242 lines
16 KiB
HTML
242 lines
16 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>log1p, log1pf, log1pl</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_log1p 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">log1p, log1pf, log1pl</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> log1pf<span class="br0">(</span> <span class="kw4">float</span> arg <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> log1p<span class="br0">(</span> <span class="kw4">double</span> arg <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> log1pl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> arg <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 log1p( arg )</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 <span class="t-c"><span class="mw-geshi c source-c"><span class="nu0">1</span><span class="sy2">+</span>arg</span></span> 的自然（底 <span class="t-c"><span class="mw-geshi c source-c">e</span></span> ）对数。若 <code>arg</code> 接近零，则此函数比表达式 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-log.html"><span class="kw660">log</span></a><span class="br0">(</span><span class="nu0">1</span><span class="sy2">+</span>arg<span class="br0">)</span></span></span> 更精确。</div>
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<div class="t-li1"><span class="t-li">4)</span> 泛型宏：若 <code>arg</code> 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>log1pl</code> 。否则，若 <code>arg</code> 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>log1p</code> 。否则调用 <code>log1pf</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>arg</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 <span class="texhtml" style="white-space: nowrap;">ln(1+arg)</span> 。</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>若出现极点错误，则返回 <code>-HUGE_VAL</code> 、 <code>-HUGE_VALF</code> 或 <code>-HUGE_VALL</code> 。</p>
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<p>若出现下溢所致的值域错误，则返回（舍入后的）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 <code>arg</code> 小于 <span class="texhtml" style="white-space: nowrap;">-1</span> 则出现定义域错误。</p>
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<p>若 <code>arg</code> 为 <span class="texhtml" style="white-space: nowrap;">-1</span> 则可能出现极点错误。</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>若参数为 ±0 ，则返回不修改的参数。</li>
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<li>若参数为 -1 ，则返回 -∞ 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_DIVBYZERO</a></span> 。</li>
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<li>若参数小于 -1 ，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>若参数为 +∞ ，则返回 +∞ 。</li>
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<li>若参数为 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>函数 <code>expm1</code> 和 <span class="t-lc"><strong class="selflink">log1p</strong></span> 对于金融计算有用：例如在计算小的日利率时： <span class="texhtml" style="white-space: nowrap;">(1+x)<span class="t-su">n<br /></span>-1</span> 能表示为 <span class="t-c"><span class="mw-geshi c source-c"><a href="c-numeric-math-expm1.html"><span class="kw659">expm1</span></a><span class="br0">(</span>n <span class="sy2">*</span> log1p<span class="br0">(</span>x<span class="br0">)</span><span class="br0">)</span></span></span> 。这些函数亦简化书写精确的反双曲函数。</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 <float.h></span>
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<span class="co2">#include <errno.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">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">"log1p(0) = %f<span class="es1">\n</span>"</span>, log1p<span class="br0">(</span><span class="nu0">0</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">"Interest earned in 2 days on $100, compounded daily at 1%%<span class="es1">\n</span>"</span>
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<span class="st0">" on a 30/360 calendar = %f<span class="es1">\n</span>"</span>,
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<span class="nu0">100</span><span class="sy2">*</span><a href="c-numeric-math-expm1.html"><span class="kw659">expm1</span></a><span class="br0">(</span><span class="nu0">2</span><span class="sy2">*</span>log1p<span class="br0">(</span><span class="nu16">0.01</span><span class="sy2">/</span><span class="nu0">360</span><span class="br0">)</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">"log(1+1e-16) = %g, but log1p(1e-16) = %g<span class="es1">\n</span>"</span>,
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<a href="c-numeric-math-log.html"><span class="kw660">log</span></a><span class="br0">(</span><span class="nu0">1</span><span class="sy2">+</span><span class="nu19">1e-16</span><span class="br0">)</span>, log1p<span class="br0">(</span><span class="nu19">1e-16</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// 特殊值</span>
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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"log1p(-0) = %f<span class="es1">\n</span>"</span>, log1p<span class="br0">(</span><span class="sy2">-</span><span class="nu16">0.0</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">"log1p(+Inf) = %f<span class="es1">\n</span>"</span>, log1p<span class="br0">(</span>INFINITY<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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<span class="kw2">errno</span> <span class="sy1">=</span> <span class="nu0">0</span><span class="sy4">;</span> <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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<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"log1p(-1) = %f<span class="es1">\n</span>"</span>, log1p<span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><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><span class="kw2">errno</span> <span class="sy1">==</span> <a href="c-error-errno_macros.html"><span class="kw478">ERANGE</span></a><span class="br0">)</span> <a href="c-io-perror.html"><span class="kw878">perror</span></a><span class="br0">(</span><span class="st0">" errno == ERANGE"</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="kw729">FE_DIVBYZERO</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_DIVBYZERO 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">log1p(0) = 0.000000
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Interest earned in 2 days on $100, compounded daily at 1%
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on a 30/360 calendar = 0.005556
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log(1+1e-16) = 0, but log1p(1e-16) = 1e-16
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log1p(-0) = -0.000000
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log1p(+Inf) = Inf
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log1p(-1) = -Inf
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errno == ERANGE: Result too large
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FE_DIVBYZERO 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>7.12.6.9 The log1p functions (p: 245)</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.10.3.9 The log1p functions (p: 522)</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>7.12.6.9 The log1p functions (p: 226)</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.9.3.9 The log1p functions (p: 459)</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-log.html"><span class="t-lines"><span>log</span><span>logf</span><span>logl</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>计算自然对数（底为 <i>e</i> ）（ <span class="mjax" style="display:none">\({\small \ln{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">ln(x)</span> ）<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-log10.html"><span class="t-lines"><span>log10</span><span>log10f</span><span>log10l</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>计算常用对数 （底为 <i>10</i> ）（ <span class="mjax" style="display:none">\({\small \log_{10}{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">log<sub>10</sub>(x)</span> ）<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-log2.html"><span class="t-lines"><span>log2</span><span>log2f</span><span>log2l</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>计算底为 <i>2</i> 的对数（ <span class="mjax" style="display:none">\({\small \log_{2}{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">log<sub>2</sub>(x)</span> ）<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-expm1.html"><span class="t-lines"><span>expm1</span><span>expm1f</span><span>expm1l</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 <i>e</i> 的给定次幂减一（ <span class="mjax" style="display:none">\({\small e^x-1}\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">e<sup>x</sup>-1</span> ）<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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