問一個非常基礎的問題

[jjyang1704]

請問重載運符是怎麼算的,
如以下代碼的結果是怎麼來的.
c1.cs
using System;
public class Fraction
{
private int num,den;
public Fraction(int num,int den)
{
this.num=num;
this.den=den;
}
public static Fraction operator+(Fraction a,Fraction b)
{
return new Fraction(a.num*b.den+b.num*a.den,a.den*b.den);
}
public static Fraction operator_(Fraction a,Fraction b)
{
return new Fraction(a.num*b.den-b.num*a.den,a.den*b.den);
}
public static Fraction operator*(Fraction a,frantion b)
{
return new Fraction(a.num*b.num,a.den*b.den);
}
public static Fraction operator/(Fraction a,Fraction b)
{
return new Fraction(a.num*b.num,a.den*b.num);
}
public static implicit operator double(Fraction f)
{
return (double)f.num/f.den;
}
}
///////////////////////////////////
c2.cs
using System;
public class Operatortest
{
public static void Main()
{
Fraction a=new Fraction(1,2);
Fraction b=new Fraction(1,11);
Fraction c=new Fraction(3,7);
Fraction d=new Fraction(27,13);
Console.WriteLine(a);
Console.WriteLine(b);
Console.WriteLine(c);
Console.WriteLine(d);
double e=a*(b-c)/d+a;
Console.WriteLine("a*(b-c)/d+a={0}",e);
}
}

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教程
运算符重载允许为运算指定用户定义的运算符实现，其中一个或两个操作数是用户定义的类或结构类型。本教程包含两个示例。第一个示例展示如何使用运算符重载创建定义复数加法的复数类。第二个示例展示如何使用运算符重载实现三值的逻辑类型。
示例 1
本示例展示如何使用运算符重载创建定义复数加法的复数类 Complex。本程序使用 ToString 方法的重载显示数字的虚部和实部以及加法结果。
// complex.cs
using System;

public struct Complex
{
public int real;
public int imaginary;

public Complex(int real, int imaginary)
{
this.real = real;
this.imaginary = imaginary;
}

// Declare which operator to overload (+), the types
// that can be added (two Complex objects), and the
// return type (Complex):
public static Complex operator +(Complex c1, Complex c2)
{
return new Complex(c1.real + c2.real, c1.imaginary + c2.imaginary);
}
// Override the ToString method to display an complex number in the suitable format:
public override string ToString()
{
return(String.Format("{0} + {1}i", real, imaginary));
}

public static void Main()
{
Complex num1 = new Complex(2,3);
Complex num2 = new Complex(3,4);

// Add two Complex objects (num1 and num2) through the
// overloaded plus operator:
Complex sum = num1 + num2;

// Print the numbers and the sum using the overriden ToString method:
Console.WriteLine("First complex number: {0}",num1);
Console.WriteLine("Second complex number: {0}",num2);
Console.WriteLine("The sum of the two numbers: {0}",sum);

}
}
输出
First complex number: 2 + 3i
Second complex number: 3 + 4i
The sum of the two numbers: 5 + 7i

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示例 2
本示例展示如何使用运算符重载实现三值的逻辑类型。该类型的可能值有 DBBool.dbTrue、DBBool.dbFalse 和 DBBool.dbNull，其中 dbNull 成员表示未知值。
注意 定义 True 和 False 运算符只对表示 True、False 和 Null（既非 True 也非 False）的类型有用，如数据库中使用的类型。
// dbbool.cs
using System;

public struct DBBool
{
// The three possible DBBool values:
public static readonly DBBool dbNull = new DBBool(0);
public static readonly DBBool dbFalse = new DBBool(-1);
public static readonly DBBool dbTrue = new DBBool(1);
// Private field that stores -1, 0, 1 for dbFalse, dbNull, dbTrue:
int value;

// Private constructor. The value parameter must be -1, 0, or 1:
DBBool(int value)
{
this.value = value;
}

