#include "complex.h"					// do not copy interface
#include <cmath>					// access: sqrt
using namespace std;					// ok within implementation

int Complex::cplxObjCnt = 0;				// define and initialize static variable

// interface implementations

Complex::Complex( double r, double i ) { re = r; im = i; cplxObjCnt += 1; }

double Complex::real() const { return re; }
double Complex::imag() const { return im; }

Complex Complex::conjugate() const { return Complex( re, -im ); }

double Complex::abs() const { return sqrt( re * re + im * im ); }

void Complex::stats() { cout << cplxObjCnt << endl; }

Complex operator+( Complex a, Complex b ) {
    return Complex( a.re + b.re, a.im + b.im );
}

Complex operator-( Complex a, Complex b ) {
    return Complex( a.re - b.re, a.im - b.im );
}

Complex operator*( Complex a, Complex b ) {
    return Complex( a.re * b.re - a.im * b.im, a.im * b.re + a.re * b.im );
}

Complex operator/( Complex a, Complex b ) {
    double dem = b.re * b.re + b.im * b.im;
    return Complex( (a.re * b.re + a.im * b.im) / dem,
		    (a.im * b.re + a.re * b.im) / dem );
}

bool operator==( Complex a, Complex b ) {
    return a.re == b.re && a.im == b.im;
}

bool operator!=( Complex a, Complex b ) {
    return ! (a == b);					// reuse code in ==
}

istream &operator>>( istream &is, Complex &c ) {
    return is >> c.re >> c.im;
}

ostream &operator<<( ostream &os, const Complex c ) {
    // let negative values, including negative zero, print the "-" sign for the imaginary value
    return os << c.re << (c.im < 0 || (c.im == 0.0 && signbit(c.im)) ? "" : "+") << c.im << "i";
}