLE_MEMBER void real(value_type __re) { __re_ = __re; }
CUDA_CALLABLE_MEMBER void imag(value_type __im) { __im_ = __im; }
CUDA_CALLABLE_MEMBER complex &operator=(double __re) {
__re_ = __re;
__im_ = value_type();
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator+=(double __re) {
__re_ += __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator-=(double __re) {
__re_ -= __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator*=(double __re) {
__re_ *= __re;
__im_ *= __re;
return *this;
}
CUDA_CALLABLE_MEMBER complex &operator/=(double __re) {
__re_ /= __re;
__im_ /= __re;
return *this; }
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator=(const complex<_Xp> &__c) {
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator+=(const complex<_Xp> &__c) {
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator-=(const complex<_Xp> &__c) {
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator*=(const complex<_Xp> &__c) {
*this = *this * __c;
return *this;
}
template <class _Xp>
CUDA_CALLABLE_MEMBER complex &operator/=(const complex<_Xp> &__c) {
*this = *this / __c;
return *this;
}
};
// constexpr
inline CUDA_CALLABLE_MEMBER complex<float>::complex(const complex<double> &__c)
: __re_(__c.real()), __im_(__c.imag()) {}
// constexpr
inline CUDA_CALLABLE_MEMBER complex<double>::complex(const complex<float> &__c)
: __re_(__c.real()), __im_(__c.imag()) {}
// 26.3.6 operators:
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator+(const complex<_Tp> &__x,
const complex<_Tp> &__y) {
complex<_Tp> __t(__x);
__t += __y;
return __t;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator+(const complex<_Tp> &__x,
const _Tp &__y) {
complex<_Tp> __t(__x);
__t += __y;
return __t;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator+(const _Tp &__x,
const complex<_Tp> &__y) {
complex<_Tp> __t(__y);
__t += __x;
return __t;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator-(const complex<_Tp> &__x,
const complex<_Tp> &__y) {
complex<_Tp> __t(__x); __t -= __y;
return __t;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator-(const complex<_Tp> &__x,
const _Tp &__y) {
complex<_Tp> __t(__x);
__t -= __y;
return __t;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator-(const _Tp &__x,
const complex<_Tp> &__y) {
complex<_Tp> __t(-__y);
__t += __x;
return __t;
}
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> operator*(const complex<_Tp> &__z,
const complex<_Tp> &__w) {
_Tp __a = __z.real();
_Tp __b = __z.imag();
_Tp __c = __w.real();
_Tp __d = __w.imag();
_Tp __ac = __a * __c;
_Tp __bd = __b * __d;
_Tp __ad = __a * __d;
_Tp __bc = __b * __c;
_Tp __x = __ac - __bd;
_Tp __y = __ad + __bc;
if (isnan(__x) && isnan(__y)) {
bool __recalc = false;
if (isinf(__a) || isinf(__b)) {
__a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
__b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
if (isnan(__c))
__c = copysign(_Tp(0), __c);
if (isnan(__d))
__d = copysign(_Tp(0), __d);
__recalc = true;
}
if (isinf(__c) || isinf(__d)) {
__c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
__d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
if (isnan(__a))
__a = copysign(_Tp(0), __a);
if (isnan(__b))
__b = copysign(_Tp(0), __b);
__recalc = true;
}
if (!__recalc &&
(isinf(__ac) || isinf(__bd) || isinf(__ad) || isinf(__bc))) {
if (isnan(__a))
__a = copysign(_Tp(0), __a);
if (isnan(__b))
__b = copysign(_Tp(0), __b);
if (isnan(__c))
__c = copysign(_Tp(0), __c);
if (isnan(__d))
__d = copysign(_Tp(0), __d);
__recalc = true;
}
if (__recalc) {
