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<p class="MsoNormal"><span style="FONT-FAMILY: 宋体"> </span><span lang="EN-US"><span class="msoIns"><ins cite="mailto:Simon%20Robinson" datetime="2001-05-24T01:47">●<span style="FONT: 7pt 'Times New Roman'"> </span></ins></span></span><span style="FONT-FAMILY: 宋体">在数学领域中，几乎包括所有的数学对象：坐标、矢量、矩阵、张量和函数等。如果编写一个程序执行某些数学或物理建模，肯定会用类表示这些对象。</span></p>
<p class="1" style="MARGIN-LEFT: 37.55pt; TEXT-INDENT: -16.1pt"><span lang="EN-US">●<span style="FONT: 7pt 'Times New Roman'"> </span></span><span style="FONT-FAMILY: 宋体">图形程序在计算屏幕上的位置时，也使用数学或相关的坐标对象。</span></p>
<p class="1" style="MARGIN-LEFT: 37.55pt; TEXT-INDENT: -16.1pt"><span lang="EN-US">●<span style="FONT: 7pt 'Times New Roman'"> </span></span><span style="FONT-FAMILY: 宋体">表示大量金钱的类</span><span lang="EN-US">(</span><span style="FONT-FAMILY: 宋体">例如，在财务程序中</span><span lang="EN-US">)</span><span style="FONT-FAMILY: 宋体">。</span></p>
<p class="1" style="MARGIN-LEFT: 37.55pt; TEXT-INDENT: -16.1pt"><span lang="EN-US">●<span style="FONT: 7pt 'Times New Roman'"> </span></span><span style="FONT-FAMILY: 宋体">字处理或文本分析程序也有表示语句、子句等的类，可以使用运算符把语句连接在一起</span><span lang="EN-US">(</span><span style="FONT-FAMILY: 宋体">这是字符串连接的一种比较复杂的版本</span><span lang="EN-US">)</span><span style="FONT-FAMILY: 宋体">。</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">另外，有许多类与运算符重载并不相关。不恰当地使用运算符重载，会使使用类型的代码很难理解。例如，把两个</span><span lang="EN-US">DateTime</span><span style="FONT-FAMILY: 宋体">对象相乘，在概念上没有任何意义。</span></p>
<h3 style="MARGIN: 8.15pt 0cm"><span><span lang="EN-US">5.4.1 </span></span><span style="FONT-FAMILY: 黑体">运算符的工作方式</span></h3>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">为了理解运算符是如何重载的，考虑一下在编译器遇到运算符时会发生什么样的情况是很有用的<span style="LETTER-SPACING: -0.5pt">——</span>我们用相加运算符</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">作为例子来讲解。假定编译器遇到下面的代码：</span></p>
<p class="2" style="MARGIN: 8.15pt 0cm 0pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">int a = 3;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">uint b = 2;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">double d = 4.0;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">long l = a + b;</span></p>
<p class="2" style="MARGIN: 0cm 0cm 8.15pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">double x = d + a;</span><span class="MsoCommentReference"><span lang="EN-US" style="DISPLAY: none; FONT-SIZE: 8pt; LETTER-SPACING: 0.2pt"> </span></span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">会发生什么情况：</span></p>
<p class="a6" style="MARGIN: 6.5pt 0cm 6.5pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">long l = a + b;</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">编译器知道它需要把两个整数加起来，并把结果赋予</span><span lang="EN-US">long</span><span style="FONT-FAMILY: 宋体">。调用一个方法把数字加在一起时，表达式</span><span lang="EN-US">a+b</span><span style="FONT-FAMILY: 宋体">是一种非常直观、方便的语法。该方法带有两个参数</span><span lang="EN-US">a</span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US">b</span><span style="FONT-FAMILY: 宋体">，并返回它们的和。所以它完成的任务与任何方法调用是一样的<span style="LETTER-SPACING: -0.5pt">——</span></span><span style="LETTER-SPACING: -0.5pt"> </span><span style="FONT-FAMILY: 宋体">给定了参数类型后，它会查找最匹配的</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符重载，把两个整数加在一起是很简单的。与一般的重载方法一样，预定义的返回类型不会因为调用的方法版本而影响编译器的选择。在本例中调用的重载方法带两个</span><span lang="EN-US">int</span><span style="FONT-FAMILY: 宋体">类型参数，返回一个</span><span lang="EN-US">int</span><span style="FONT-FAMILY: 宋体">，这个返回值随后会转换为</span><span lang="EN-US">long</span><span style="FONT-FAMILY: 宋体">。</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">下一行代码让编译器使用</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符的另一个重载：</span></p>
<p class="2" style="MARGIN: 6.5pt 0cm 6.5pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">double x = d + a;</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">在这个例子中，参数是一个</span><span lang="EN-US">double</span><span style="FONT-FAMILY: 宋体">类型的数据和一个</span><span lang="EN-US">int</span><span style="FONT-FAMILY: 宋体">类型的数据，但</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符没有带这种复合参数的重载形式，所以编译器认为，最匹配的</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符重载是把两个</span><span lang="EN-US">double</span><span style="FONT-FAMILY: 宋体">作为其参数的版本，并隐式地把</span><span lang="EN-US">int</span><span style="FONT-FAMILY: 宋体">转换为</span><span lang="EN-US">double</span><span style="FONT-FAMILY: 宋体">。把两个</span><span lang="EN-US">double</span><span style="FONT-FAMILY: 宋体">加在一起与把两个整数加在一起完全不同，浮点数存储为一个尾数和一个指数。把它们加在一起要按位移动一个</span><span lang="EN-US">double</span><span style="FONT-FAMILY: 宋体">的尾数，让两个指数有相同的值，然后把尾数加起来，然后移动所得尾数的位，调整其指数，保证答案有尽可能高的精度。</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">现在，看看如果编译器遇到下面的代码，会发生什么：</span></p>
