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<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">这段代码会告诉编译器，如果有</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US">double</span><span style="FONT-FAMILY: 宋体">的相乘操作，编译器就使参数的顺序反序，调用另一个运算符重载。在某种程度上，喜欢哪一个是由用户自己决定的。在本章的示例代码中，我们使用第二个版本，它看起来比较简洁。利用这个版本可以编写出维护性更好的代码，因为不需要复制代码，就可在两个独立的重载中执行相乘操作。</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">要重载的下一个运算符是矢量相乘。在数学上，矢量相乘有两种方式，但这里我们感兴趣的是点积或内积，其结果实际上是一个标量。这就是我们介绍这个例子的原因，所以算术运算符不必返回与定义它们的类相同的类型。</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">在数学上，如果有两个矢量</span><span lang="EN-US">(x, y, z)</span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US">(X, Y, Z)</span><span style="FONT-FAMILY: 宋体">，其内积就是</span><span lang="EN-US">x*X + y*Y + z*Z</span><span style="FONT-FAMILY: 宋体">的值。两个矢量这样相乘是很奇怪的，但这是很有效的，因为它可以用于计算各种其他的数。当然，如果要使用</span><span lang="EN-US">Direct3D </span><span style="FONT-FAMILY: 宋体">或</span><span lang="EN-US">DirectDraw</span><span style="FONT-FAMILY: 宋体">编写代码来显示复杂的</span><span lang="EN-US">3D</span><span style="FONT-FAMILY: 宋体">图形，在计算对象放在屏幕上的什么位置时，常常需要编写代码来计算矢量的内积，作为中间步骤。这里我们关心的是编写出</span><span lang="EN-US">double X = 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，并计算出它们的点积。相关的运算符重载如下所示：</span></p>
<p class="2" style="MARGIN: 8.15pt 0cm 0pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; public static double operator * (Vector lhs, Vector rhs)</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; {</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return lhs.x * rhs.x + lhs.y * rhs.y + lhs.z * rhs.z;</span></p>
<p class="2" style="MARGIN: 0cm 0cm 8.15pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; }</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">定义了算术运算符后，就可以用一个简单的测试方法来看看它们是否能正常运行：</span></p>
<p class="a6" style="MARGIN: 8.15pt 0cm 0pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">static void Main()</span></p>
<p class="a6" 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">&nbsp;&nbsp; // stuff to demonstrate arithmetic operations</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Vector vect1, vect2, vect3;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; vect1 = new Vector(1.0, 1.5, 2.0);</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; vect2 = new Vector(0.0, 0.0,</span><span style="FONT-FAMILY: 宋体">&ndash;</span><span lang="EN-US">10.0);</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; vect3 = vect1 + vect2;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Console.WriteLine(&quot;vect1 = &quot; + vect1);</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Console.WriteLine(&quot;vect2 = &quot; + vect2);</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Console.WriteLine(&quot;vect3 = vect1 + vect2 = &quot; + vect3);</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Console.WriteLine(&quot;2*vect3 = &quot; + 2*vect3);</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; vect3 += vect2;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Console.WriteLine(&quot;vect3+=vect2 gives &quot; + vect3);</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; vect3 = vect1*2;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Console.WriteLine(&quot;Setting vect3=vect1*2 gives &quot; + vect3);</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; double dot = vect1*vect3;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Console.WriteLine(&quot;vect1*vect3 = &quot; + dot);</span></p>
<p class="a6" style="MARGIN: 0cm 0cm 4.9pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">}</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">运行代码，得到如下所示的结果：</span></p>
<p class="a3" style="MARGIN-TOP: 8.15pt; TEXT-INDENT: 21.45pt"><span lang="EN-US">Vectors2</span></p>
<p class="a6" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">vect1 = ( 1 , 1.5 , 2 )</span></p>