__x = _Tp(INFINITY) * (__a * __c - __b * __d);
__y = _Tp(INFINITY) * (__a * __d + __b * __c);
}
} return complex<_Tp>(__x, __y);
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator*(const complex<_Tp> &__x,
const _Tp &__y) {
complex<_Tp> __t(__x);
__t *= __y;
return __t;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator*(const _Tp &__x,
const complex<_Tp> &__y) {
complex<_Tp> __t(__y);
__t *= __x;
return __t;
}
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> operator/(const complex<_Tp> &__z,
const complex<_Tp> &__w) {
int __ilogbw = 0;
_Tp __a = __z.real();
_Tp __b = __z.imag();
_Tp __c = __w.real();
_Tp __d = __w.imag();
_Tp __logbw = logb(fmax(fabs(__c), fabs(__d)));
if (isfinite(__logbw)) {
__ilogbw = static_cast<int>(__logbw);
__c = scalbn(__c, -__ilogbw);
__d = scalbn(__d, -__ilogbw);
}
_Tp __denom = __c * __c + __d * __d;
_Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
_Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
if (isnan(__x) && isnan(__y)) {
if ((__denom == _Tp(0)) && (!isnan(__a) || !isnan(__b))) {
__x = copysign(_Tp(INFINITY), __c) * __a;
__y = copysign(_Tp(INFINITY), __c) * __b;
} else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d)) {
__a = copysign(isinf(__a) ? _Tp(1) : _Tp(0), __a);
__b = copysign(isinf(__b) ? _Tp(1) : _Tp(0), __b);
__x = _Tp(INFINITY) * (__a * __c + __b * __d);
__y = _Tp(INFINITY) * (__b * __c - __a * __d);
} else if (isinf(__logbw) && __logbw > _Tp(0) && isfinite(__a) &&
isfinite(__b)) {
__c = copysign(isinf(__c) ? _Tp(1) : _Tp(0), __c);
__d = copysign(isinf(__d) ? _Tp(1) : _Tp(0), __d);
__x = _Tp(0) * (__a * __c + __b * __d);
__y = _Tp(0) * (__b * __c - __a * __d);
}
}
return complex<_Tp>(__x, __y);
}
template <>
CUDA_CALLABLE_MEMBER complex<float> operator/(const complex<float> &__z,
const complex<float> &__w) {
int __ilogbw = 0;
float __a = __z.real();
float __b = __z.imag();
float __c = __w.real();
float __d = __w.imag();
float __logbw = logbf(fmaxf(fabsf(__c), fabsf(__d)));
if (isfinite(__logbw)) {
__ilogbw = static_cast<int>(__logbw);
__c = scalbnf(__c, -__ilogbw);
__d = scalbnf(__d, -__ilogbw);
} float __denom = __c * __c + __d * __d;
float __x = scalbnf((__a * __c + __b * __d) / __denom, -__ilogbw);
float __y = scalbnf((__b * __c - __a * __d) / __denom, -__ilogbw);
if (isnan(__x) && isnan(__y)) {
if ((__denom == float(0)) && (!isnan(__a) || !isnan(__b))) {
#pragma warning(suppress : 4756) // Ignore INFINITY related warning
__x = copysignf(INFINITY, __c) * __a;
#pragma warning(suppress : 4756) // Ignore INFINITY related warning
__y = copysignf(INFINITY, __c) * __b;
} else if ((isinf(__a) || isinf(__b)) && isfinite(__c) && isfinite(__d)) {
__a = copysignf(isinf(__a) ? float(1) : float(0), __a);
__b = copysignf(isinf(__b) ? float(1) : float(0), __b);
#pragma warning(suppress : 4756) // Ignore INFINITY related warning
__x = INFINITY * (__a * __c + __b * __d);
#pragma warning(suppress : 4756) // Ignore INFINITY related warning
__y = INFINITY * (__b * __c - __a * __d);
} else if (isinf(__logbw) && __logbw > float(0) && isfinite(__a) &&
isfinite(__b)) {
__c = copysignf(isinf(__c) ? float(1) : float(0), __c);
__d = copysignf(isinf(__d) ? float(1) : float(0), __d);
__x = float(0) * (__a * __c + __b * __d);
__y = float(0) * (__b * __c - __a * __d);
}
}
return complex<float>(__x, __y);
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator/(const complex<_Tp> &__x,
const _Tp &__y) {
return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator/(const _Tp &__x,
const complex<_Tp> &__y) {
complex<_Tp> __t(__x);
