2022-08-04 06:59:33 +00:00
<!DOCTYPE HTML>
< html lang = "zh" class = "sidebar-visible no-js light" >
< head >
<!-- Book generated using mdBook -->
< meta charset = "UTF-8" >
< title > 复数 - Go语言圣经< / title >
<!-- Custom HTML head -->
< meta content = "text/html; charset=utf-8" http-equiv = "Content-Type" >
< meta name = "description" content = "<The Go Programming Language>中文版" >
< meta name = "viewport" content = "width=device-width, initial-scale=1" >
< meta name = "theme-color" content = "#ffffff" / >
< link rel = "icon" href = "../favicon.svg" >
< link rel = "shortcut icon" href = "../favicon.png" >
< link rel = "stylesheet" href = "../css/variables.css" >
< link rel = "stylesheet" href = "../css/general.css" >
< link rel = "stylesheet" href = "../css/chrome.css" >
< link rel = "stylesheet" href = "../css/print.css" media = "print" >
<!-- Fonts -->
< link rel = "stylesheet" href = "../FontAwesome/css/font-awesome.css" >
< link rel = "stylesheet" href = "../fonts/fonts.css" >
<!-- Highlight.js Stylesheets -->
< link rel = "stylesheet" href = "../highlight.css" >
< link rel = "stylesheet" href = "../tomorrow-night.css" >
< link rel = "stylesheet" href = "../ayu-highlight.css" >
<!-- Custom theme stylesheets -->
< link rel = "stylesheet" href = "../style.css" >
< / head >
< body >
<!-- Provide site root to javascript -->
< script type = "text/javascript" >
var path_to_root = "../";
var default_theme = window.matchMedia("(prefers-color-scheme: dark)").matches ? "navy" : "light";
< / script >
<!-- Work around some values being stored in localStorage wrapped in quotes -->
< script type = "text/javascript" >
try {
var theme = localStorage.getItem('mdbook-theme');
var sidebar = localStorage.getItem('mdbook-sidebar');
if (theme.startsWith('"') & & theme.endsWith('"')) {
localStorage.setItem('mdbook-theme', theme.slice(1, theme.length - 1));
}
if (sidebar.startsWith('"') & & sidebar.endsWith('"')) {
localStorage.setItem('mdbook-sidebar', sidebar.slice(1, sidebar.length - 1));
}
} catch (e) { }
< / script >
<!-- Set the theme before any content is loaded, prevents flash -->
< script type = "text/javascript" >
var theme;
try { theme = localStorage.getItem('mdbook-theme'); } catch(e) { }
if (theme === null || theme === undefined) { theme = default_theme; }
var html = document.querySelector('html');
html.classList.remove('no-js')
html.classList.remove('light')
html.classList.add(theme);
html.classList.add('js');
< / script >
<!-- Hide / unhide sidebar before it is displayed -->
< script type = "text/javascript" >
var html = document.querySelector('html');
var sidebar = 'hidden';
if (document.body.clientWidth >= 1080) {
try { sidebar = localStorage.getItem('mdbook-sidebar'); } catch(e) { }
sidebar = sidebar || 'visible';
}
html.classList.remove('sidebar-visible');
html.classList.add("sidebar-" + sidebar);
< / script >
< nav id = "sidebar" class = "sidebar" aria-label = "Table of contents" >
< div class = "sidebar-scrollbox" >
< ol class = "chapter" > < li class = "chapter-item expanded affix " > < a href = "../index.html" > Go语言圣经< / a > < / li > < li class = "chapter-item expanded affix " > < a href = "../preface.html" > 前言< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch1/ch1.html" > < strong aria-hidden = "true" > 1.< / strong > 入门< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../ch1/ch1-01.html" > < strong aria-hidden = "true" > 1.1.< / strong > Hello, World< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch1/ch1-02.html" > < strong aria-hidden = "true" > 1.2.< / strong > 命令行参数< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch1/ch1-03.html" > < strong aria-hidden = "true" > 1.3.< / strong > 查找重复的行< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch1/ch1-04.html" > < strong aria-hidden = "true" > 1.4.< / strong > GIF动画< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch1/ch1-05.html" > < strong aria-hidden = "true" > 1.5.< / strong > 获取URL< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch1/ch1-06.html" > < strong aria-hidden = "true" > 1.6.< / strong > 并发获取多个URL< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch1/ch1-07.html" > < strong aria-hidden = "true" > 1.7.