316 lines
20 KiB
HTML
316 lines
20 KiB
HTML
<!DOCTYPE html>
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<html lang="zh" dir="ltr" class="client-nojs" xmlns="http://www.w3.org/1999/xhtml" xml:lang="zh">
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<head><meta http-equiv="x-ua-compatible" content="ie=edge">
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
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<title>nextafter, nextafterf, nextafterl, nexttoward, nexttowardf, nexttowardl</title>
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<link rel="stylesheet" href="ext.css" />
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<link rel="stylesheet" href="site_modules.css" />
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</head>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-c_numeric_math_nextafter skin-cppreference2 action-view cpp-navbar">
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<div id="cpp-content-base">
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<div id="content"><a id="top"></a>
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<h1 id="firstHeading" class="firstHeading">nextafter, nextafterf, nextafterl, nexttoward, nexttowardf, nexttowardl</h1>
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<div id="bodyContent">
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<div id="contentSub"><span class="subpages">< <a href="c.html">c</a>‎ | <a href="c-numeric.html">numeric</a>‎ | <a href="c-numeric-math.html">math</a></span></div>
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<div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr" xml:lang="zh">
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<table class="t-dcl-begin">
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<tbody>
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<tr class="t-dsc-header">
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<td>
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<div>定义于头文件 <code><math.h></code></div>
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</td>
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<td></td>
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<td></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<div><span class="mw-geshi c source-c"><span class="kw4">float</span> nextafterf<span class="br0">(</span> <span class="kw4">float</span> from, <span class="kw4">float</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(1)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="kw4">double</span> nextafter<span class="br0">(</span> <span class="kw4">double</span> from, <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(2)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> nextafterl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(3)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="kw4">float</span> nexttowardf<span class="br0">(</span> <span class="kw4">float</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(4)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="kw4">double</span> nexttoward<span class="br0">(</span> <span class="kw4">double</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(5)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> nexttowardl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> from, <span class="kw4">long</span> <span class="kw4">double</span> to <span class="br0">)</span><span class="sy4">;</span></span></div>
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</td>
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<td>(6)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dsc-header">
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<td>
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<div>定义于头文件 <code><tgmath.h></code></div>
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</td>
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<td></td>
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<td></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="co2">#define nextafter(from, to)</span></span></div>
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</td>
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<td>(7)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl t-since-c99">
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<td>
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<div><span class="mw-geshi c source-c"><span class="co2">#define nexttoward(from, to)</span></span></div>
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</td>
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<td>(8)</td>
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<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
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</tr>
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<tr class="t-dcl-sep">
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<td></td>
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<td></td>
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<td></td>
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</tr>
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</tbody>
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</table>
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<div class="t-li1"><span class="t-li">1-3)</span> 首先，转换两个参数为函数的类型，然后返回 <code>from</code> 于 <code>to</code> 方向的下个可表示值。若 <code>from</code> 等于 <code>to</code> ，则返回 <code>to</code> 。</div>
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<div class="t-li1"><span class="t-li">4-6)</span> 首先，转换两个参数为函数的类型，然后返回 <code>from</code> 于 <code>to</code> 方向的下个可表示值。若 <code>from</code> 等于 <code>to</code> ，则返回从 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 转换到函数返回类型的 <code>to</code> ，而不带范围或精度的损失。</div>
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<div class="t-li1"><span class="t-li">7)</span> 泛型宏：若任何参数拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 类型，则调用 <code>nextafterl</code> 。否则，若任何参数拥有整数类型或 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span></span></span> 类型，则调用 <code>nextafter</code> 。否则调用 <code>nextafterf</code> 。</div>
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<div class="t-li1"><span class="t-li">8)</span> 泛型宏：若任何参数拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 类型，则调用 <code>nexttowardl</code> 。否则，若任何参数拥有整数类型或 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span></span></span> 类型，则调用 <code>nexttoward</code> 。否则调用 <code>nexttowardf</code> 。</div>
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<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
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<table class="t-par-begin">
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<tr class="t-par">
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<td>from, to</td>
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<td>-</td>
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<td>浮点值</td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