<p class="a6" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">vect2 = ( 0 , 0 ,</span><span style="FONT-FAMILY: 宋体">&ndash;</span><span lang="EN-US">10 )</span></p>
<p class="a6" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">vect3 = vect1 + vect2 = ( 1 , 1.5 ,</span><span style="FONT-FAMILY: 宋体">&ndash;</span><span lang="EN-US">8 )</span></p>
<p class="a6" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">2*vect3 = ( 2 , 3 ,</span><span style="FONT-FAMILY: 宋体">&ndash;</span><span lang="EN-US">16 )</span></p>
<p class="a6" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">vect3+=vect2 gives ( 1 , 1.5 ,</span><span style="FONT-FAMILY: 宋体">&ndash;</span><span lang="EN-US">18 )</span></p>
<p class="a6" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">Setting vect3=vect1*2 gives ( 2 , 3 , 4 )</span></p>
<p class="a6" style="MARGIN: 0cm 0cm 8.15pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">vect1*vect3 = 14.5</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">这说明，运算符重载会给出正确的结果，但如果仔细看看测试代码，就会惊奇地注意到，实际上我们使用的是没有重载的运算符<span style="LETTER-SPACING: -1pt">&mdash;&mdash;</span></span><span style="LETTER-SPACING: -1pt"> </span><span style="FONT-FAMILY: 宋体">相加赋值运算符</span><span lang="EN-US">+=</span><span style="FONT-FAMILY: 宋体">：</span></p>
<p class="2" style="MARGIN: 8.15pt 0cm 0pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; vect3 += vect2;</span></p>
<p class="a6" style="MARGIN: 0cm 0cm 8.15pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp; Console.WriteLine(&quot;vect3 += vect2 gives &quot; + vect3);</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">虽然</span><span lang="EN-US">+=</span><span style="FONT-FAMILY: 宋体">一般用作运算符，但实际上其操作分为两个部分：相加和赋值。与</span><span lang="EN-US">C++</span><span style="FONT-FAMILY: 宋体">不同，</span><span lang="EN-US">C#</span><span style="FONT-FAMILY: 宋体">不允许重载</span><span lang="EN-US">=</span><span style="FONT-FAMILY: 宋体">运算符，但如果重载</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符，编译器就会自动使用</span><span lang="EN-US">+</span><span style="FONT-FAMILY: 宋体">运算符的重载来执行</span><span lang="EN-US">+=</span><span style="FONT-FAMILY: 宋体">运算符的操作。&ndash;</span><span lang="EN-US">=</span><span style="FONT-FAMILY: 宋体">、</span><span lang="EN-US">&amp;=</span><span style="FONT-FAMILY: 宋体">、</span><span lang="EN-US">*=</span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US">/=</span><span style="FONT-FAMILY: 宋体">赋值运算符也遵循此规则。</span></p>
<h4 style="TEXT-INDENT: 21.45pt"><span><span lang="EN-US">2. </span></span><span style="FONT-FAMILY: 黑体">比较运算符重载</span></h4>
<p class="MsoNormal"><span><span lang="EN-US">C#</span></span><span style="FONT-FAMILY: 宋体">中有</span><span lang="EN-US">6</span><span style="FONT-FAMILY: 宋体">个比较运算符，它们分为</span><span lang="EN-US">3</span><span style="FONT-FAMILY: 宋体">对：</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'">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span lang="EN-US">== </span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US"> !=</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'">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span lang="EN-US">&gt; </span><span style="FONT-FAMILY: 宋体">和</span> <span lang="EN-US">&lt;</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'">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span lang="EN-US">&gt;= </span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US"> &lt;=</span></p>