__t /= __y;
return __t;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator+(const complex<_Tp> &__x) {
return __x;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> operator-(const complex<_Tp> &__x) {
return complex<_Tp>(-__x.real(), -__x.imag());
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER bool operator==(const complex<_Tp> &__x,
const complex<_Tp> &__y) {
return __x.real() == __y.real() && __x.imag() == __y.imag();
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER bool operator==(const complex<_Tp> &__x,
const _Tp &__y) {
return __x.real() == __y && __x.imag() == 0;
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER bool operator==(const _Tp &__x,
const complex<_Tp> &__y) {
return __x == __y.real() && 0 == __y.imag();
}
template <class _Tp>inline CUDA_CALLABLE_MEMBER bool operator!=(const complex<_Tp> &__x,
const complex<_Tp> &__y) {
return !(__x == __y);
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER bool operator!=(const complex<_Tp> &__x,
const _Tp &__y) {
return !(__x == __y);
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER bool operator!=(const _Tp &__x,
const complex<_Tp> &__y) {
return !(__x == __y);
}
// 26.3.7 values:
// real
template <class _Tp>
inline CUDA_CALLABLE_MEMBER _Tp real(const complex<_Tp> &__c) {
return __c.real();
}
inline CUDA_CALLABLE_MEMBER double real(double __re) { return __re; }
inline CUDA_CALLABLE_MEMBER float real(float __re) { return __re; }
// imag
template <class _Tp>
inline CUDA_CALLABLE_MEMBER _Tp imag(const complex<_Tp> &__c) {
return __c.imag();
}
inline CUDA_CALLABLE_MEMBER double imag(double __re) { return 0; }
inline CUDA_CALLABLE_MEMBER float imag(float __re) { return 0; }
// abs
template <class _Tp>
inline CUDA_CALLABLE_MEMBER _Tp abs(const complex<_Tp> &__c) {
return hypot(__c.real(), __c.imag());
}
// arg
template <class _Tp>
inline CUDA_CALLABLE_MEMBER _Tp arg(const complex<_Tp> &__c) {
return atan2(__c.imag(), __c.real());
}
inline CUDA_CALLABLE_MEMBER double arg(double __re) { return atan2(0., __re); }
inline CUDA_CALLABLE_MEMBER float arg(float __re) { return atan2f(0.F, __re); }
// norm
template <class _Tp>
inline CUDA_CALLABLE_MEMBER _Tp norm(const complex<_Tp> &__c) {
if (isinf(__c.real()))
return fabs(__c.real());
if (isinf(__c.imag()))
return fabs(__c.imag());
return __c.real() * __c.real() + __c.imag() * __c.imag();
}
inline CUDA_CALLABLE_MEMBER double norm(double __re) { return __re * __re; }
inline CUDA_CALLABLE_MEMBER float norm(float __re) { return __re * __re; }
// conj
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> conj(const complex<_Tp> &__c) {
return complex<_Tp>(__c.real(), -__c.imag());
}
inline CUDA_CALLABLE_MEMBER complex<double> conj(double __re) {
return complex<double>(__re);
}
inline CUDA_CALLABLE_MEMBER complex<float> conj(float __re) {
return complex<float>(__re);
}
// proj
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> proj(const complex<_Tp> &__c) {
complex<_Tp> __r = __c;
if (isinf(__c.real()) || isinf(__c.imag()))
__r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
return __r;
}
inline CUDA_CALLABLE_MEMBER complex<double> proj(double __re) {
if (isinf(__re))
__re = fabs(__re);
return complex<double>(__re);
}
inline CUDA_CALLABLE_MEMBER complex<float> proj(float __re) {
if (isinf(__re))
__re = fabs(__re);
return complex<float>(__re);
}
// polar
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> polar(const _Tp &__rho,
const _Tp &__theta = _Tp(0)) {
if (isnan(__rho) || signbit(__rho))
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
if (isnan(__theta)) {
if (isinf(__rho))
