complex.h 8.05 KB
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411
/*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