C++重载数学运算符（实例演示）

四则运算符（+、-、*、/、+=、-=、*=、/=）和关系运算符（>、<、<=、>=、==、!=）都是数学运算符，它们在实际开发中非常常见，被重载的几率也很高，并且有着相似的重载格式。本节以复数类 Complex 为例对它们进行重载，重在演示运算符重载的语法以及规范。

复数能够进行完整的四则运算，但不能进行完整的关系运算：我们只能判断两个复数是否相等，但不能比较它们的大小，所以不能对 >、<、<=、>= 进行重载。下面是具体的代码：

  #include <iostream>  #include <cmath>  using namespace std;    //复数类  class Complex{  public:  //构造函数      Complex(double real = 0.0, double imag = 0.0): m_real(real), m_imag(imag){ }  public:  //运算符重载      //以全局函数的形式重载      friend Complex operator+(const Complex &c1, const Complex &c2);      friend Complex operator-(const Complex &c1, const Complex &c2);      friend Complex operator*(const Complex &c1, const Complex &c2);      friend Complex operator/(const Complex &c1, const Complex &c2);      friend bool operator==(const Complex &c1, const Complex &c2);      friend bool operator!=(const Complex &c1, const Complex &c2);      //以成员函数的形式重载      Complex & operator+=(const Complex &c);      Complex & operator-=(const Complex &c);      Complex & operator*=(const Complex &c);      Complex & operator/=(const Complex &c);  public:  //成员函数      double real() const{ return m_real; }      double imag() const{ return m_imag; }  private:      double m_real;  //实部      double m_imag;  //虚部  };    //重载+运算符  Complex operator+(const Complex &c1, const Complex &c2){      Complex c;      c.m_real = c1.m_real + c2.m_real;      c.m_imag = c1.m_imag + c2.m_imag;      return c;  }  //重载-运算符  Complex operator-(const Complex &c1, const Complex &c2){      Complex c;      c.m_real = c1.m_real - c2.m_real;      c.m_imag = c1.m_imag - c2.m_imag;      return c;  }  //重载*运算符  (a+bi) * (c+di) = (ac-bd) + (bc+ad)i  Complex operator*(const Complex &c1, const Complex &c2){      Complex c;      c.m_real = c1.m_real * c2.m_real - c1.m_imag * c2.m_imag;      c.m_imag = c1.m_imag * c2.m_real + c1.m_real * c2.m_imag;      return c;  }  //重载/运算符  (a+bi) / (c+di) = [(ac+bd) / (c²+d²)] + [(bc-ad) / (c²+d²)]i  Complex operator/(const Complex &c1, const Complex &c2){      Complex c;      c.m_real = (c1.m_real*c2.m_real + c1.m_imag*c2.m_imag) / (pow(c2.m_real, 2) + pow(c2.m_imag, 2));      c.m_imag = (c1.m_imag*c2.m_real - c1.m_real*c2.m_imag) / (pow(c2.m_real, 2) + pow(c2.m_imag, 2));      return c;  }  //重载==运算符  bool operator==(const Complex &c1, const Complex &c2){      if( c1.m_real == c2.m_real && c1.m_imag == c2.m_imag ){          return true;      }else{          return false;      }  }  //重载!=运算符  bool operator!=(const Complex &c1, const Complex &c2){      if( c1.m_real != c2.m_real || c1.m_imag != c2.m_imag ){          return true;      }else{          return false;      }  }    //重载+=运算符  Complex & Complex::operator+=(const Complex &c){      this->m_real += c.m_real;      this->m_imag += c.m_imag;      return *this;  }  //重载-=运算符  Complex & Complex::operator-=(const Complex &c){      this->m_real -= c.m_real;      this->m_imag -= c.m_imag;      return *this;  }  //重载*=运算符  Complex & Complex::operator*=(const Complex &c){      this->m_real = this->m_real * c.m_real - this->m_imag * c.m_imag;      this->m_imag = this->m_imag * c.m_real + this->m_real * c.m_imag;      return *this;  }  //重载/=运算符  Complex & Complex::operator/=(const Complex &c){      this->m_real = (this->m_real*c.m_real + this->m_imag*c.m_imag) / (pow(c.m_real, 2) + pow(c.m_imag, 2));      this->m_imag = (this->m_imag*c.m_real - this->m_real*c.m_imag) / (pow(c.m_real, 2) + pow(c.m_imag, 2));      return *this;  }    int main(){      Complex c1(25, 35);      Complex c2(10, 20);      Complex c3(1, 2);      Complex c4(4, 9);      Complex c5(34, 6);      Complex c6(80, 90);           Complex c7 = c1 + c2;      Complex c8 = c1 - c2;      Complex c9 = c1 * c2;      Complex c10 = c1 / c2;      cout<<"c7 = "<<c7.real()<<" + "<<c7.imag()<<"i"<<endl;      cout<<"c8 = "<<c8.real()<<" + "<<c8.imag()<<"i"<<endl;      cout<<"c9 = "<<c9.real()<<" + "<<c9.imag()<<"i"<<endl;      cout<<"c10 = "<<c10.real()<<" + "<<c10.imag()<<"i"<<endl;           c3 += c1;      c4 -= c2;      c5 *= c2;      c6 /= c2;      cout<<"c3 = "<<c3.real()<<" + "<<c3.imag()<<"i"<<endl;      cout<<"c4 = "<<c4.real()<<" + "<<c4.imag()<<"i"<<endl;      cout<<"c5 = "<<c5.real()<<" + "<<c5.imag()<<"i"<<endl;      cout<<"c6 = "<<c6.real()<<" + "<<c6.imag()<<"i"<<endl;           if(c1 == c2){          cout<<"c1 == c2"<<endl;      }      if(c1 != c2){          cout<<"c1 != c2"<<endl;      }           return 0;  }

运行结果：
c7 = 35 + 55i
c8 = 15 + 15i
c9 = -450 + 850i
c10 = 1.9 + -0.3i
c3 = 26 + 37i
c4 = -6 + -11i
c5 = 220 + 4460i
c6 = 5.2 + 1.592i
c1 != c2

需要注意的是，我们以全局函数的形式重载了 +、-、*、/、==、!=，以成员函数的形式重载了 +=、-=、*=、/=，而且应该坚持这样做，不能一股脑都写作成员函数或者全局函数。