< / strong > Web服务< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch1/ch1-08.html" > < strong aria-hidden = "true" > 1.8.< / strong > 本章要点< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "../ch2/ch2.html" > < strong aria-hidden = "true" > 2.< / strong > 程序结构< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../ch2/ch2-01.html" > < strong aria-hidden = "true" > 2.1.< / strong > 命名< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch2/ch2-02.html" > < strong aria-hidden = "true" > 2.2.< / strong > 声明< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch2/ch2-03.html" > < strong aria-hidden = "true" > 2.3.< / strong > 变量< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch2/ch2-04.html" > < strong aria-hidden = "true" > 2.4.< / strong > 赋值< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch2/ch2-05.html" > < strong aria-hidden = "true" > 2.5.< / strong > 类型< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch2/ch2-06.html" > < strong aria-hidden = "true" > 2.6.< / strong > 包和文件< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch2/ch2-07.html" > < strong aria-hidden = "true" > 2.7.< / strong > 作用域< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "../ch3/ch3.html" > < strong aria-hidden = "true" > 3.< / strong > 基础数据类型< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../ch3/ch3-01.html" > < strong aria-hidden = "true" > 3.1.< / strong > 整型< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch3/ch3-02.html" > < strong aria-hidden = "true" > 3.2.< / strong > 浮点数< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch3/ch3-03.html" class = "active" > < strong aria-hidden = "true" > 3.3.< / strong > 复数< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch3/ch3-04.html" > < strong aria-hidden = "true" > 3.4.< / strong > 布尔型< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch3/ch3-05.html" > < strong aria-hidden = "true" > 3.5.< / strong > 字符串< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch3/ch3-06.html" > < strong aria-hidden = "true" > 3.6.< / strong > 常量< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "../ch4/ch4.html" > < strong aria-hidden = "true" > 4.< / strong > 复合数据类型< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../ch4/ch4-01.html" > < strong aria-hidden = "true" > 4.1.< / strong > 数组< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch4/ch4-02.html" > < strong aria-hidden = "true" > 4.2.< / strong > Slice< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch4/ch4-03.html" > < strong aria-hidden = "true" > 4.3.< / strong > Map< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch4/ch4-04.html" > < strong aria-hidden = "true" > 4.4.< / strong > 结构体< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch4/ch4-05.html" > < strong aria-hidden = "true" > 4.5.< / strong > JSON< / a > < / li > < li class = "chapter-item expanded " > < a href = "../ch4/ch4-06.html" > < s
< div id = "sidebar-resize-handle" class = "sidebar-resize-handle" > < / div >
< / nav >
< div id = "page-wrapper" class = "page-wrapper" >
< div class = "page" >
< div id = "menu-bar-hover-placeholder" > < / div >
< div id = "menu-bar" class = "menu-bar sticky bordered" >
< div class = "left-buttons" >
< button id = "sidebar-toggle" class = "icon-button" type = "button" title = "Toggle Table of Contents" aria-label = "Toggle Table of Contents" aria-controls = "sidebar" >
< i class = "fa fa-bars" > < / i >
< / button >
< button id = "theme-toggle" class = "icon-button" type = "button" title = "Change theme" aria-label = "Change theme" aria-haspopup = "true" aria-expanded = "false" aria-controls = "theme-list" >
< i class = "fa fa-paint-brush" > < / i >
< / button >
< ul id = "theme-list" class = "theme-popup" aria-label = "Themes" role = "menu" >
< li role = "none" > < button role = "menuitem" class = "theme" id = "light" > Light (default)< / button > < / li >
< li role = "none" > < button role = "menuitem" class = "theme" id = "rust" > Rust< / button > < / li >
< li role = "none" > < button role = "menuitem" class = "theme" id = "coal" > Coal< / button > < / li >
< li role = "none" > < button role = "menuitem" class = "theme" id = "navy" > Navy< / button > < / li >