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<p>若不出现错误，则返回 <code>from</code> 于 <code>to</code> 的方向的下个可表示值。若 <code>from</code> 等于 <code>to</code> ，则返回 <code>to</code> ，转换到函数的类型。</p>
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<p>若出现上溢所致的值域错误，则返回 <code>±HUGE_VAL</code> 、 <code>±HUGE_VALF</code> 或 <code>±HUGE_VALL</code> （所带符号同 <code>from</code> ）。</p>
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<p>若出现下溢所致的值域错误，则返回正确结果。</p>
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<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">错误处理</span></h3>
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<p>报告 <a href="c-numeric-math-math_errhandling.html">math_errhandling</a> 中指定的错误。</p>
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<p>若实现支持 IEEE 浮点算术（ IEC 60559 ），则</p>
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<ul>
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<li>若 <code>from</code> 有限，但期待的结果无限，则引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INEXACT</a></span> 和 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_OVERFLOW</a></span> 。</li>
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<li>若 <code>from</code> 不等于 <code>to</code> 且结果为非正规或零，则引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INEXACT</a></span> 和 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_UNDERFLOW</a></span> 。</li>
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<li>任何情况下，返回值独立于当前舍入模式。</li>
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<li>若 <code>from</code> 或 <code>to</code> 为 NaN ，则返回 NaN</li>
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</ul>
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<h3><span class="mw-headline" id=".E6.B3.A8.E8.A7.A3">注解</span></h3>
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<p><a rel="nofollow" class="external text" href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/nextafter.html">POSIX 指定</a>上溢和下溢条件是值域错误（可以设置 errno ）。</p>
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<p>IEC 60559 推荐凡在 <code>from==to</code> 时返回 <code>from</code> 。这些函数替而返回 <code>to</code> ，这使得围绕零的行为一致： <code>nextafter(-0.0, +0.0)</code> 返回 <code>+0.0</code> 而 <code>nextafter(+0.0, -0.0)</code> 返回 <code>–0.0</code> 。</p>
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<p><code>nextafter</code> 常通过操纵 IEEE 表示实现（ <a rel="nofollow" class="external text" href="https://github.com/bminor/glibc/blob/master/math/s_nextafter.c">glibc</a> ）（ <a rel="nofollow" class="external text" href="https://github.com/ifduyue/musl/blob/master/src/math/nextafter.c">musl</a> ）。</p>
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<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
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<div class="t-example">
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<div class="t-example-live-link"></div>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="c source-c">
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<pre class="de1"><span class="co2">#include <math.h></span>
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<span class="co2">#include <stdio.h></span>
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<span class="co2">#include <float.h></span>
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<span class="co2">#include <fenv.h></span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="kw4">void</span><span class="br0">)</span>
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<span class="br0">{</span>
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<span class="kw4">float</span> from1 <span class="sy1">=</span> <span class="nu0">0</span>, to1 <span class="sy1">=</span> nextafterf<span class="br0">(</span>from1, <span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw849">printf</span></a><span class="br0">(</span><span class="st0">"The next representable float after %.2f is %.20g (%a)<span class="es1">\n</span>"</span>, from1, to1, to1<span class="br0">)</span><span class="sy4">;</span>
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<span class="kw4">float</span> from2 <span class="sy1">=</span> <span class="nu0">1</span>, to2 <span class="sy1">=</span> nextafterf<span class="br0">(</span>from2, <span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw849">printf</span></a><span class="br0">(</span><span class="st0">"The next representable float after %.2f is %.20f (%a)<span class="es1">\n</span>"</span>, from2, to2, to2<span class="br0">)</span><span class="sy4">;</span>
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<span class="kw4">double</span> from3 <span class="sy1">=</span> nextafter<span class="br0">(</span><span class="nu16">0.1</span>, <span class="nu0">0</span><span class="br0">)</span>, to3 <span class="sy1">=</span> <span class="nu16">0.1</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw849">printf</span></a><span class="br0">(</span><span class="st0">"The number 0.1 lies between two valid doubles:<span class="es1">\n</span>"</span>
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<span class="st0">" %.56f (%a)<span class="es1">\n</span>and %.55f (%a)<span class="es1">\n</span>"</span>, from3, from3, to3, to3<span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// nextafter 和 nexttoward 间的差异：</span>
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<span class="kw4">long</span> <span class="kw4">double</span> dir <span class="sy1">=</span> nextafterl<span class="br0">(</span>from1, <span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 第一个非正规 long double</span>
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<span class="kw4">float</span> x <span class="sy1">=</span> nextafterf<span class="br0">(</span>from1, dir<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 首先转换 dir 为 float ，给出 0</span>
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<a href="c-io-fprintf.html"><span class="kw849">printf</span></a><span class="br0">(</span><span class="st0">"Using nextafter, next float after %.2f (%a) is %.20g (%a)<span class="es1">\n</span>"</span>,
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from1, from1, x, x<span class="br0">)</span><span class="sy4">;</span>
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x <span class="sy1">=</span> nexttowardf<span class="br0">(</span>from1, dir<span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw849">printf</span></a><span class="br0">(</span><span class="st0">"Using nexttoward, next float after %.2f (%a) is %.20g (%a)<span class="es1">\n</span>"</span>,
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from1, from1, x, x<span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// 特殊值</span>
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<span class="br0">{</span>
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<span class="co2">#pragma STDC FENV_ACCESS ON</span>
