254 lines
20 KiB
HTML
254 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>remquo, remquof, remquol</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_remquo 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">remquo, remquof, remquol</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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<td>
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<div><span class="mw-geshi c source-c"><span class="kw4">float</span> remquof<span class="br0">(</span> <span class="kw4">float</span> x, <span class="kw4">float</span> y, <span class="kw4">int</span> <span class="sy2">*</span>quo <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> remquo<span class="br0">(</span> <span class="kw4">double</span> x, <span class="kw4">double</span> y, <span class="kw4">int</span> <span class="sy2">*</span>quo <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> remquol<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> x, <span class="kw4">long</span> <span class="kw4">double</span> y, <span class="kw4">int</span> <span class="sy2">*</span>quo <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-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 remquo( x, y, quo )</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-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> 计算除法运算 <span class="t-c"><span class="mw-geshi c source-c">x<span class="sy2">/</span>y</span></span> 的浮点余数，如 <span class="t-lc"><a href="c-numeric-math-remainder.html">remainder()</a></span> 函数所为。另外，将存储 <span class="t-c"><span class="mw-geshi c source-c">x<span class="sy2">/</span>y</span></span> 的至少最低三位及符号于 <span class="t-c"><span class="mw-geshi c source-c">quo</span></span> ，这足以确定结果在周期中的八分位。</div>
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<div class="t-li1"><span class="t-li">4)</span> 泛型宏：若任何非指针参数拥有 <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>remquol</code> 。否则，若任何非指针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>remquo</code> 。否则，调用 <code>remquof</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>x, y</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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<tr class="t-par">
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<td>quo</td>
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<td>-</td>
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<td>指向存储 <span class="t-c"><span class="mw-geshi c source-c">x<span class="sy2">/</span>y</span></span> 的符号和某些位的整数的指针</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>若成功，则返回定义于 <span class="t-lc"><a href="c-numeric-math-remainder.html">remainder</a></span> 的 <span class="t-c"><span class="mw-geshi c source-c">x<span class="sy2">/</span>y</span></span> 的余数，并存储 <span class="t-c"><span class="mw-geshi c source-c">x<span class="sy2">/</span>y</span></span> 的符号和至少后三位有效数字于 <span class="t-c"><span class="mw-geshi c source-c"><span class="sy2">*</span>quo</span></span> （正式而言，存储的值的符号是 <span class="t-c"><span class="mw-geshi c source-c">x<span class="sy2">/</span>y</span></span> 的符号，而绝对值与 <span class="t-c"><span class="mw-geshi c source-c">x<span class="sy2">/</span>y</span></span> 的整数商的绝对值对于 <span class="texhtml" style="white-space: nowrap;">modulo 2<span class="t-su">n<br /></span></span> 同余，其中 <span class="texhtml" style="white-space: nowrap;">n</span> 是实现定义的大于或等于 <span class="texhtml" style="white-space: nowrap;">3</span> 的整数）。</p>
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<p>若 <code>y</code> 为零，则存储于 <span class="t-c"><span class="mw-geshi c source-c"><span class="sy2">*</span>quo</span></span> 的值未指定。</p>
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<p>若出现定义域错误，则返回实现定义值（受支持平台上为 NaN ）。</p>
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<p>若出现下溢所致的值域错误，则若支持非正规值则返回正确结果。</p>
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<p>若 <code>y</code> 为零，但不出现定义域错误，则返回零。</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 <code>y</code> 为零则可能出现定义域错误。</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>当前<a href="c-numeric-fenv-FE_round.html">舍入模式</a>无效。</li>
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<li>决不引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INEXACT</a></span> 。</li>
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<li>若 <code>x</code> 为 ±∞ 且 <code>y</code> 非 NaN ，则返回 NaN 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</li>
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<li>若 <code>y</code> 为 ±0 且 <code>x</code> 非 NaN ，则返回 NaN 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 。</li>
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<li>若 <code>x</code> 或 <code>y</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.E6.84.8F">注意</span></h3>
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<p><a rel="nofollow" class="external text" href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/remquo.html">POSIX 要求</a>若 <code>x</code> 为无穷大或 <code>y</code> 为零则出现定义域错误。</p>
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<p>此函数在实现周期可准确表示为浮点值的周期函数时有用：对非常大的 <code>x</code> 计算 <span class="texhtml" style="white-space: nowrap;">sin(πx)</span> 时，直接调用 <span class="t-lc"><a href="c-numeric-math-sin.html">sin</a></span> 可能导致巨大误差，但若首先以 <code>remquo</code> 减小参数，则商的低位可用来确定结果在周期中的八分位，同时余数可用来计算拥有高精度的值。</p>
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<p>某些平台上硬件支持此运算（而例如在 Intel CPU 上， <code>FPREM1</code> 在完成时于商中准确保留 3 位精度）。</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 <stdio.h></span>
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<span class="co2">#include <math.h></span>
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<span class="co2">#include <fenv.h></span>
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<span class="co2">#pragma STDC FENV_ACCESS ON</span>
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<span class="kw4">double</span> cos_pi_x_naive<span class="br0">(</span><span class="kw4">double</span> x<span class="br0">)</span>
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<span class="br0">{</span>
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<span class="kw4">double</span> pi <span class="sy1">=</span> <a href="c-numeric-math-acos.html"><span class="kw672">acos</span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">return</span> <a href="c-numeric-math-cos.html"><span class="kw669">cos</span></a><span class="br0">(</span>pi <span class="sy2">*</span> x<span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span>
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<span class="co1">// 周期为 2 ，值为 (0;0.5) 正， (0.5;1.5) 负， (1.5,2) 正</span>
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<span class="kw4">double</span> cos_pi_x_smart<span class="br0">(</span><span class="kw4">double</span> x<span class="br0">)</span>
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<span class="br0">{</span>
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<span class="kw4">int</span> quadrant<span class="sy4">;</span>
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<span class="kw4">double</span> rem <span class="sy1">=</span> remquo<span class="br0">(</span>x, <span class="nu0">1</span>, <span class="sy3">&</span>quadrant<span class="br0">)</span><span class="sy4">;</span>
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quadrant <span class="sy1">=</span> <span class="br0">(</span><span class="kw4">unsigned</span><span class="br0">)</span>quadrant <span class="sy2">%</span> <span class="nu0">4</span><span class="sy4">;</span> <span class="co1">// 保留 2 位以确定象限</span>