< li role = "none" > < button role = "menuitem" class = "theme" id = "ayu" > Ayu< / button > < / li >
< / ul >
< button id = "search-toggle" class = "icon-button" type = "button" title = "Search. (Shortkey: s)" aria-label = "Toggle Searchbar" aria-expanded = "false" aria-keyshortcuts = "S" aria-controls = "searchbar" >
< i class = "fa fa-search" > < / i >
< / button >
< / div >
< h1 class = "menu-title" > Go语言圣经< / h1 >
< div class = "right-buttons" >
< a href = "../print.html" title = "Print this book" aria-label = "Print this book" >
< i id = "print-button" class = "fa fa-print" > < / i >
< / a >
< a href = "https://github.com/gopl-zh/gopl-zh.github.com" title = "Git repository" aria-label = "Git repository" >
< i id = "git-repository-button" class = "fa fa-github" > < / i >
< / a >
< a href = "https://github.com/gopl-zh/gopl-zh.github.com/edit/master/./ch3/ch3-03.md" title = "Suggest an edit" aria-label = "Suggest an edit" >
< i id = "git-edit-button" class = "fa fa-edit" > < / i >
< / a >
< / div >
< / div >
< div id = "search-wrapper" class = "hidden" >
< form id = "searchbar-outer" class = "searchbar-outer" >
< input type = "search" id = "searchbar" name = "searchbar" placeholder = "Search this book ..." aria-controls = "searchresults-outer" aria-describedby = "searchresults-header" >
< / form >
< div id = "searchresults-outer" class = "searchresults-outer hidden" >
< div id = "searchresults-header" class = "searchresults-header" > < / div >
< ul id = "searchresults" >
< / ul >
< / div >
< / div >
<!-- Apply ARIA attributes after the sidebar and the sidebar toggle button are added to the DOM -->
< script type = "text/javascript" >
document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
document.getElementById('sidebar').setAttribute('aria-hidden', sidebar !== 'visible');
Array.from(document.querySelectorAll('#sidebar a')).forEach(function(link) {
link.setAttribute('tabIndex', sidebar === 'visible' ? 0 : -1);
});
< / script >
< div id = "content" class = "content" >
<!-- Page table of contents -->
< div class = "sidetoc" > < nav class = "pagetoc" > < / nav > < / div >
< main >
<!-- 头部 -->
< ul dir = "auto" >
2022-08-24 10:48:15 +00:00
< li > < em > KusonStack一站式可编程配置技术栈(Go): < a href = "https://github.com/KusionStack/kusion" > https://github.com/KusionStack/kusion< / a > < / em > < / li >
< li > < em > KCL 配置编程语言(Rust): < a href = "https://github.com/KusionStack/KCLVM" > https://github.com/KusionStack/KCLVM< / a > < / em > < / li >
< li > < em > 凹语言™: < a href = "https://github.com/wa-lang/wa" > https://github.com/wa-lang/wa< / a > < / em > < / li >
2022-08-04 06:59:33 +00:00
< / ul >
< hr >
< h2 id = "33-复数" > < a class = "header" href = "#33-复数" > 3.3. 复数< / a > < / h2 >
< p > Go语言提供了两种精度的复数类型： ， ， ： < / p >
< pre > < code class = "language-Go" > var x complex128 = complex(1, 2) // 1+2i
var y complex128 = complex(3, 4) // 3+4i
fmt.Println(x*y) // " (-5+10i)"
fmt.Println(real(x*y)) // " -5"
fmt.Println(imag(x*y)) // " 10"
< / code > < / pre >
< p > 如果一个浮点数面值或一个十进制整数面值后面跟着一个i， ， ， ： < / p >
< pre > < code class = "language-Go" > fmt.Println(1i * 1i) // " (-1+0i)" , i^2 = -1
< / code > < / pre >
< p > 在常量算术规则下， （ ） ， ， ： < / p >
< pre > < code class = "language-Go" > x := 1 + 2i
y := 3 + 4i
< / code > < / pre >
< p > 复数也可以用==和!=进行相等比较。只有两个复数的实部和虚部都相等的时候它们才是相等的（译注：浮点数的相等比较是危险的，需要特别小心处理精度问题）。< / p >
< p > math/cmplx包提供了复数处理的许多函数， < / p >
< pre > < code class = "language-Go" > fmt.Println(cmplx.Sqrt(-1)) // " (0+1i)"
< / code > < / pre >
< p > 下面的程序使用complex128复数算法来生成一个Mandelbrot图像。< / p >
< p > < u > < i > gopl.io/ch3/mandelbrot< / i > < / u > < / p >
< pre > < code class = "language-Go" > // Mandelbrot emits a PNG image of the Mandelbrot fractal.
package main
import (
" image"
" image/color"
" image/png"
" math/cmplx"
" os"
)
func main() {
const (
xmin, ymin, xmax, ymax = -2, -2, +2, +2
width, height = 1024, 1024
)
img := image.NewRGBA(image.Rect(0, 0, width, height))
for py := 0; py < height; py++ {
y := float64(py)/height*(ymax-ymin) + ymin
for px := 0; px < width; px++ {
x := float64(px)/width*(xmax-xmin) + xmin
z := complex(x, y)
// Image point (px, py) represents complex value z.
