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chai2010
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ch3/ch3-03.html
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ch3/ch3-03.html
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<meta charset="UTF-8">
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<meta http-equiv="X-UA-Compatible" content="IE=edge" />
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<title>復數 | Go编程语言</title>
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<title>複數 | Go编程语言</title>
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<meta content="text/html; charset=utf-8" http-equiv="Content-Type">
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<meta name="description" content="">
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<meta name="generator" content="GitBook 2.5.2">
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<body>
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<div class="book" data-level="3.3" data-chapter-title="復數" data-filepath="ch3/ch3-03.md" data-basepath=".." data-revision="Wed Dec 16 2015 10:54:29 GMT+0800 (中国标准时间)">
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<div class="book" data-level="3.3" data-chapter-title="複數" data-filepath="ch3/ch3-03.md" data-basepath=".." data-revision="Mon Dec 21 2015 12:51:02 GMT+0800 (中国标准时间)">
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<div class="book-summary">
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@@ -146,7 +146,7 @@
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<b>0.5.</b>
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緻謝
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致謝
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</a>
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@@ -212,7 +212,7 @@
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<b>1.3.</b>
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査找重復的行
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査找重複的行
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</a>
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<b>1.4.</b>
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GIF動畫
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GIF動畵
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</a>
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@@ -257,7 +257,7 @@
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<b>1.6.</b>
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併髮穫取多個URL
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併發穫取多個URL
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</a>
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@@ -479,7 +479,7 @@
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<b>3.3.</b>
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復數
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複數
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</a>
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@@ -494,7 +494,7 @@
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<b>3.4.</b>
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佈爾型
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布爾型
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</a>
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@@ -544,7 +544,7 @@
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<b>4.</b>
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復閤數據類型
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複合數據類型
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</a>
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@@ -857,7 +857,7 @@
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<b>6.2.</b>
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基於指鍼對象的方法
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基於指針對象的方法
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</a>
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<b>6.4.</b>
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方法值和方法錶達式
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方法值和方法表達式
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</a>
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@@ -953,7 +953,7 @@
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<b>7.1.</b>
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接口是閤約
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接口是合約
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</a>
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<b>7.9.</b>
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示例: 錶達式求值
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示例: 表達式求值
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</a>
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<b>7.11.</b>
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基於類型斷言識彆錯誤類型
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基於類型斷言識别錯誤類型
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</a>
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<b>8.2.</b>
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示例: 併髮的Clock服務
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示例: 併發的Clock服務
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</a>
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<b>8.3.</b>
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示例: 併髮的Echo服務
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示例: 併發的Echo服務
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</a>
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<b>8.6.</b>
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示例: 併髮的Web爬蟲
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示例: 併發的Web爬蟲
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</a>
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<b>8.7.</b>
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基於select的多路復用
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基於select的多路複用
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</a>
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<b>8.8.</b>
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示例: 併髮的字典遍歷
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示例: 併發的字典遍歷
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</a>
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<b>8.9.</b>
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併髮的退齣
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併發的退齣
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</a>
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<b>9.</b>
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基於共享變量的併髮
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基於共享變量的併發
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</a>
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<b>9.4.</b>
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內存衕步
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內存同步
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</a>
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<b>9.7.</b>
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示例: 併髮的非阻塞緩存
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示例: 併發的非阻塞緩存
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</a>
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<b>9.8.</b>
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Goroutines和綫程
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Goroutines和線程
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</a>
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<b>12.1.</b>
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為何需要反射?
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爲何需要反射?
