complex.h
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/*RTS Complex number class. This class is CUDA compatible,
and can therefore be used in CUDA code and on CUDA devices.
*/
#ifndef RTS_COMPLEX
#define RTS_COMPLEX
#include "cuda_callable.h"
#include <cmath>
#include <string>
#include <sstream>
#include <iostream>
namespace rts
{
template <class T>
struct complex
{
T r, i;
//default constructor
CUDA_CALLABLE complex()
{
r = 0.0;
i = 0.0;
}
//access methods
CUDA_CALLABLE T real()
{
return r;
}
CUDA_CALLABLE T real(T r_val)
{
r = r_val;
return r_val;
}
CUDA_CALLABLE T imag()
{
return i;
}
CUDA_CALLABLE T imag(T i_val)
{
i = i_val;
return i_val;
}
//constructor when given real and imaginary values
CUDA_CALLABLE complex(T r, T i)
{
this->r = r;
this->i = i;
}
//return the current value multiplied by i
CUDA_CALLABLE complex<T> imul()
{
complex<T> result;
result.r = -i;
result.i = r;
return result;
}
//ARITHMETIC OPERATORS--------------------
//binary + operator (returns the result of adding two complex values)
CUDA_CALLABLE complex<T> operator+ (const complex<T> rhs)
{
complex<T> result;
result.r = r + rhs.r;
result.i = i + rhs.i;
return result;
}
CUDA_CALLABLE complex<T> operator+ (const T rhs)
{
complex<T> result;
result.r = r + rhs;
result.i = i;
return result;
}
//binary - operator (returns the result of adding two complex values)
CUDA_CALLABLE complex<T> operator- (const complex<T> rhs)
{
complex<T> result;
result.r = r - rhs.r;
result.i = i - rhs.i;
return result;
}
//binary - operator (returns the result of adding two complex values)
CUDA_CALLABLE complex<T> operator- (const T rhs)
{
complex<T> result;
result.r = r - rhs;
result.i = i;
return result;
}
//binary MULTIPLICATION operators (returns the result of multiplying complex values)
CUDA_CALLABLE complex<T> operator* (const complex<T> rhs)
{
complex<T> result;
result.r = r * rhs.r - i * rhs.i;
result.i = r * rhs.i + i * rhs.r;
return result;
}
CUDA_CALLABLE complex<T> operator* (const T rhs)
{
return complex<T>(r * rhs, i * rhs);
}
//binary DIVISION operators (returns the result of dividing complex values)
CUDA_CALLABLE complex<T> operator/ (const complex<T> rhs)
{
complex<T> result;
T denom = rhs.r * rhs.r + rhs.i * rhs.i;
result.r = (r * rhs.r + i * rhs.i) / denom;
result.i = (- r * rhs.i + i * rhs.r) / denom;
return result;
}
CUDA_CALLABLE complex<T> operator/ (const T rhs)
{
return complex<T>(r / rhs, i / rhs);
}
//ASSIGNMENT operators-----------------------------------
CUDA_CALLABLE complex<T> & operator=(const complex<T> &rhs)
{
//check for self-assignment
if(this != &rhs)
{
this->r = rhs.r;
this->i = rhs.i;
}
return *this;
}
CUDA_CALLABLE complex<T> & operator=(const T &rhs)
{
this->r = rhs;
this->i = 0;
return *this;
}
//arithmetic assignment operators
CUDA_CALLABLE complex<T> operator+=(const complex<T> &rhs)
{
*this = *this + rhs;
return *this;
}
CUDA_CALLABLE complex<T> operator+=(const T &rhs)
{
*this = *this + rhs;
return *this;
}
CUDA_CALLABLE complex<T> operator*=(const complex<T> &rhs)
{
*this = *this * rhs;
return *this;
}
CUDA_CALLABLE complex<T> operator*=(const T &rhs)
{
*this = *this * rhs;
return *this;
}
//divide and assign
CUDA_CALLABLE complex<T> operator/=(const complex<T> &rhs)
{
*this = *this / rhs;
return *this;
}
CUDA_CALLABLE complex<T> operator/=(const T &rhs)
{
*this = *this / rhs;
return *this;
}
//absolute value operator (returns the absolute value of the complex number)
CUDA_CALLABLE T abs()
{
return std::sqrt(r * r + i * i);
}
CUDA_CALLABLE complex<T> log()
{
complex<T> result;
result.r = std::log(std::sqrt(r * r + i * i));
result.i = std::atan2(i, r);