// Implicit conversion from bool to DBBool. Maps true to
// DBBool.dbTrue and false to DBBool.dbFalse:
public static implicit operator DBBool(bool x)
{
return x? dbTrue: dbFalse;
}

// Explicit conversion from DBBool to bool. Throws an
// exception if the given DBBool is dbNull, otherwise returns
// true or false:
public static explicit operator bool(DBBool x)
{
if (x.value == 0) throw new InvalidOperationException();
return x.value > 0;
}

// Equality operator. Returns dbNull if either operand is dbNull,
// otherwise returns dbTrue or dbFalse:
public static DBBool operator ==(DBBool x, DBBool y)
{
if (x.value == 0 || y.value == 0) return dbNull;
return x.value == y.value? dbTrue: dbFalse;
}

// Inequality operator. Returns dbNull if either operand is
// dbNull, otherwise returns dbTrue or dbFalse:
public static DBBool operator !=(DBBool x, DBBool y)
{
if (x.value == 0 || y.value == 0) return dbNull;
return x.value != y.value? dbTrue: dbFalse;
}

// Logical negation operator. Returns dbTrue if the operand is
// dbFalse, dbNull if the operand is dbNull, or dbFalse if the
// operand is dbTrue:
public static DBBool operator !(DBBool x)
{
return new DBBool(-x.value);
}

// Logical AND operator. Returns dbFalse if either operand is
// dbFalse, dbNull if either operand is dbNull, otherwise dbTrue:
public static DBBool operator &(DBBool x, DBBool y)
{
return new DBBool(x.value < y.value? x.value: y.value);
}

// Logical OR operator. Returns dbTrue if either operand is
// dbTrue, dbNull if either operand is dbNull, otherwise dbFalse:
public static DBBool operator |(DBBool x, DBBool y)
{
return new DBBool(x.value > y.value? x.value: y.value);
}

// Definitely true operator. Returns true if the operand is
// dbTrue, false otherwise:
public static bool operator true(DBBool x)
{
return x.value > 0;
}

// Definitely false operator. Returns true if the operand is
// dbFalse, false otherwise:
public static bool operator false(DBBool x)
{
return x.value < 0;
}

// Overload the conversion from DBBool to string:
public static implicit operator string(DBBool x)
{
return x.value > 0 ? "dbTrue"
: x.value < 0 ? "dbFalse"
: "dbNull";
}

// Override the Object.Equals(object o) method:
public override bool Equals(object o)
{
try
{
return (bool) (this == (DBBool) o);
}
catch
{
return false;
}
}

// Override the Object.GetHashCode() method:
public override int GetHashCode()
{
return value;
}

// Override the ToString method to convert DBBool to a string:
public override string ToString()
{
switch (value)
{
case -1:
return "DBBool.False";
case 0:
return "DBBool.Null";
case 1:
return "DBBool.True";
default:
throw new InvalidOperationException();
}
}
}

class Test
{
static void Main()
{
DBBool a, b;
a = DBBool.dbTrue;
b = DBBool.dbNull;

Console.WriteLine( "!{0} = {1}", a, !a);
Console.WriteLine( "!{0} = {1}", b, !b);
Console.WriteLine( "{0} & {1} = {2}", a, b, a & b);
Console.WriteLine( "{0} | {1} = {2}", a, b, a | b);
// Invoke the true operator to determine the Boolean
// value of the DBBool variable:
if (b)
Console.WriteLine("b is definitely true");
else
Console.WriteLine("b is not definitely true");
}
}
输出
!DBBool.True = DBBool.False
!DBBool.Null = DBBool.Null
DBBool.True & DBBool.Null = DBBool.Null
DBBool.True | DBBool.Null = DBBool.True
b is not definitely true

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运算符重载教程
ms-help://MS.MSDNQTR.2003FEB.2052/csref/html/vcwlkOperatorOverloadingTutorial.htm