<p class="2" style="MARGIN: 8.15pt 0cm 0pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">Vector vect1, vect2, vect3;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">// initialise vect1 and vect2</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">vect3 = vect1 + vect2;</span></p>
<p class="2" style="MARGIN: 0cm 0cm 8.15pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">vect1 = vect1*2;</span></p>
<p class="MsoNormal" style="TEXT-INDENT: 0cm; LINE-HEIGHT: 15pt"><span style="FONT-FAMILY: 宋体">其中，</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">是结构，稍后再定义它。编译器知道它需要把两个</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">加起来，即</span><span lang="EN-US">vect1 </span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US"> vect2</span><span style="FONT-FAMILY: 宋体">。它会查找</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符的重载，把两个</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">作为参数。</span></p>
<p class="MsoNormal" style="LINE-HEIGHT: 15pt"><span style="FONT-FAMILY: 宋体">如果编译器找到这样的运算符定义，就调用它的实现。如果找不到，就要看看有没有可以用作最佳匹配的其他</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符重载，例如某个运算符重载的参数是其他数据类型，但可以隐式地转换为</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">实例。如果编译器找不到合适的运算符重载，就会产生一个编译错误，就像找不到其他方法调用的合适重载一样。</span></p>
<h3 style="MARGIN: 8.15pt 0cm"><span><span lang="EN-US">5.4.2 </span></span><span style="FONT-FAMILY: 黑体">运算符重载的示例：</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 黑体">结构</span></h3>
<p class="MsoNormal" style="LINE-HEIGHT: 15pt"><span><span style="FONT-FAMILY: 宋体">本节将开发一个结构</span><span lang="EN-US">Vector</span></span><span style="FONT-FAMILY: 宋体">，来演示运算符重载，这个结构</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">表示一个三维矢量。如果数学不是你的强项，不必担心，我们会使这个例子尽可能简单。三维矢量只是三个数字的一个集合，说明物体和原点之间的距离，表示数字的变量是</span><span lang="EN-US">x</span><span style="FONT-FAMILY: 宋体">、</span><span lang="EN-US">y</span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US">z</span><span style="FONT-FAMILY: 宋体">，</span><span lang="EN-US">x</span><span style="FONT-FAMILY: 宋体">表示物体与原点在</span><span lang="EN-US">x</span><span style="FONT-FAMILY: 宋体">方向上的距离，</span><span lang="EN-US">y</span><span style="FONT-FAMILY: 宋体">表示它与原点在</span><span lang="EN-US">y</span><span style="FONT-FAMILY: 宋体">方向上的距离，</span><span lang="EN-US">z</span><span style="FONT-FAMILY: 宋体">表示高度。把这</span><span lang="EN-US">3</span><span style="FONT-FAMILY: 宋体">个数字组合起来，就得到总距离。例如，如果</span><span lang="EN-US">x=3.0, y=3.0, z=1.0</span><span style="FONT-FAMILY: 宋体">，一般可以写作</span><span lang="EN-US">(3.0, 3.0, 1.0)</span><span style="FONT-FAMILY: 宋体">，表示物体与原点在</span><span lang="EN-US">x</span><span style="FONT-FAMILY: 宋体">方<span style="LETTER-SPACING: -0.2pt">向上的距离是</span></span><span lang="EN-US" style="LETTER-SPACING: -0.2pt">3</span><span style="FONT-FAMILY: 宋体; LETTER-SPACING: -0.2pt">，与原点在</span><span lang="EN-US" style="LETTER-SPACING: -0.2pt">y</span><span style="FONT-FAMILY: 宋体; LETTER-SPACING: -0.2pt">方向上的距离是</span><span lang="EN-US" style="LETTER-SPACING: -0.2pt">3</span><span style="FONT-FAMILY: 宋体; LETTER-SPACING: -0.2pt">，高度为</span><span lang="EN-US" style="LETTER-SPACING: -0.2pt">1</span><span style="FONT-FAMILY: 宋体; LETTER-SPACING: -0.2pt">。</span></p>