<p class="MsoNormal"><span lang="EN-US">C#</span><span style="FONT-FAMILY: 宋体">要求成对重载比较运算符。如果重载了</span><span lang="EN-US">==</span><span style="FONT-FAMILY: 宋体">，也必须重载！</span><span lang="EN-US">=</span><span style="FONT-FAMILY: 宋体">，否则会产生编译错误。另外，比较运算符必须返回</span><span lang="EN-US">bool</span><span style="FONT-FAMILY: 宋体">类型的值。这是它们与算术运算符的根本区别。两个数相加或相减的结果，理论上取决于数的类型。而两个</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">的相乘会得到一个标量。另一个例子是</span><span lang="EN-US">.NET</span><span style="FONT-FAMILY: 宋体">基类</span><span lang="EN-US">System.DateTime</span><span style="FONT-FAMILY: 宋体">，两个</span><span lang="EN-US">DateTime</span><span style="FONT-FAMILY: 宋体">相减，得到的结果不是</span><span lang="EN-US">DateTime</span><span style="FONT-FAMILY: 宋体">，而是一个</span><span lang="EN-US">System.TimeSpan</span><span style="FONT-FAMILY: 宋体">实例，但比较运算得到的如果不是</span><span lang="EN-US">bool</span><span style="FONT-FAMILY: 宋体">类型的值，就没有任何意义。</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">在重载</span><span lang="EN-US">==</span><span style="FONT-FAMILY: 楷体_GB2312">和</span><span lang="EN-US">!=</span><span style="FONT-FAMILY: 楷体_GB2312">时，还应重载从</span><span lang="EN-US">System.Object</span><span style="FONT-FAMILY: 楷体_GB2312">中继承的</span><span lang="EN-US">Equals()</span><span style="FONT-FAMILY: 楷体_GB2312">和</span><span lang="EN-US">GetHashCode()</span><span style="FONT-FAMILY: 楷体_GB2312">方法，否则会产生一个编译警告。原因是</span><span lang="EN-US">Equals()</span><span style="FONT-FAMILY: 楷体_GB2312">方法应执行与</span><span lang="EN-US">==</span><span style="FONT-FAMILY: 楷体_GB2312">运算符相同的相等逻辑。</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">除了这些区别外，重载比较运算符所遵循的规则与算术运算符相同。但比较两个数并不像想象的那么简单，例如，如果比较两个对象引用，就是比较存储对象的内存地址。比较运算符很少进行这样的比较，所以必须编写运算符，比较对象的值，返回相应的布尔结果。下面给</span><span lang="EN-US">Vector</span><span style="FONT-FAMILY: 宋体">类重载</span><span lang="EN-US">== </span><span style="FONT-FAMILY: 宋体">和</span><span lang="EN-US"> !=</span><span style="FONT-FAMILY: 宋体">运算符。首先是</span><span lang="EN-US">== </span><span style="FONT-FAMILY: 宋体">的执行代码：</span></p>
<p class="2" style="MARGIN: 8.15pt 0cm 0pt 21.45pt; TEXT-INDENT: 18.45pt"><span><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; public static bool operator = = (Vector lhs, Vector rhs)&nbsp; </span></span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; {</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; if (lhs.x = = rhs.x &amp;&amp; lhs.y = = rhs.y &amp;&amp; lhs.z = = rhs.z)</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return true;</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; else</span></p>
<p class="2" style="MARGIN-LEFT: 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return false;</span></p>
<p class="2" style="MARGIN: 0cm 0cm 8.15pt 21.45pt; TEXT-INDENT: 18.45pt"><span lang="EN-US">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; }</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 宋体">这种方式仅根据矢量组成部分的值，来对它们进行等于比较。对于大多数结构，这就是我们希望的，但在某些情况下，可能需要仔细考虑等于的含义，例如，如果有嵌入的类，是应比较对同一个对象的引用</span><span lang="EN-US">(</span><span style="FONT-FAMILY: 宋体">浅度比较</span><span lang="EN-US">)</span><span style="FONT-FAMILY: 宋体">，还是应比较对象的值是否相等</span><span lang="EN-US">(</span><span style="FONT-FAMILY: 宋体">深度比较</span><span lang="EN-US">)</span><span style="FONT-FAMILY: 宋体">？</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">不要通过调用从</span><span lang="EN-US">System.Object</span><span style="FONT-FAMILY: 楷体_GB2312">中继承的</span><span lang="EN-US">Equals()</span><span style="FONT-FAMILY: 楷体_GB2312">方法的实例版本，来重载比较运算符，如果这么做，就会在</span><span lang="EN-US">objA</span><span style="FONT-FAMILY: 楷体_GB2312">是</span><span lang="EN-US">null</span><span style="FONT-FAMILY: 楷体_GB2312">时计算</span><span lang="EN-US">(objA==objB)</span><span style="FONT-FAMILY: 楷体_GB2312">，这会产生一个异常，因为</span><span lang="EN-US">.NET</span><span style="FONT-FAMILY: 楷体_GB2312">运行库会试图计算</span><span lang="EN-US">null.Equals(objB)</span><span style="FONT-FAMILY: 楷体_GB2312">。采用其他方法</span><span lang="EN-US">(</span><span style="FONT-FAMILY: 楷体_GB2312">重写</span><span lang="EN-US">Equals()</span><span style="FONT-FAMILY: 楷体_GB2312">方法，调用比较运算符</span><span lang="EN-US">)</span><span style="FONT-FAMILY: 楷体_GB2312">比较安全。</span></p>