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</a>
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<b>12.4.</b>
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示例: 編碼S錶達式
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示例: 編碼S表達式
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</a>
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<b>12.6.</b>
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示例: 解碼S錶達式
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示例: 解碼S表達式
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</a>
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@@ -1975,50 +1975,14 @@
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</li>
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<li class="chapter " data-level="14" data-path="exercise/ex.html">
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<a href="../exercise/ex.html">
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<i class="fa fa-check"></i>
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<b>14.</b>
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習題解答
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</a>
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<ul class="articles">
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<li class="chapter " data-level="14.1" data-path="exercise/ex-ch1.html">
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<a href="../exercise/ex-ch1.html">
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<i class="fa fa-check"></i>
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<b>14.1.</b>
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第一章 入門
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</a>
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</li>
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</ul>
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</li>
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<li class="chapter " data-level="15" data-path="errata.html">
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<li class="chapter " data-level="14" data-path="errata.html">
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<a href="../errata.html">
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<i class="fa fa-check"></i>
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<b>15.</b>
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<b>14.</b>
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勘誤
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</a>
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<section class="normal" id="section-">
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<h2 id="33-復數">3.3. 復數</h2>
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<p>TODO</p>
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<h2 id="33-複數">3.3. 複數</h2>
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<p>Go提供了兩種精度的複數類似, complex64 和 complex128, 分别對應 float32 和 float64精度. 內置的 complex 函數用於構建複數, 內建的 real 和 imag 函數返迴複數的實部和虛部:</p>
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<pre><code class="lang-Go"><span class="hljs-keyword">var</span> x <span class="hljs-typename">complex128</span> = <span class="hljs-built_in">complex</span>(<span class="hljs-number">1</span>, <span class="hljs-number">2</span>) <span class="hljs-comment">// 1+2i</span>
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<span class="hljs-keyword">var</span> y <span class="hljs-typename">complex128</span> = <span class="hljs-built_in">complex</span>(<span class="hljs-number">3</span>, <span class="hljs-number">4</span>) <span class="hljs-comment">// 3+4i</span>
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fmt.Println(x*y) <span class="hljs-comment">// "(-5+10i)"</span>
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fmt.Println(<span class="hljs-built_in">real</span>(x*y)) <span class="hljs-comment">// "-5"</span>
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fmt.Println(<span class="hljs-built_in">imag</span>(x*y)) <span class="hljs-comment">// "10"</span>
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</code></pre>
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<p>如果一個浮點數面值或一個十進製整數面值後面跟着一個i, 例如 3.141592i 或 2i, 它將構成一個複數的虛部, 複數的實部是0:</p>
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<pre><code class="lang-Go">fmt.Println(<span class="hljs-number">1i</span> * <span class="hljs-number">1i</span>) <span class="hljs-comment">// "(-1+0i)", i^2 = -1</span>
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</code></pre>
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<p>在常量算術規則下, 一個複數常量可以加到另一個常量(整數或浮點數, 實部或虛部), 我們可以用自然的方式寫複數, 就像 1+2i, 或與之等價的寫法 2i+1. 上面x和y的聲明語句還可以簡化:</p>
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<pre><code class="lang-Go">x := <span class="hljs-number">1</span> + <span class="hljs-number">2i</span>
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y := <span class="hljs-number">3</span> + <span class="hljs-number">4i</span>
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</code></pre>
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<p>複數也可以用 == 和 != 進行相等比較. 隻有兩個複數的實部和虛部都相等的時候它們纔是相等的.</p>
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<p>math/cmplx 包提供了複數處理的許多函數, 例如求複數的平方根函數和求冪函數.</p>
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<pre><code class="lang-Go">fmt.Println(cmplx.Sqrt(-<span class="hljs-number">1</span>)) <span class="hljs-comment">// "(0+1i)"</span>
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</code></pre>
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<p>下面的程序使用complex128複數算法來生成一個Mandelbrot圖像.</p>
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<pre><code class="lang-Go">gopl.io/ch3/mandelbrot
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<span class="hljs-comment">// Mandelbrot emits a PNG image of the Mandelbrot fractal.</span>
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<span class="hljs-keyword">package</span> main
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<span class="hljs-keyword">import</span> (
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<span class="hljs-string">"image"</span>
