通过 Complex 类学习的知识

前言：侯捷老师讲的真不错，做个总结。

源码

// complex.h
#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__

// complex_test.cpp
#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;
}

学到的知识

• 写一个头文件的时候要使用 #ifndef

#ifndef __MYCOMPLEX__
#define __MYCOMPLEX__

#endif   //__MYCOMPLEX__

目的就是 #include 的顺序可以随意。不用规定谁在谁前面。

• 什么是「友元函数」

由上面的例子可以看到，类中有一个函数：

friend complex& __doapl (complex *, const complex&);

这个函数要使用到 complex 类内部的东西。所以要在 complex 类的内部定义「友元函数」。

• 如果类的一个函数不会修改类的数据，那么请做一个 const 标记。

double real () const { return re; }

原因如下：

#include <iostream>

using namespace std;

class A {
public:
    A(int h = 0):h(h){}
    int foo() {
        return h;
    }
private:
    int h;
};
int main() {
    const A a = A(10);
    a.foo();
    return 0;
}

这样写就会报错，原因是 a.foo() 在编译器看来可能修改 a 的数据，但是 a 是 const 所以会报错。

• 传递尽可能使用引用，传递引用的时候如果不修改尽量使用 const。

• 相同 class 的各个 objects 互为 friends（友元）

• inline 减少函数调用的开销，加上以后编译器会判断用不用 inline。

• 操作符会调用左值，操作符重载有两种写法，一种写在类里面一种写在类外面。