return complex<_Tp>(__rho, __theta);
return complex<_Tp>(__theta, __theta);
}
if (isinf(__theta)) {
if (isinf(__rho))
return complex<_Tp>(__rho, _Tp(NAN));
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
}
_Tp __x = __rho * cos(__theta);
if (isnan(__x))
__x = 0;
_Tp __y = __rho * sin(__theta);
if (isnan(__y))
__y = 0;
return complex<_Tp>(__x, __y);
}
// log
template <class _Tp>inline CUDA_CALLABLE_MEMBER complex<_Tp> log(const complex<_Tp> &__x) {
return complex<_Tp>(log(abs(__x)), arg(__x));
}
// log10
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> log10(const complex<_Tp> &__x) {
return log(__x) / log(_Tp(10));
}
// sqrt
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> sqrt(const complex<_Tp> &__x) {
if (isinf(__x.imag()))
return complex<_Tp>(_Tp(INFINITY), __x.imag());
if (isinf(__x.real())) {
if (__x.real() > _Tp(0))
return complex<_Tp>(__x.real(), isnan(__x.imag())
? __x.imag()
: copysign(_Tp(0), __x.imag()));
return complex<_Tp>(isnan(__x.imag()) ? __x.imag() : _Tp(0),
copysign(__x.real(), __x.imag()));
}
return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
}
// exp
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> exp(const complex<_Tp> &__x) {
_Tp __i = __x.imag();
if (isinf(__x.real())) {
if (__x.real() < _Tp(0)) {
if (!isfinite(__i))
__i = _Tp(1);
} else if (__i == 0 || !isfinite(__i)) {
if (isinf(__i))
__i = _Tp(NAN);
return complex<_Tp>(__x.real(), __i);
}
} else if (isnan(__x.real()) && __x.imag() == 0)
return __x;
_Tp __e = exp(__x.real());
return complex<_Tp>(__e * cos(__i), __e * sin(__i));
}
// pow
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> pow(const complex<_Tp> &__x,
const complex<_Tp> &__y) {
return exp(__y * log(__x));
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> pow(const complex<_Tp> &__x,
const _Tp &__y) {
return pow(__x, complex<_Tp>(__y));
}
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> pow(const _Tp &__x,
const complex<_Tp> &__y) {
return pow(complex<_Tp>(__x), __y);
}
// asinh
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> asinh(const complex<_Tp> &__x) {
const _Tp __pi(atan2(+0., -0.));
if (isinf(__x.real())) {
if (isnan(__x.imag()))
return __x;
if (isinf(__x.imag()))
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
}
if (isnan(__x.real())) {
if (isinf(__x.imag()))
return complex<_Tp>(__x.imag(), __x.real());
if (__x.imag() == 0)
return __x;
return complex<_Tp>(__x.real(), __x.real());
}
if (isinf(__x.imag()))
return complex<_Tp>(copysign(__x.imag(), __x.real()),
copysign(__pi / _Tp(2), __x.imag()));
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
return complex<_Tp>(copysign(__z.real(), __x.real()),
copysign(__z.imag(), __x.imag()));
}
// acosh
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> acosh(const complex<_Tp> &__x) {
const _Tp __pi(atan2(+0., -0.));
if (isinf(__x.real())) {
if (isnan(__x.imag()))
return complex<_Tp>(fabs(__x.real()), __x.imag());
if (isinf(__x.imag()))
if (__x.real() > 0)
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
else
return complex<_Tp>(-__x.real(),
copysign(__pi * _Tp(0.75), __x.imag()));
if (__x.real() < 0)
return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
}
if (isnan(__x.real())) {
if (isinf(__x.imag()))
return complex<_Tp>(fabs(__x.imag()), __x.real());
return complex<_Tp>(__x.real(), __x.real());
}
if (isinf(__x.imag()))
return complex<_Tp>(fabs(__x.imag()), copysign(__pi / _Tp(2), __x.imag()));
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
return complex<_Tp>(copysign(__z.real(), _Tp(0)),
copysign(__z.imag(), __x.imag()));
