43.复数运算

complex_test.cpp

#pragma once

#include <iostream>
#include "complex.h"

using namespace std;

ostream&
operator << (ostream& os, const complex& x)
{
	return os << '(' << real(x) << ',' << imag(x) << ')';
}

int main()
{
	complex c1(2, 1);
	complex c2(4, 0);

	cout << c1 << endl;
	cout << c2 << endl;

	cout << c1 + c2 << endl;
	cout << c1 - c2 << endl;
	cout << c1 * c2 << endl;
	cout << c1 / 2 << endl;

	cout << conj(c1) << endl;
	cout << norm(c1) << endl;
	cout << polar(10, 4) << endl;

	cout << (c1 += c2) << endl;

	cout << (c1 == c2) << endl;
	cout << (c1 != c2) << endl;
	cout << +c2 << endl;
	cout << -c2 << endl;

	cout << (c2 - 2) << endl;
	cout << (5 + c2) << endl;

	return 0;
}

complex.h

#pragma once
#ifndef __MYCOMPLEX__
#define __MYCOMPLEX__

class complex;
complex&
__doapl(complex* ths, const complex& r);
complex&
__doami(complex* ths, const complex& r);
complex&
__doaml(complex* ths, const complex& r);


class complex
{
public:
	complex(double r = 0, double i = 0) : re(r), im(i) { }
	complex& operator += (const complex&);
	complex& operator -= (const complex&);
	complex& operator *= (const complex&);
	complex& operator /= (const complex&);
	double real() const { return re; }
	double imag() const { return im; }
private:
	double re, im;

	friend complex& __doapl(complex*, const complex&);
	friend complex& __doami(complex*, const complex&);
	friend complex& __doaml(complex*, const complex&);
};


inline complex&
__doapl(complex* ths, const complex& r)
{
	ths->re += r.re;
	ths->im += r.im;
	return *ths;
}

inline complex&
complex::operator += (const complex& r)
{
	return __doapl(this, r);
}

inline complex&
__doami(complex* ths, const complex& r)
{
	ths->re -= r.re;
	ths->im -= r.im;
	return *ths;
}

inline complex&
complex::operator -= (const complex& r)
{
	return __doami(this, r);
}

inline complex&
__doaml(complex* ths, const complex& r)
{
	double f = ths->re * r.re - ths->im * r.im;
	ths->im = ths->re * r.im + ths->im * r.re;
	ths->re = f;
	return *ths;
}

inline complex&
complex::operator *= (const complex& r)
{
	return __doaml(this, r);
}

inline double
imag(const complex& x)
{
	return x.imag();
}

inline double
real(const complex& x)
{
	return x.real();
}

inline complex
operator + (const complex& x, const complex& y)
{
	return complex(real(x) + real(y), imag(x) + imag(y));
}

inline complex
operator + (const complex& x, double y)
{
	return complex(real(x) + y, imag(x));
}

inline complex
operator + (double x, const complex& y)
{
	return complex(x + real(y), imag(y));
}

inline complex
operator - (const complex& x, const complex& y)
{
	return complex(real(x) - real(y), imag(x) - imag(y));
}

inline complex
operator - (const complex& x, double y)
{
	return complex(real(x) - y, imag(x));
}

inline complex
operator - (double x, const complex& y)
{
	return complex(x - real(y), -imag(y));
}

inline complex
operator * (const complex& x, const complex& y)
{
	return complex(real(x) * real(y) - imag(x) * imag(y),
		real(x) * imag(y) + imag(x) * real(y));
}

inline complex
operator * (const complex& x, double y)
{
	return complex(real(x) * y, imag(x) * y);
}

inline complex
operator * (double x, const complex& y)
{
	return complex(x * real(y), x * imag(y));
}

complex
operator / (const complex& x, double y)
{
	return complex(real(x) / y, imag(x) / y);
}

inline complex
operator + (const complex& x)
{
	return x;
}

inline complex
operator - (const complex& x)
{
	return complex(-real(x), -imag(x));
}

inline bool
operator == (const complex& x, const complex& y)
{
	return real(x) == real(y) && imag(x) == imag(y);
}

inline bool
operator == (const complex& x, double y)
{
	return real(x) == y && imag(x) == 0;
}

inline bool
operator == (double x, const complex& y)
{
	return x == real(y) && imag(y) == 0;
}

inline bool
operator != (const complex& x, const complex& y)
{
	return real(x) != real(y) || imag(x) != imag(y);
}

inline bool
operator != (const complex& x, double y)
{
	return real(x) != y || imag(x) != 0;
}

inline bool
operator != (double x, const complex& y)
{
	return x != real(y) || imag(y) != 0;
}

#include <cmath>

inline complex
polar(double r, double t)
{
	return complex(r * cos(t), r * sin(t));
}

inline complex
conj(const complex& x)
{
	return complex(real(x), -imag(x));
}

inline double
norm(const complex& x)
{
	return real(x) * real(x) + imag(x) * imag(x);
}

#endif   //__MYCOMPLEX__

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