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<span class="kw4">double</span> pi <span class="sy1">=</span> <a href="c-numeric-math-acos.html"><span class="kw672">acos</span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">switch</span><span class="br0">(</span>quadrant<span class="br0">)</span> <span class="br0">{</span>
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<span class="kw1">case</span> <span class="nu0">0</span><span class="sy4">:</span> <span class="kw1">return</span> <a href="c-numeric-math-cos.html"><span class="kw669">cos</span></a><span class="br0">(</span>pi <span class="sy2">*</span> rem<span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">case</span> <span class="nu0">1</span><span class="sy4">:</span> <span class="kw1">return</span> <span class="sy2">-</span><a href="c-numeric-math-cos.html"><span class="kw669">cos</span></a><span class="br0">(</span>pi <span class="sy2">*</span> rem<span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">case</span> <span class="nu0">2</span><span class="sy4">:</span> <span class="kw1">return</span> <span class="sy2">-</span><a href="c-numeric-math-cos.html"><span class="kw669">cos</span></a><span class="br0">(</span>pi <span class="sy2">*</span> rem<span class="br0">)</span><span class="sy4">;</span>
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<span class="kw1">case</span> <span class="nu0">3</span><span class="sy4">:</span> <span class="kw1">return</span> <a href="c-numeric-math-cos.html"><span class="kw669">cos</span></a><span class="br0">(</span>pi <span class="sy2">*</span> rem<span class="br0">)</span><span class="sy4">;</span>
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<span class="br0">}</span><span class="sy4">;</span>
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<span class="br0">}</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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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"cos(pi * 0.25) = %f<span class="es1">\n</span>"</span>, cos_pi_x_naive<span class="br0">(</span><span class="nu16">0.25</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"cos(pi * 1.25) = %f<span class="es1">\n</span>"</span>, cos_pi_x_naive<span class="br0">(</span><span class="nu16">1.25</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"cos(pi * 1000000000000.25) = %f<span class="es1">\n</span>"</span>, cos_pi_x_naive<span class="br0">(</span><span class="nu16">1000000000000.25</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"cos(pi * 1000000000001.25) = %f<span class="es1">\n</span>"</span>, cos_pi_x_naive<span class="br0">(</span><span class="nu16">1000000000001.25</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"cos(pi * 1000000000000.25) = %f<span class="es1">\n</span>"</span>, cos_pi_x_smart<span class="br0">(</span><span class="nu16">1000000000000.25</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"cos(pi * 1000000000001.25) = %f<span class="es1">\n</span>"</span>, cos_pi_x_smart<span class="br0">(</span><span class="nu16">1000000000001.25</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// 错误处理</span>
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<a href="c-numeric-fenv-feclearexcept.html"><span class="kw717">feclearexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw728">FE_ALL_EXCEPT</span></a><span class="br0">)</span><span class="sy4">;</span>
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<span class="kw4">int</span> quo<span class="sy4">;</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"remquo(+Inf, 1) = %.1f<span class="es1">\n</span>"</span>, remquo<span class="br0">(</span>INFINITY, <span class="nu0">1</span>, <span class="sy3">&</span>quo<span class="br0">)</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="kw718">fetestexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw731">FE_INVALID</span></a><span class="br0">)</span><span class="br0">)</span> <a href="c-io-puts.html"><span class="kw835">puts</span></a><span class="br0">(</span><span class="st0">" FE_INVALID raised"</span><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>可能的输出：</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">cos(pi * 0.25) = 0.707107
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cos(pi * 1.25) = -0.707107
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cos(pi * 1000000000000.25) = 0.707123
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cos(pi * 1000000000001.25) = -0.707117
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cos(pi * 1000000000000.25) = 0.707107
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cos(pi * 1000000000001.25) = -0.707107
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remquo(+Inf, 1) = -nan
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FE_INVALID raised</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-11">
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<ul>
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<li>C11 标准（ISO/IEC 9899:2011）：</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>7.12.10.3 The remquo functions (p: 255)</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: 373-375)</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.10.7.3 The remquo functions (p: 529)</li>
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</ul>
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</dd>
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</dl>
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<div class="t-ref-std-c99">
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<ul>
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<li>C99 标准（ISO/IEC 9899:1999）：</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>7.12.10.3 The remquo functions (p: 236)</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>7.22 Type-generic math <tgmath.h> (p: 335-337)</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.9.7.3 The remquo functions (p: 465)</li>
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</ul>
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</dd>
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</dl>
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</div>
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<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">
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-math-div.html"><span class="t-lines"><span>div</span><span>ldiv</span><span>lldiv</span></span></a></div>
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<div><span class="t-lines"><span></span><span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算整数除法的商和余数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-math-fmod.html"><span class="t-lines"><span>fmod</span><span>fmodf</span><span>fmodl</span></span></a></div>
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<div><span class="t-lines"><span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算浮点除法运算的余数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="c-numeric-math-remainder.html"><span class="t-lines"><span>remainder</span><span>remainderf</span><span>remainderl</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
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</div>
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</td>
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<td>计算浮点除法运算的带符号余数<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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</table>
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</div>
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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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