img.Set(px, py, mandelbrot(z))
}
}
png.Encode(os.Stdout, img) // NOTE: ignoring errors
}
func mandelbrot(z complex128) color.Color {
const iterations = 200
const contrast = 15
var v complex128
for n := uint8(0); n < iterations; n++ {
v = v*v + z
if cmplx.Abs(v) > 2 {
return color.Gray{255 - contrast*n}
}
}
return color.Black
}
< / code > < / pre >
< p > 用于遍历1024x1024图像每个点的两个嵌套的循环对应-2到+2区间的复数平面。程序反复测试每个点对应复数值平方值加一个增量值对应的点是否超出半径为2的圆。如果超过了， ， ， ， < / p >
< p > < img src = "../images/ch3-03.png" alt = "" / > < / p >
< p > < strong > 练习 3.5： < / strong > 实现一个彩色的Mandelbrot图像， ， < / p >
< p > < strong > 练习 3.6： < / strong > 升采样技术可以降低每个像素对计算颜色值和平均值的影响。简单的方法是将每个像素分成四个子像素，实现它。< / p >
< p > < strong > 练习 3.7： < / strong > 另一个生成分形图像的方式是使用牛顿法来求解一个复数方程，例如$z^4-1=0$。每个起点到四个根的迭代次数对应阴影的灰度。方程根对应的点用颜色表示。< / p >
< p > < strong > 练习 3.8： < / strong > 通过提高精度来生成更多级别的分形。使用四种不同精度类型的数字实现相同的分形： （ ； ） ？ ？ < / p >
< p > < strong > 练习 3.9： < / strong > 编写一个web服务器， < / p >
<!-- 公众号 -->
< hr >
< table >
< tr >
< td >
< img width = "222px" src = "https://chai2010.cn/advanced-go-programming-book/css.png" >
< / td >
< td >
< img width = "222px" src = "https://chai2010.cn/advanced-go-programming-book/cch.png" >
< / td >
< / tr >
< / table >
< div id = "giscus-container" > < / div >
< footer class = "page-footer" >
< span > © 2015-2016 | < a href = "https://github.com/gopl-zh" > Go语言圣经中文版< / a > , 仅学习交流使用< / span >
< / footer >
< / main >
< nav class = "nav-wrapper" aria-label = "Page navigation" >
<!-- Mobile navigation buttons -->
< a rel = "prev" href = "../ch3/ch3-02.html" class = "mobile-nav-chapters previous" title = "Previous chapter" aria-label = "Previous chapter" aria-keyshortcuts = "Left" >
< i class = "fa fa-angle-left" > < / i >
< / a >
< a rel = "next" href = "../ch3/ch3-04.html" class = "mobile-nav-chapters next" title = "Next chapter" aria-label = "Next chapter" aria-keyshortcuts = "Right" >
< i class = "fa fa-angle-right" > < / i >
< / a >
< div style = "clear: both" > < / div >
< / nav >
< / div >
< / div >
< nav class = "nav-wide-wrapper" aria-label = "Page navigation" >
< a rel = "prev" href = "../ch3/ch3-02.html" class = "nav-chapters previous" title = "Previous chapter" aria-label = "Previous chapter" aria-keyshortcuts = "Left" >
< i class = "fa fa-angle-left" > < / i >
< / a >
< a rel = "next" href = "../ch3/ch3-04.html" class = "nav-chapters next" title = "Next chapter" aria-label = "Next chapter" aria-keyshortcuts = "Right" >
< i class = "fa fa-angle-right" > < / i >
< / a >
< / nav >
< / div >
< script type = "text/javascript" >
window.playground_copyable = true;
< / script >
< script src = "../elasticlunr.min.js" type = "text/javascript" charset = "utf-8" > < / script >
< script src = "../mark.min.js" type = "text/javascript" charset = "utf-8" > < / script >
< script src = "../searcher.js" type = "text/javascript" charset = "utf-8" > < / script >
< script src = "../clipboard.min.js" type = "text/javascript" charset = "utf-8" > < / script >
< script src = "../highlight.js" type = "text/javascript" charset = "utf-8" > < / script >
< script src = "../book.js" type = "text/javascript" charset = "utf-8" > < / script >
< script type = "text/javascript" charset = "utf-8" >
var pagePath = "ch3/ch3-03.md"
< / script >
<!-- Custom JS scripts -->
< script type = "text/javascript" src = "../js/custom.js" > < / script >
< script type = "text/javascript" src = "../js/bigPicture.js" > < / script >
< / body >
< / html >