<p class="MsoNormal" style="LINE-HEIGHT: 15pt"><span style="FONT-FAMILY: 宋体">矢量可以与矢量或数字相加或相乘。在这里我们使用术语“标量”</span><span lang="EN-US">(scalar)</span><span style="FONT-FAMILY: 宋体">，它是数字的数学用语<span style="LETTER-SPACING: -1pt">——</span></span><span style="LETTER-SPACING: -1pt"> </span><span style="FONT-FAMILY: 宋体">在</span><span lang="EN-US">C#</span><span style="FONT-FAMILY: 宋体">中，就是一个</span><span lang="EN-US">double</span><span style="FONT-FAMILY: 宋体">。相加的作用是很明显的。如果先移动</span><span lang="EN-US">(3.0, 3.0, 1.0)</span><span style="FONT-FAMILY: 宋体">，再移动</span><span lang="EN-US">(2.0, </span><span style="FONT-FAMILY: 宋体">–</span><span lang="EN-US">4.0, </span><span style="FONT-FAMILY: 宋体">–</span><span lang="EN-US">4.0)</span><span style="FONT-FAMILY: 宋体">，总移动量就是把这两个矢量加起来。矢量的相加是指把每个元素分别相加，因此得到</span><span lang="EN-US">(5.0, </span><span style="FONT-FAMILY: 宋体">–</span><span lang="EN-US">1.0,</span><span style="FONT-FAMILY: 宋体">–</span><span lang="EN-US">3.0)</span><span style="FONT-FAMILY: 宋体">。此时，数学表达式总是写成</span><span lang="EN-US">c=a+b</span><span style="FONT-FAMILY: 宋体">，其中</span><span lang="EN-US">a</span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US">b</span><span style="FONT-FAMILY: 宋体">是矢量，</span><span lang="EN-US">c</span><span style="FONT-FAMILY: 宋体">是结果矢量。这与使用</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">结构的方式是一样的。</span></p>
<p class="a3" style="MARGIN-TOP: 8.15pt; TEXT-INDENT: 21.45pt"><span style="FONT-FAMILY: 黑体">注意：</span></p>
<p class="a1" style="MARGIN-BOTTOM: 8.15pt; TEXT-INDENT: 21.45pt"><span style="FONT-FAMILY: 楷体_GB2312">这个例子是作为一个结构来开发的，而不是类，但这并不重要。运算符重载用于结构和类时，其工作方式是一样的。</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">下面是</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">的定义<span style="LETTER-SPACING: -1pt">——</span></span> <span style="FONT-FAMILY: 宋体">包含成员字段、构造函数和一个</span><span lang="EN-US">ToString()</span><span style="FONT-FAMILY: 宋体">重写方法，以便查看</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">的内容，最后是运算符重载：</span></p>
<p class="2" style="MARGIN: 8.15pt 0cm 0pt 21.45pt; TEXT-INDENT: 18.45pt"><span><span lang="EN-US">namespace Wrox.ProCSharp.OOCSharp</span></span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">{</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> struct Vector</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> {</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> public double x, y, z;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> </span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> public Vector(double x, double y, double z)</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> {</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> this.x = x;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> this.y = y;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> this.z = z;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> }</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> </span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> public Vector(Vector rhs)</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> {</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> x = rhs.x;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> y = rhs.y;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> z = rhs.z;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> }</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> </span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> public override string ToString()</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> {</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> return "( " + x + " , " + y + " , " + z + " )"; </span></p>
<p class="2" style="MARGIN: 0cm 0cm 8.15pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> }</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">这里提供了两个构造函数，通过传递每个元素的值，或者提供另一个复制其值的</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">，来指定矢量的初始值。第二个构造函数带一个</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">参数，通常称为复制构造函数，因为它们允许通过复制另一个实例来初始化一个类或结构实例。注意，为了简单起见，把字段设置为</span><span lang="EN-US">public</span><span style="FONT-FAMILY: 宋体">。也可以把它们设置为</span><span lang="EN-US">private</span><span style="FONT-FAMILY: 宋体">，编写相应的属性来访问它们，这样做不会改变这个程序的功能，只是代码会复杂一些。</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">下面是</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">结构的有趣部分<span style="LETTER-SPACING: -1pt">——</span></span><span style="LETTER-SPACING: -1pt"> </span><span style="FONT-FAMILY: 宋体">为</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符提供支持的运算符重载：</span></p>
<p class="2" style="MARGIN: 8.15pt 0cm 0pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US"> public static Vector operator + (Vector lhs, Vector rhs)</span></p>
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