#ifndef _COMPLEX_H
#define _COMPLEX_H

/* COMPLEX.H header file		
 * use for complex arithmetic in C 
 (part of them are from "C Tools for Scientists and Engineers" by L. Baker)
*/
extern double cos(double);
extern double sin(double);
struct __COMPLEX{ double x,y; };
typedef struct __COMPLEX COMPLEX;

/* for below, X, Y are complex structures, and one is returned */

/*//real part of the complex multiplication */
#define CMULTR(X,Y) ((X).x*(Y).x-(X).y*(Y).y)
/*//image part of the complex multiplication */
#define CMULTI(X,Y) ((X).y*(Y).x+(X).x*(Y).y)
/*// used in the Division : real part of the division */
#define CDRN(X,Y) ((X).x*(Y).x+(Y).y*(X).y)
/*// used in the Division : image part of the division */
#define CDIN(X,Y) ((X).y*(Y).x-(X).x*(Y).y)
/*// used in the Division : denumerator of the division */
#define CNORM(X) ((X).x*(X).x+(X).y*(X).y)
/*//real part of the complex */
#define CREAL(X) ((double)((X).x))
/*//conjunction value */
#define CONJG(z,X) {(z).x=(X).x;(z).y= -(X).y;}
/*//conjunction value */
#define CONJ(X) {(X).y= -(X).y;}
/*//muliply : z could not be same variable as X or Y, same rule for other Macro */
#define CMULT(z,X,Y) {(z).x=CMULTR((X),(Y));(z).y=CMULTI((X),(Y));}
/*//division */
#define CDIV(z,X,Y){double d=CNORM(Y); (z).x=CDRN(X,Y)/d; (z).y=CDIN(X,Y)/d;}
/*//addition */
#define CADD(z,X,Y) {(z).x=(X).x+(Y).x;(z).y=(X).y+(Y).y;}
/*//subtraction */
#define CSUB(z,X,Y) {(z).x=(X).x-(Y).x;(z).y=(X).y-(Y).y;}
/*//assign */
#define CLET(to,from) {(to).x=(from).x;(to).y=(from).y;}
/*//abstract value(magnitude) */
#define cabs(X) sqrt((X).y*(X).y+(X).x*(X).x)
/*//real to complex */
#define CMPLX(X,real,imag) {(X).x=(real);(X).y=(imag);}
/*//multiply with real */
#define CTREAL(z,X,real) {(z).x=(X).x*(real);(z).y=(X).y*(real);}

#define CEXP(z,phase) {(z).x = cos(phase); (z).y = sin(phase); }
/* implementation using function : for compatibility */
COMPLEX compdiv(COMPLEX ne,COMPLEX de);
COMPLEX compexp(double theta);
COMPLEX compmult(double scalar,COMPLEX compnum);
COMPLEX compprod(COMPLEX compnum1, COMPLEX compnum2);
COMPLEX comp2sum(COMPLEX summand1, COMPLEX summand2);
COMPLEX comp3sum(COMPLEX summand1, COMPLEX summand2, COMPLEX summand3);
COMPLEX compsubtract(COMPLEX complexA, COMPLEX complexB);
double  REAL(COMPLEX compnum);

#endif