}
// atanh
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> atanh(const complex<_Tp> &__x) {
const _Tp __pi(atan2(+0., -0.));
if (isinf(__x.imag())) {
return complex<_Tp>(copysign(_Tp(0), __x.real()),
copysign(__pi / _Tp(2), __x.imag()));
}
if (isnan(__x.imag())) {
if (isinf(__x.real()) || __x.real() == 0)
return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
return complex<_Tp>(__x.imag(), __x.imag());
}
if (isnan(__x.real())) { return complex<_Tp>(__x.real(), __x.real());
}
if (isinf(__x.real())) {
return complex<_Tp>(copysign(_Tp(0), __x.real()),
copysign(__pi / _Tp(2), __x.imag()));
}
if (fabs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0)) {
return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()),
copysign(_Tp(0), __x.imag()));
}
complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
return complex<_Tp>(copysign(__z.real(), __x.real()),
copysign(__z.imag(), __x.imag()));
}
// sinh
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> sinh(const complex<_Tp> &__x) {
if (isinf(__x.real()) && !isfinite(__x.imag()))
return complex<_Tp>(__x.real(), _Tp(NAN));
if (__x.real() == 0 && !isfinite(__x.imag()))
return complex<_Tp>(__x.real(), _Tp(NAN));
if (__x.imag() == 0 && !isfinite(__x.real()))
return __x;
return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()),
cosh(__x.real()) * sin(__x.imag()));
}
// cosh
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> cosh(const complex<_Tp> &__x) {
if (isinf(__x.real()) && !isfinite(__x.imag()))
return complex<_Tp>(fabs(__x.real()), _Tp(NAN));
if (__x.real() == 0 && !isfinite(__x.imag()))
return complex<_Tp>(_Tp(NAN), __x.real());
if (__x.real() == 0 && __x.imag() == 0)
return complex<_Tp>(_Tp(1), __x.imag());
if (__x.imag() == 0 && !isfinite(__x.real()))
return complex<_Tp>(fabs(__x.real()), __x.imag());
return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()),
sinh(__x.real()) * sin(__x.imag()));
}
// tanh
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> tanh(const complex<_Tp> &__x) {
if (isinf(__x.real())) {
if (!isfinite(__x.imag()))
return complex<_Tp>(_Tp(1), _Tp(0));
return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
}
if (isnan(__x.real()) && __x.imag() == 0)
return __x;
_Tp __2r(_Tp(2) * __x.real());
_Tp __2i(_Tp(2) * __x.imag());
_Tp __d(cosh(__2r) + cos(__2i));
return complex<_Tp>(sinh(__2r) / __d, sin(__2i) / __d);
}
// asin
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> asin(const complex<_Tp> &__x) {
complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// acos
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> acos(const complex<_Tp> &__x) {
const _Tp __pi(atan2(+0., -0.));
if (isinf(__x.real())) {
if (isnan(__x.imag()))
return complex<_Tp>(__x.imag(), __x.real());
if (isinf(__x.imag())) {
if (__x.real() < _Tp(0))
return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
}
if (__x.real() < _Tp(0))
return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
}
if (isnan(__x.real())) {
if (isinf(__x.imag()))
return complex<_Tp>(__x.real(), -__x.imag());
return complex<_Tp>(__x.real(), __x.real());
}
if (isinf(__x.imag()))
return complex<_Tp>(__pi / _Tp(2), -__x.imag());
if (__x.real() == 0)
return complex<_Tp>(__pi / _Tp(2), -__x.imag());
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
if (signbit(__x.imag()))
return complex<_Tp>(fabs(__z.imag()), fabs(__z.real()));
return complex<_Tp>(fabs(__z.imag()), -fabs(__z.real()));
}
// atan
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> atan(const complex<_Tp> &__x) {
complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// sin