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<span class="hljs-string">"image/color"</span>
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<span class="hljs-string">"image/png"</span>
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<span class="hljs-string">"math/cmplx"</span>
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<span class="hljs-string">"os"</span>
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)
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<span class="hljs-keyword">func</span> main() {
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<span class="hljs-keyword">const</span> (
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xmin, ymin, xmax, ymax = -<span class="hljs-number">2</span>, -<span class="hljs-number">2</span>, +<span class="hljs-number">2</span>, +<span class="hljs-number">2</span>
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width, height = <span class="hljs-number">1024</span>, <span class="hljs-number">1024</span>
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)
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img := image.NewRGBA(image.Rect(<span class="hljs-number">0</span>, <span class="hljs-number">0</span>, width, height))
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<span class="hljs-keyword">for</span> py := <span class="hljs-number">0</span>; py < height; py++ {
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y := <span class="hljs-typename">float64</span>(py)/height*(ymax-ymin) + ymin
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<span class="hljs-keyword">for</span> px := <span class="hljs-number">0</span>; px < width; px++ {
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x := <span class="hljs-typename">float64</span>(px)/width*(xmax-xmin) + xmin
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z := <span class="hljs-built_in">complex</span>(x, y)
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<span class="hljs-comment">// Image point (px, py) represents complex value z.</span>
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img.Set(px, py, mandelbrot(z))
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}
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}
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png.Encode(os.Stdout, img) <span class="hljs-comment">// <span class="hljs-doctag">NOTE:</span> ignoring errors</span>
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}
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<span class="hljs-keyword">func</span> mandelbrot(z <span class="hljs-typename">complex128</span>) color.Color {
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<span class="hljs-keyword">const</span> iterations = <span class="hljs-number">200</span>
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<span class="hljs-keyword">const</span> contrast = <span class="hljs-number">15</span>
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<span class="hljs-keyword">var</span> v <span class="hljs-typename">complex128</span>
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<span class="hljs-keyword">for</span> n := <span class="hljs-typename">uint8</span>(<span class="hljs-number">0</span>); n < iterations; n++ {
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v = v*v + z
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<span class="hljs-keyword">if</span> cmplx.Abs(v) > <span class="hljs-number">2</span> {
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<span class="hljs-keyword">return</span> color.Gray{<span class="hljs-number">255</span> - contrast*n}
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}
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}
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<span class="hljs-keyword">return</span> color.Black
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}
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</code></pre>
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<p>遍歷1024x1024圖像每個點的兩個嵌套的循環對應 -2 到 +2 區間的複數平面. 程序反複測試每個點對應複數值平方值加一個增量值對應的點是否超齣半徑爲2的圓. 如果超過了, 通過根據逃逸的迭代次數對應的灰度顔色來代替. 如果不是, 該點屬於Mandelbrot集合, 使用黑色顔色標記. 最終程序將生成的PNG格式分形圖像圖像輸齣到標準輸齣, 如圖3.3所示.</p>
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<p><strong>練習3.5:</strong> 實現一個綵色的Mandelbrot圖像, 使用 image.NewRGBA 創建圖像, 使用 color.RGBA 或 color.YCbCr 生成顔色.</p>
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<p><strong>練習3.6:</strong> 超采樣技術可以降低每個像素對計算顔色值和平均值的影響. 簡單的方法是將每個像素分層四個子像素, 實現它.</p>
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<p><strong>練習3.7:</strong> 另一個生成分形圖像的方式是使用牛頓法來求解一個複數方程, 例如 z^4 − 1 = 0. 每個起點到四個根的迭代次數對應陰影的灰度. 方程根對應的點用顔色表示.</p>
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<p><img src="../images/ch3-03.png" alt=""></p>
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<p><strong>練習3.8:</strong> 通過提高精度來生成更多級别的分形. 使用四種不同精度類型的數字實現相同的分形: complex64, complex128, big.Float, and big.Rat. (後面兩種類型在 math/big 包聲明. Float是有指定限精度的浮點數; Rat是無效精度的有理數.) 它們間的性能和內存使用對比如何? 當渲染圖可見時縮放的級别是多少?</p>
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||||
<p><strong>練習3.9:</strong> 編寫一個web服務器, 用於給客戶端生成分形的圖像. 運行客戶端用過HTTP參數參數指定x,y和zoom參數.</p>
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||||
|
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</section>
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@@ -2074,7 +2110,7 @@
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<a href="../ch3/ch3-02.html" class="navigation navigation-prev " aria-label="Previous page: 浮點數"><i class="fa fa-angle-left"></i></a>
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<a href="../ch3/ch3-04.html" class="navigation navigation-next " aria-label="Next page: 佈爾型"><i class="fa fa-angle-right"></i></a>
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<a href="../ch3/ch3-04.html" class="navigation navigation-next " aria-label="Next page: 布爾型"><i class="fa fa-angle-right"></i></a>
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</div>
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</div>
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Block a user