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<a href="c-numeric-fenv-feclearexcept.html"><span class="kw716">feclearexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw727">FE_ALL_EXCEPT</span></a><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw4">double</span> from4 <span class="sy1">=</span> <a href="c-types-limits.html"><span class="kw378">DBL_MAX</span></a>, to4 <span class="sy1">=</span> nextafter<span class="br0">(</span>from4, INFINITY<span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw849">printf</span></a><span class="br0">(</span><span class="st0">"The next representable double after %.2g (%a) is %.23f (%a)<span class="es1">\n</span>"</span>,
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from4, from4, to4, to4<span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">if</span><span class="br0">(</span><a href="c-numeric-fenv-fetestexcept.html"><span class="kw717">fetestexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw731">FE_OVERFLOW</span></a><span class="br0">)</span><span class="br0">)</span> <a href="c-io-puts.html"><span class="kw834">puts</span></a><span class="br0">(</span><span class="st0">" raised FE_OVERFLOW"</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">if</span><span class="br0">(</span><a href="c-numeric-fenv-fetestexcept.html"><span class="kw717">fetestexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw729">FE_INEXACT</span></a><span class="br0">)</span><span class="br0">)</span> <a href="c-io-puts.html"><span class="kw834">puts</span></a><span class="br0">(</span><span class="st0">" raised FE_INEXACT"</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span> <span class="co1">// 结束 FENV_ACCESS 块</span>
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<span class="kw4">float</span> from5 <span class="sy1">=</span> <span class="nu16">0.0</span>, to5 <span class="sy1">=</span> nextafter<span class="br0">(</span>from5, <span class="sy2">-</span><span class="nu16">0.0</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw849">printf</span></a><span class="br0">(</span><span class="st0">"nextafter(+0.0, -0.0) gives %.2g (%a)<span class="es1">\n</span>"</span>, to5, to5<span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span></pre></div>
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</div>
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<p>输出：</p>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="text source-text">
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<pre class="de1">The next representable float after 0.00 is 1.4012984643248170709e-45 (0x1p-149)
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The next representable float after 1.00 is 1.00000011920928955078 (0x1.000002p+0)
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The number 0.1 lies between two valid doubles:
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0.09999999999999999167332731531132594682276248931884765625 (0x1.9999999999999p-4)
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and 0.1000000000000000055511151231257827021181583404541015625 (0x1.999999999999ap-4)
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Using nextafter, next float after 0.00 (0x0p+0) is 0 (0x0p+0)
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Using nexttoward, next float after 0.00 (0x0p+0) is 1.4012984643248170709e-45 (0x1p-149)
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The next representable double after 1.8e+308 (0x1.fffffffffffffp+1023) is inf (inf)
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raised FE_OVERFLOW
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raised FE_INEXACT
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nextafter(+0.0, -0.0) gives -0 (-0x0p+0)</pre></div>
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</div>
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</div>
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<h3><span class="mw-headline" id=".E5.BC.95.E7.94.A8">引用</span></h3>
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<div class="t-ref-std-17">
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<ul>
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<li>C17 标准（ISO/IEC 9899:2018）：</li>
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</ul>
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<dl>
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<dd>
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<ul>
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<li>7.12.11.3 The nextafter functions (p: 187)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>7.12.11.4 The nexttoward functions (p: 187)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>7.25 Type-generic math <tgmath.h> (p: 272-273)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>F.10.8.3 The nextafter functions (p: 386)</li>
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</ul>
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</dd>
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</dl>
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<dl>
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<dd>
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<ul>
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<li>F.10.8.4 The nexttoward functions (p: 386)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</div>
|
|
<div class="t-ref-std-11">
|
|
<ul>
|
|
<li>C11 标准（ISO/IEC 9899:2011）：</li>
|
|
</ul>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.12.11.3 The nextafter functions (p: 256)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.12.11.4 The nexttoward functions (p: 257)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.25 Type-generic math <tgmath.h> (p: 373-375)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>F.10.8.3 The nextafter functions (p: 529)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>F.10.8.4 The nexttoward functions (p: 529)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</div>
|
|
<div class="t-ref-std-c99">
|
|
<ul>
|
|
<li>C99 标准（ISO/IEC 9899:1999）：</li>
|
|
</ul>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.12.11.3 The nextafter functions (p: 237)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.12.11.4 The nexttoward functions (p: 238)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.22 Type-generic math <tgmath.h> (p: 335-337)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>F.9.8.3 The nextafter functions (p: 466)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>F.9.8.4 The nexttoward functions (p: 466)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</div>
|
|
<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
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<table class="t-dsc-begin"></table>
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</div>
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<div class="visualClear"></div>
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</div>
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</div>
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</div>
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</body>
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</html>
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