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> sin(const complex<_Tp> &__x) {
complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// cos
template <class _Tp>
inline CUDA_CALLABLE_MEMBER complex<_Tp> cos(const complex<_Tp> &__x) {
return cosh(complex<_Tp>(-__x.imag(), __x.real()));
}
// tan
template <class _Tp>
CUDA_CALLABLE_MEMBER complex<_Tp> tan(const complex<_Tp> &__x) {
complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
template <class _Tp, class _CharT, class _Traits>
std::basic_istream<_CharT, _Traits> &
operator>>(std::basic_istream<_CharT, _Traits> &__is, complex<_Tp> &__x) {
if (__is.good()) {
ws(__is);
if (__is.peek() == _CharT('(')) {
__is.get(); _Tp __r;
__is >> __r;
if (!__is.fail()) {
ws(__is);
_CharT __c = __is.peek();
if (__c == _CharT(',')) {
__is.get();
_Tp __i;
__is >> __i;
if (!__is.fail()) {
ws(__is);
__c = __is.peek();
if (__c == _CharT(')')) {
__is.get();
__x = complex<_Tp>(__r, __i);
} else
__is.setstate(std::ios_base::failbit);
} else
__is.setstate(std::ios_base::failbit);
} else if (__c == _CharT(')')) {
__is.get();
__x = complex<_Tp>(__r, _Tp(0));
} else
__is.setstate(std::ios_base::failbit);
} else
__is.setstate(std::ios_base::failbit);
} else {
_Tp __r;
__is >> __r;
if (!__is.fail())
__x = complex<_Tp>(__r, _Tp(0));
else
__is.setstate(std::ios_base::failbit);
}
} else
__is.setstate(std::ios_base::failbit);
return __is;
}
template <class _Tp, class _CharT, class _Traits>
std::basic_ostream<_CharT, _Traits> &
operator<<(std::basic_ostream<_CharT, _Traits> &__os, const complex<_Tp> &__x) {
std::basic_ostringstream<_CharT, _Traits> __s;
__s.flags(__os.flags());
__s.imbue(__os.getloc());
__s.precision(__os.precision());
__s << '(' << __x.real() << ',' << __x.imag() << ')';
return __os << __s.str();
}
//} // close namespace cuda_complex
template <class U, class V>
CUDA_CALLABLE_MEMBER auto operator*(const complex<U> &complexNumber,
const V &scalar) -> complex<U> {
return complex<U>{real(complexNumber) * scalar, imag(complexNumber) * scalar};
}
template <class U, class V>
CUDA_CALLABLE_MEMBER auto operator*(const V &scalar,
const complex<U> &complexNumber)
-> complex<U> {
return complex<U>{real(complexNumber) * scalar, imag(complexNumber) * scalar};
}
template <class U, class V>
CUDA_CALLABLE_MEMBER auto operator+(const complex<U> &complexNumber,
const V &scalar) -> complex<U> {
return complex<U>{real(complexNumber) + scalar, imag(complexNumber)};
}
template <class U, class V>
CUDA_CALLABLE_MEMBER auto operator+(const V &scalar,
const complex<U> &complexNumber)
-> complex<U> {
return complex<U>{real(complexNumber) + scalar, imag(complexNumber)};
}
template <class U, class V>
CUDA_CALLABLE_MEMBER auto operator-(const complex<U> &complexNumber,
const V &scalar) -> complex<U> {
return complex<U>{real(complexNumber) - scalar, imag(complexNumber)};
}
template <class U, class V>
CUDA_CALLABLE_MEMBER auto operator-(const V &scalar,
const complex<U> &complexNumber)
-> complex<U> {
return complex<U>{scalar - real(complexNumber), imag(complexNumber)};
}
template <class U, class V>
CUDA_CALLABLE_MEMBER auto operator/(const complex<U> &complexNumber,
const V scalar) -> complex<U> {
return complex<U>{real(complexNumber) / scalar, imag(complexNumber) / scalar};
}
template <class U, class V>
CUDA_CALLABLE_MEMBER auto operator/(const V scalar,
const complex<U> &complexNumber)
-> complex<U> {
return complex<U>{scalar, 0} / complexNumber;
}
using ComplexDouble = complex<double>;
using ComplexFloat = complex<float>;
#endif // CUDA_COMPLEX_HPP
}