return result;
}
CUDA_CALLABLE complex<T> exp()
{
complex<T> result;
T e_r = std::exp(r);
result.r = e_r * std::cos(i);
result.i = e_r * std::sin(i);
return result;
}
/*CUDA_CALLABLE complex<T> pow(int y)
{
return pow((double)y);
}*/
CUDA_CALLABLE complex<T> pow(T y)
{
complex<T> result;
result = log() * y;
return result.exp();
}
CUDA_CALLABLE complex<T> sqrt()
{
complex<T> result;
//convert to polar coordinates
T a = std::sqrt(r*r + i*i);
T theta = std::atan2(i, r);
//find the square root
T a_p = std::sqrt(a);
T theta_p = theta/2.0;
//convert back to cartesian coordinates
result.r = a_p * std::cos(theta_p);
result.i = a_p * std::sin(theta_p);
return result;
}
std::string toStr()
{
std::stringstream ss;
ss<<"("<<r<<","<<i<<")";
return ss.str();
}
//COMPARISON operators
CUDA_CALLABLE bool operator==(complex<T> rhs)
{
if(r == rhs.r && i == rhs.i)
return true;
return false;
}
CUDA_CALLABLE bool operator==(T rhs)
{
if(r == rhs && i == (T)0.0)
return true;
return false;
}
};
} //end RTS namespace
//addition
template<typename T>
CUDA_CALLABLE static rts::complex<T> operator+(const double a, const rts::complex<T> b)
{
return rts::complex<T>(a + b.r, b.i);
}
//subtraction with a real value
template<typename T>
CUDA_CALLABLE static rts::complex<T> operator-(const double a, const rts::complex<T> b)
{
return rts::complex<T>(a - b.r, -b.i);
}
//minus sign
template<typename T>
CUDA_CALLABLE static rts::complex<T> operator-(const rts::complex<T> &rhs)
{
return rts::complex<T>(-rhs.r, -rhs.i);
}
//multiply a T value by a complex value
template<typename T>
CUDA_CALLABLE static rts::complex<T> operator*(const double a, const rts::complex<T> b)
{
return rts::complex<T>((T)a * b.r, (T)a * b.i);
}
//divide a T value by a complex value
template<typename T>
CUDA_CALLABLE static rts::complex<T> operator/(const double a, const rts::complex<T> b)
{
//return complex<T>(a * b.r, a * b.i);
rts::complex<T> result;
T denom = b.r * b.r + b.i * b.i;
result.r = (a * b.r) / denom;
result.i = -(a * b.i) / denom;
return result;
}
//POW function
/*template<typename T>
CUDA_CALLABLE static complex<T> pow(complex<T> x, int y)
{
return x.pow(y);
}*/
template<typename T>
CUDA_CALLABLE static rts::complex<T> pow(rts::complex<T> x, T y)
{
return x.pow(y);
}
//log function
template<typename T>
CUDA_CALLABLE static rts::complex<T> log(rts::complex<T> x)
{
return x.log();
}
//exp function
template<typename T>
CUDA_CALLABLE static rts::complex<T> exp(rts::complex<T> x)
{
return x.exp();
}
//sqrt function
template<typename T>
CUDA_CALLABLE static rts::complex<T> sqrt(rts::complex<T> x)
{
return x.sqrt();
}
template <typename T>
CUDA_CALLABLE static T abs(rts::complex<T> a)
{
return a.abs();
}
template <typename T>
CUDA_CALLABLE static T real(rts::complex<T> a)
{
return a.r;
}
//template <typename T>
CUDA_CALLABLE static float real(float a)
{
return a;
}
template <typename T>
CUDA_CALLABLE static T imag(rts::complex<T> a)
{
return a.i;
}
//trigonometric functions
template<class A>
CUDA_CALLABLE rts::complex<A> sin(const rts::complex<A> x)
{
rts::complex<A> result;
result.r = std::sin(x.r) * std::cosh(x.i);
result.i = std::cos(x.r) * std::sinh(x.i);
return result;
}
template<class A>
CUDA_CALLABLE rts::complex<A> cos(const rts::complex<A> x)
{
rts::complex<A> result;
result.r = std::cos(x.r) * std::cosh(x.i);
result.i = -(std::sin(x.r) * std::sinh(x.i));
return result;
}
template<class A>
std::ostream& operator<<(std::ostream& os, rts::complex<A> x)
{
os<<x.toStr();
return os;
}
#if __GNUC__ > 3 && __GNUC_MINOR__ > 7
template<class T> using rtsComplex = rts::complex<T>;
#endif
#endif